A method for predicting the compressive response of a composite laminate after impact

Abstract

This application discloses a method for predicting the post-impact compressive response of composite laminates, relating to the field of impact damage in carbon fiber reinforced composite laminates. The method establishes a benchmark finite element model for post-impact compressive analysis of composite laminates; it uniformly represents the measured damage information of the composite laminate after impact, establishing a spatial correspondence between the uniformly represented damage information set and the layup elements, interlaminar interface elements, and surface nodes of the benchmark finite element model, forming damage assignment results; the measured damage information includes interlaminar damage information, surface pit deformation information, and intralaminar damage information; the damage assignment results are mapped to the benchmark finite element model, and post-impact compressive finite element analysis is performed using a finite element model containing measured damage characteristics, outputting the predicted results of the post-impact compressive response of the composite laminate. This application can improve the accuracy of compressive response prediction under unknown specific impact conditions.

Description

Technical Field

[0001] This application relates to the field of impact damage in carbon fiber reinforced composite laminates, and in particular to a method for predicting the post-impact compression response of composite laminates. Background Technology

[0002] Carbon fiber reinforced composite laminates have been widely used in main load-bearing structures in aerospace and other fields due to their advantages such as high specific strength, high specific stiffness, good corrosion resistance, and strong design flexibility. However, these structures are susceptible to low-speed impact loads during manufacturing, assembly, transportation, and service, such as tool drops, maintenance collisions, and foreign object impacts, which can cause damage such as delamination, matrix cracking, fiber breakage, and surface pitting within the structure.

[0003] Low-velocity impact damage is highly concealed; the structural surface often shows only slight pitting or even no visible traces, but extensive interlaminar and intralaminar damage may have already formed internally. This damage compromises the integrity of the composite material structure and induces local stiffness degradation, local instability, buckling propagation, and strength reduction during subsequent compression, significantly reducing the structure's residual compressive load-bearing capacity after impact. Therefore, accurately characterizing the true damage state after impact and further predicting its impact on subsequent compressive response are key technical issues in the damage-tolerant design and engineering evaluation of composite materials.

[0004] Existing methods for predicting the residual compressive strength of composite laminates after impact mainly include the following categories: The first category comprises simplified prediction methods based on the empirical relationship between damage characteristic parameters and residual compressive strength. These methods typically extract characteristic parameters such as damage projected area, pit depth, damage length, and damage width from non-destructive testing or surface measurement results, establishing empirical formulas to quickly estimate the residual compressive strength after impact. While computationally efficient, these methods essentially use only a few low-dimensional characteristic parameters to simplify the description of complex real damage, making it difficult to accurately reflect the layer-by-layer distribution of damage in the thickness direction, irregular boundary morphology, and the coupling effects of multiple damage modes. Therefore, the prediction results are usually rather coarse.

[0005] The second category is the finite element method based on regular geometric damage equivalence. This type of method typically obtains the approximate extent of damage based on non-destructive testing results and simplifies the actual impact damage in the finite element model into regular regions such as ellipses, circles, rectangles, or local stiffness-weakening areas. Subsequent residual strength analysis is then conducted through geometric or material parameter equivalence. While this method is relatively convenient for modeling, it significantly simplifies the actual damage morphology, making it difficult to reflect the irregular expansion characteristics of layered damage at different interlayer interfaces and its coupling influence with surface pits and intralayer damage. It easily underestimates or even ignores the role of certain key damage features in the subsequent compressive response, leading to discrepancies between the predicted residual compressive strength, buckling mode, and failure behavior and the actual situation.

[0006] The third category comprises residual strength prediction methods based on continuous finite element analysis of low-velocity impact and post-impact compression. These methods typically begin by explicitly simulating the low-velocity impact process using dynamic simulation to obtain the delamination, matrix damage, fiber damage, and surface deformation states of the laminate under impact. Then, through restart analysis and predefined fields, the damage state at the end of the impact analysis is inherited into the subsequent compression analysis model, predicting residual compressive strength and failure modes in a continuous analysis manner. This type of method can establish a complete analytical chain from impact damage formation to compressive failure evolution, but it relies on known impact parameters such as the impactor's mass, velocity, contact position, attitude, and boundary constraints. However, in real-world engineering scenarios, these impact process parameters are often difficult to obtain completely. In practice, the current damage state can usually only be obtained through detection methods after the impact occurs, thus limiting the engineering applicability of this type of method.

[0007] With the development of detection technologies such as ultrasonic C-scanning, X-ray CT, and three-dimensional surface contour measurement, the internal and surface damage information of composite laminates after impact can be obtained relatively easily. This provides the conditions for directly predicting residual compressive properties based on the measured damage state. However, there is still a lack of a systematic method that can effectively map the measured internal and surface damage after impact into a finite element model and directly conduct post-impact compression analysis based on this model.

[0008] Therefore, it is necessary to propose a method for predicting the post-impact compressive response of composite laminates based on measured damage mapping. This method allows for the direct construction of a finite element analysis model using the current measured damage state of the structure under unknown specific impact conditions. It also comprehensively considers the influence of various damage modes, such as intralaminar damage, interlaminar damage, and surface pitting, on the structural response, thereby improving the realism, accuracy, and engineering applicability of the predictions of residual compressive strength, buckling mode, and failure behavior. Summary of the Invention

[0009] The purpose of this application is to provide a method for predicting the compression response of composite laminates after impact, which can improve the accuracy of compression response prediction under unknown specific impact conditions.

[0010] To achieve the above objectives, this application provides the following solution: This application provides a method for predicting the post-impact compressive response of composite laminates, including: Establish a benchmark finite element model for post-impact compression analysis of composite laminates; Obtain measured damage information of composite laminates after impact; the measured damage information includes interlaminar damage information, surface pit deformation information, and intralaminar damage information; The measured damage information is uniformly characterized to obtain a set of damage information after uniform characterization. Establish the spatial correspondence between the unified damage information set and the plywood elements, interlayer interface elements and surface nodes of the benchmark finite element model to form the damage assignment result; The damage assignment results are mapped to the benchmark finite element model to obtain a finite element model for post-impact compression analysis that includes the measured damage characteristics. A finite element model for post-impact compression analysis, incorporating measured damage characteristics, was used to perform post-impact compression finite element analysis, and the predicted results of the post-impact compression response of the composite laminate were output.

[0011] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a method for predicting the compression response of composite laminates after impact. By acquiring measured interlaminar damage information, intralaminar damage information, and surface pit information, and mapping them uniformly into a benchmark finite element model, the compression analysis model after impact is made closer to the actual damage state. Moreover, it does not depend on the specific impact conditions and can improve the accuracy of the compression response prediction results. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of this application or related technologies, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 A flowchart illustrating a method for predicting the post-impact compression response of a composite laminate, provided in an embodiment of this application; Figure 2 A schematic diagram illustrating the principle of a method for predicting the post-impact compression response of a composite laminate, as provided in an embodiment of this application. Figure 3 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0014] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0015] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0016] Terminology Explanation: Composite laminate: A composite laminate is a plate-like structure formed by stacking multiple layers of unidirectional fiber-reinforced composite materials in a predetermined layup sequence and then curing them. The fiber orientations in each layup can be different to meet the load-bearing and performance requirements of the structure in different directions.

[0017] Low-velocity impact: Low-velocity impact refers to the impact loading process in which an impactor acts on the surface of a composite laminate at a relatively low velocity. Compared with high-velocity impact, low-velocity impact usually does not cause complete penetration of the material, but it is more likely to cause damage such as matrix cracking, local fiber breakage, and delamination inside the material, and the surface damage marks are often not obvious.

[0018] Low-velocity impact damage refers to the damage state of composite material structures under low-velocity impact loads, typically including various forms such as surface pitting, intralaminar damage, and interlaminar damage. This type of damage is usually characterized by inconspicuous surface marks but severe internal damage.

[0019] Post-impact compression: This refers to the stress process of a composite material structure under compressive load after experiencing impact damage. It is typically used to evaluate the impact damage on the subsequent compressive performance of the structure. In the field of composite materials, it is a test method for assessing the remaining load-bearing capacity of composite materials after impact damage.

[0020] Residual compressive strength: refers to the ultimate strength or maximum load-bearing capacity of a composite material structure under compressive load after experiencing impact damage. This indicator is used to characterize the residual load-bearing capacity of a structure after damage and is an important parameter for evaluating damage tolerance performance.

[0021] Buckling mode: refers to the deformation pattern exhibited by a structure when it becomes unstable under compressive load, including local buckling, global buckling, and their extended forms. Buckling mode can reflect the impact of damage on structural stability and failure path.

[0022] Damage behavior: refers to the response process of a structure from initial damage to final failure under load, which usually includes damage initiation, propagation, local instability, buckling development and final fracture or failure.

[0023] Measured damage mapping: refers to the process of converting and introducing real damage information obtained from nondestructive testing or surface measurement into a finite element model to construct the initial damage state for post-impact compression analysis.

[0024] Surface pits: These refer to the localized depressions formed on the impacted surface of a composite material structure after an impact. They not only reflect the damage characteristics of the impacted surface but may also influence the buckling response and failure behavior under subsequent compressive loads as localized geometric defects.

[0025] Intra-laminar damage refers to damage occurring within a single ply, typically including matrix cracking and fiber breakage. Intra-laminar damage alters the local stiffness and strength of a single ply and affects damage propagation behavior under subsequent loads.

[0026] Interlaminar damage refers to damage occurring between adjacent ply interfaces, typically manifesting as delamination. Interlaminar damage weakens the load transfer capacity between adjacent plies and significantly affects the stability and residual load-bearing capacity of the structure.

[0027] Existing methods for predicting the residual compressive strength of composite laminates after impact are as follows: Existing technology 1: Residual compressive strength calculation method based on non-destructive testing results and material parameter reduction This existing method is mainly used to calculate the residual compressive strength of composite laminates after impact based on non-destructive testing results. A representative scheme can be found in Chinese Patent Publication No. CN102607935A, entitled "A Method for Calculating the Residual Compressive Strength of Composite Laminates with Impact Damage". This existing method generally includes the following steps: S1. Perform non-destructive testing on composite laminates with impact damage to obtain information on the location of the damage within the laminate surface and in the thickness direction; S2. Establish a finite element model corresponding to the configuration of the laminate under test and the boundary conditions of the compression test. S3. Based on the damage location information obtained from nondestructive testing, identify the corresponding damaged elements and damaged layups in the finite element model. S4. The elastic constant of the material containing the damaged ply is reduced and softened to equivalently characterize the impact of impact damage on local bearing capacity. S5. Calculate the remaining compressive strength of the laminate by performing calculations on the finite element model.

[0028] The advantage of this method lies in its ability to incorporate non-destructive testing results into the finite element analysis process, enabling rapid calculation of residual compressive strength after impact. Its core principle is to determine the location and ply of the damage based on the testing results, and then to perform an equivalent characterization of the impact damage by subtracting the corresponding ply material parameters.

[0029] However, this method is essentially still a material parameter equivalent weakening method at the layup level. It does not explicitly separate and model intralayer damage from interlayer damage, nor does it reconstruct the true damage boundary morphology. At the same time, it does not adequately consider the local geometric defects caused by surface pits. Therefore, its predictive ability for buckling modes, local instability behavior, and failure evolution processes remains limited.

[0030] Existing technology 2: Residual strength assessment method based on continuous finite element analysis of low-velocity impact and post-impact compression This existing method is mainly used to continuously evaluate the residual strength of composite material structures after impact under known impact conditions. A representative scheme can be found in Chinese Patent Publication No. CN107092721A, entitled "A Method for Evaluating the Residual Strength of Composite Material Structures with Low-Voltage Impact Damage". This existing method generally includes the following steps: S1. Establish the relationship between impact energy and damage characteristic parameters based on the results of low-velocity impact tests; S2. Using the impact damage theory, the maximum contact force and maximum pit depth under the corresponding impact energy are obtained; S3. Establish a finite element model of progressive damage from low-speed impact; S4. Correct the finite element model of the low-speed impact progressive damage. S5. Establish a finite element model of residual strength including impact damage; S6. Solve the remaining strength finite element model to obtain the remaining strength value of the structure.

[0031] This method links the impact damage formation process with the subsequent residual strength assessment process, enabling continuous analysis of the damage state. Its core lies in combining impact test results, impact damage theory, and finite element simulation to model the initial impact damage state and further evaluate the residual strength.

[0032] However, the application of this type of approach relies on the fact that the impact parameters are known or can be estimated from experimental and theoretical relationships. In real engineering scenarios, the impact mass, velocity, attitude, and contact location of the structure are often difficult to fully ascertain; typically, the current damage state can only be obtained after the impact. Therefore, while this method is suitable for analysis under known impact conditions, it cannot directly meet the engineering prediction needs under the condition of "known current damage, unknown specific impact process".

[0033] Existing technology 3: Residual compressive strength analysis method based on impact damage area and stiffness attenuation This existing method is mainly used to analyze the residual compressive strength of composite laminates after impact damage based on low-speed impact simulation results. A representative scheme can be found in Chinese Patent Publication No. CN106202598A, entitled "A Method for Analyzing the Residual Compressive Strength of Composite Materials After Impact Damage". This existing method generally includes the following steps: S1. Select an appropriate impact damage failure criterion based on the failure characteristics of composite laminates; S2. Use a dynamic finite element program to simulate the low-speed impact process of the laminate and calculate the damage area under impact. S3. Based on the damage area obtained from the impact simulation, stiffness attenuation processing is applied to the damaged area after low-speed impact. S4. Establish a global-local finite element analysis model and perform compression analysis on the damaged structure; S5. Obtain the residual compressive strength of the composite laminate after impact based on the finite element calculation results.

[0034] This method can utilize the impact simulation results to conduct subsequent residual strength analysis. Its core lies in weakening the stiffness of the corresponding region in the finite element model based on the damage area formed by the impact.

[0035] However, this type of scheme mainly relies on impact simulation to obtain the initial damage state and uses damage area and regional stiffness attenuation as the main characterization methods. It is difficult to reflect the layer-by-layer distribution characteristics of real damage in the thickness direction, the influence of irregular damage boundaries and geometric defects such as pits on the compressive buckling response.

[0036] While existing technologies can analyze and predict the residual compressive strength of composite laminates after impact to some extent, they still have the following drawbacks: (1) The most significant drawback is that it is difficult to accurately map the actual damage state after impact into the finite element model. Existing techniques typically characterize impact damage using methods such as empirical mapping of damage characteristic parameters, equivalence of regular geometric regions, local stiffness attenuation, or reduction of ply material parameters. While these methods can reflect the impact of damage on the structural load-bearing capacity to some extent, their description and characterization of the actual damage state of composite materials after impact are still relatively coarse. They struggle to simultaneously reflect the actual distribution characteristics and coupling effects of multiple damage forms, including intralaminar damage, interlaminar damage, and surface pitting. Because the initial damage state in the finite element model deviates from the actual structure, it affects the accuracy of subsequent predictions of residual compressive strength, buckling mode, and failure behavior.

[0037] (2) Secondary disadvantage 1: The existing technology is not suitable for real engineering scenarios. Methods based on continuous analysis of low-velocity impact and post-impact compression typically require accurate knowledge of initial conditions such as the impactor's mass, velocity, contact location, contact posture, and boundary constraints. However, in real-world engineering scenarios, the complete process of structural impact is often difficult to ascertain. In many cases, the current damage state can only be obtained after the impact through non-destructive testing, making it difficult to accurately reconstruct the actual impact conditions. Therefore, while such methods are suitable for research and analysis under known impact conditions, they cannot directly meet the engineering assessment needs under conditions of "known current damage, unknown specific impact process."

[0038] (3) Secondary disadvantage 2: Limited predictive ability of buckling modes and failure behavior. Because existing technologies typically employ simplified characterization or equivalent treatments in the damage modeling stage, they struggle to accurately reflect the impact of real damage on the local stiffness, local geometric defects, and stability characteristics of a structure. Therefore, although some methods can provide estimates of the remaining compressive strength, their predictions of the local instability location, buckling propagation mode, and final failure behavior of a structure under compressive loads are still not accurate or comprehensive enough.

[0039] To address the aforementioned shortcomings, this application aims to propose a method for predicting the post-impact compressive response of composite laminates based on measured damage mapping. Under the condition of unknown specific impact conditions, a finite element analysis model is directly constructed based on the current measured damage state of the structure, and the internal damage information and surface damage information are mapped to the initial damage state required for post-impact compressive analysis. This enables the prediction of the residual compressive strength, buckling mode, and failure behavior of composite laminates after impact, thereby improving the accuracy and engineering applicability of the prediction results.

[0040] In one exemplary embodiment, such as Figure 1 As shown, a method for predicting the post-impact compression response of composite laminates is provided. This method is executed by a computer device, specifically by a computer device such as a terminal or server alone, or by a terminal and server together. In the embodiments of this application, the method includes the following steps 101 to 106.

[0041] Step 101: Establish the benchmark finite element model for post-impact compression analysis of composite laminates.

[0042] Step 102: Obtain the measured damage information of the composite laminate after impact; the measured damage information includes interlaminar damage information, surface pit deformation information and intralaminar damage information.

[0043] Step 103: Perform unified characterization on the measured damage information to obtain a unified characterization set of damage information.

[0044] Step 104: Establish the spatial correspondence between the unified damage information set and the plywood elements, interlayer interface elements and surface nodes of the benchmark finite element model to form the damage assignment result.

[0045] Step 105: Map the damage assignment results to the benchmark finite element model to obtain a finite element model for post-impact compression analysis that includes the measured damage characteristics.

[0046] Step 106: Perform post-impact compression finite element analysis using a finite element model that includes measured damage characteristics, and output the predicted results of the post-impact compression response of the composite laminate.

[0047] Implementing steps 101 to 106 above mainly solves the technical problem of how to accurately map the measured internal damage, surface pits, and other real damage information of composite laminates after impact to the finite element model under unknown specific impact conditions, construct the initial damage state for post-impact compression analysis, and achieve accurate prediction of the residual compressive strength, buckling mode, and failure behavior of the structure after impact.

[0048] In another exemplary embodiment of this application, step 101 is used to establish a benchmark finite element model corresponding to the geometry, layup type, material constitutive model, and post-impact compression test boundary conditions of the composite laminate, providing a basis for subsequent mapping of measured damage information and post-impact compression simulation analysis. Step 101 can be replaced by steps 201 to 205.

[0049] Step 201: Establish the geometric model of the composite laminate.

[0050] Based on the actual geometric dimensions, thickness information, and ply structure of the composite laminate specimens, a geometric model for post-impact compression analysis is established. This geometric model can be constructed based on the specimen's length, width, total thickness, thickness of each ply, and ply sequence.

[0051] Composite laminates can be modeled using shell elements, continuous shell elements, or solid elements. To explicitly describe interlaminar damage, interlaminar interfaces should be pre-defined between adjacent plies to serve as the basis for subsequent setting of interface elements, contact interfaces, or interface separation determination surfaces.

[0052] Step 202: Determine the finite element mesh generation rules for the geometric model.

[0053] Based on the mapping requirements of subsequent measured damage information and the accuracy requirements of post-impact compression analysis, the finite element mesh generation rules of the geometric model are determined.

[0054] Specifically, the grid feature length within the locally encrypted region is first determined. When intralayer damage is characterized using a continuous damage mechanics model, the characteristic length of the local mesh can also be determined by combining the material's elastic parameters, strength parameters, and fracture toughness parameters, preferably satisfying the following: ; in, These are the principal and transverse elastic moduli of the ply fibers, respectively. These are the strength parameters corresponding to fiber tension, fiber compression, matrix tension, and matrix compression, respectively. These are the fracture toughness parameters under the corresponding damage modes of fiber tension, fiber compression, matrix tension, and matrix compression, respectively.

[0055] To balance the accuracy of measured damage mapping with the precision and efficiency of finite element simulation, a locally refined mesh is used in the impact damage area and its adjacent region. This locally refined region is determined based on the envelope of the measured damage area within the laminated plate surface after impact, and a buffer extension zone is set around this envelope to ensure that the stress gradient, deformation gradient, and local buckling response near the damage boundary can be accurately characterized. Let the dimensions of the measured damage area in the two in-plane directions be... and The size of the local encryption region and It can be represented as: ; in, To buffer the spread distance, its size is not less than the local mesh feature length. 10 times. The mesh feature length within the locally refined region is taken as determined above. A more sparse grid can be used for global regions far from the damaged area, and its global grid feature length is [not specified]. Take as Furthermore, a transition grid is set between the local encrypted region and the global region to reduce the adverse effects of abrupt changes in grid size on computational stability and analysis accuracy.

[0056] To facilitate the regular mapping of measured damage information to the finite element model, a structured mesh or a meshing method with regular topological correspondences is preferred. This ensures that the distribution of elements within each ply and the distribution of interface elements between layers have clear numbering and spatial correspondences. This method allows the ply regions within each layer and the interface regions between layers to form a regular array in the in-plane direction, thus facilitating the mapping of measured damage areas, surface pit contours, and other information to the corresponding nodes, elements, or interface elements.

[0057] The above can be summarized as follows: Based on the envelope of the measured damage area within the laminate surface after impact, the formula is used... and Determine the local encryption area; based on The process involves determining the grid feature length within a local encrypted region; dividing the local encrypted region into grids according to the grid feature length, and dividing the global region into grids according to twice the grid feature length; and setting a transition grid between the local encrypted region and the global region. The global region refers to the region whose distance to the local encrypted region is greater than a preset distance threshold. The grid length of the transition grid is greater than the grid feature length but less than twice the grid feature length.

[0058] Step 203: Determine the material constitutive model for intralayer damage and the interface constitutive model for interlayer damage.

[0059] Determine the material constitutive model for intralayer damage: To meet the characterization requirements of intralaminar damage in post-impact compression analysis of composite laminates, a material constitutive model for intralaminar damage is established. The intralaminar damage mainly includes matrix damage and fiber damage. This constitutive model can be determined by combining damage criteria, constitutive relations, damage evolution laws, material stiffness degradation mechanisms, and failure element handling methods applicable to composite laminate failure analysis, serving as the constitutive basis for subsequently incorporating measured intralaminar damage information.

[0060] As one implementation, the intralayer damage constitutive model can be established based on shell elements, continuous shell elements, or solid elements; the damage criteria used may include the Hashin criterion, Puck criterion, LaRC series criteria, or other criteria applicable to intralayer failure analysis of composite materials; the damage evolution mode used may include instantaneous reduction, bilinear degradation, exponential degradation, etc.; the constitutive model can be implemented through user material subroutines.

[0061] Determining the interface constitutive model for interlayer damage: To meet the characterization requirements of interlaminar damage in post-impact compression analysis of composite laminates, an interface constitutive model for interlaminar damage between adjacent plies is established. The interface damage initiation criterion, damage evolution law, interface stiffness parameters, fracture toughness parameters, and mixed-mode damage determination method are given as the basis for subsequent interface analysis that incorporates measured interlaminar damage information.

[0062] As one implementation method, the interlaminar damage interface constitutive model can be an interlaminar fracture analysis model based on the Virtual Crack Closure Technique (VCCT), or an interface damage model based on the Cohesive Zone Model (CZM).

[0063] Step 204: Set the post-impact compression boundary conditions.

[0064] Based on the conditions of post-impact compression tests or engineering analysis, the boundary conditions, constraint methods, and compression loading methods of the composite laminate finite element model are set to form a benchmark finite element model for post-impact compression analysis.

[0065] The boundary conditions may include specimen support conditions, clamping conditions, end constraint forms, and buckling-resistant fixture constraint conditions; the loading method may include displacement loading, force loading, or other equivalent compressive loading methods.

[0066] Step 205: Combine the geometric model, finite element mesh generation rules, material constitutive model of intralaminar damage, interface constitutive model of interlaminar damage, and post-impact compression boundary conditions to form the baseline finite element model for post-impact compression analysis of composite laminates.

[0067] The baseline finite element model formed in this step is the basic model for post-impact compression analysis that has not yet incorporated measured damage information. Subsequently, measured damage information such as interlaminar damage, intralaminar damage, and surface pits can be introduced on this model to construct a post-impact compression finite element model containing measured damage.

[0068] In another exemplary embodiment of this application, after a low-speed impact, the composite laminate typically exhibits three types of damage: interlaminar damage, intralaminar damage, and surface pitting. Step 102 described above is used to obtain measured damage information of the structure after impact, providing basic data for subsequent damage characterization, unified description, and finite element mapping.

[0069] (1) Obtain interlaminar damage information after impact of composite laminate The general process for acquiring interlaminar damage information is as follows: Non-destructive testing of the impacted composite laminate is performed using an ultrasonic C-scanning device to obtain raw time-of-flight (TOF) data; the raw TOF data undergoes effective detection area extraction, outlier correction, noise suppression, and smoothing to obtain preprocessed TOF data; based on the preprocessed TOF data, background and non-background regions are determined, and the non-background region is considered as the projection area of ​​the interlaminar damage onto the scanning plane; the position of the interlaminar damage in the planar direction is determined based on the coordinates of each sampling point within the non-background region in the scanning plane coordinate system; the range of the interlaminar damage in the planar direction is determined based on the boundary contour of the non-background region, the projection length of the projection region, and the projection width; and the process is then carried out according to the formula... and For inter-layer damage with a known location and extent in the planar direction, inter-layer interfaces are assigned, and the inter-layer interface number to which each sampling point in the non-background area belongs is determined; among which, Sampling points The corresponding inter-layer interface number, Sampling points in non-background areas The measured flight time For the first Reference flight time of each interlayer interface For the first The depth of the interface between each layer from the front surface The equivalent propagation velocity of ultrasound in composite laminates is given. Based on the interlayer interface number of each sampling point, cluster analysis and region consistency correction are performed using the planar coordinates and time-of-flight information of the sampling points to obtain the preliminary allocation results of the damage regions at each interlayer interface. Based on the preliminary allocation results of the damage regions at each interlayer interface, assuming that the damage in the next layer continuously fills the projection range of the damage in the upper layer, the final damage region of each interlayer interface is represented as: The final damage area at each interlayer interface is used as the interlayer damage information of the composite laminate after impact; among which, For the first The final damaged area of ​​the interlayer interface, For the first Preliminary allocation results of interlayer interface damage regions For the first The final damaged area at the interlayer interface.

[0070] The more detailed process is as follows: Ultrasonic C-scanning equipment was used to perform non-destructive testing on composite laminates after impact, and time-of-flight (TOF) data was used as the main basis for obtaining interlaminar damage and interlaminar interface allocation.

[0071] For TOF scan results, the non-background area can be directly regarded as the projection area of ​​inter-layer damage in the scanning plane, so there is no need to further identify the presence of inter-layer damage. After effective detection region extraction, outlier correction, noise suppression, and smoothing of the raw TOF data, the position of the inter-layer damage in the planar direction can be determined by the coordinates of each sampling point in the non-background area in the scanning plane coordinate system; the range of the inter-layer damage in the planar direction can be determined by the boundary contour, projection length, and projection width of the non-background area; the distribution characteristics of the inter-layer damage in the planar direction can be characterized by the shape of the non-background area, the boundary contour, and the relative spatial distribution relationship between multiple damage sub-regions.

[0072] When it is necessary to further determine the interlaminar interface to which the interlaminar damage belongs, the interlaminar interface can be assigned to each sampling point in the non-background area by combining the laminate ply thickness and the ultrasonic propagation time information in the material. Specifically, a corresponding reference time of flight can be established based on the thickness direction position of each candidate interlaminar interface in the laminate; for single-sided scanning, if the first... The depth of each candidate interlayer interface from the scanning surface is Then its reference flight time can be expressed as: ; The measured flight time of each sampling point in the non-background area The sampling points are determined by comparing the time of flight with the baseline flight time of each candidate interlayer interface and using the following formula. Inter-layer interface number: ; in, Sampling points The corresponding interlayer interface number. Furthermore, cluster analysis and region consistency correction can be performed by combining the planar coordinates and time-of-flight information of the sampling points to improve the stability and accuracy of the interlayer interface allocation results. Thus, the [number]th [interlayer interface number] can be obtained. Preliminary allocation results of inter-layer interfaces: ; in, This refers to the non-background region in the TOF result. This indicates that the assignment was made without considering occlusion. Interlayer damage area at each interlayer interface.

[0073] Considering that shallow damage may obscure deeper damage, and assuming that the next layer of damage continuously fills the projection range of the upper layer of damage, the first... The final damage region at each interlayer interface can be recursively represented as: ; And the top-level interface satisfies: ; in, Indicates the first after considering occlusion. Each layer has an interlayer damage region. Through the above processing, interlayer damage information at each interlayer interface considering the shading effect can be obtained, and this interlayer damage information can be used as the input basis for subsequent finite element mapping.

[0074] For example, in addition to ultrasonic C-scan, interlaminar damage information can also be obtained using ultrasonic phased array, ultrasonic A-scan / B-scan, infrared thermography, or X-ray non-destructive testing.

[0075] (2) Obtain surface pit deformation information of composite laminate after impact The depth of the dents and residual deformation of the impact surface are measured using depth gauges, dial gauges, laser displacement sensors or three-dimensional surface contour measurement equipment to obtain the depth distribution and boundary contour information of the dents.

[0076] Among them, depth gauges can be used to directly measure the local depth of pits; dial gauges and laser displacement sensors can be used to measure the linear displacement of the impact surface at preset sampling points or preset scanning paths, and further used to calculate the distribution of residual deformation on the surface; three-dimensional surface contour measurement equipment can be used to directly obtain the three-dimensional surface morphology of the impact area, thereby obtaining the depth distribution and boundary contour information of the pit.

[0077] Specifically, the measured height of the specimen surface after impact can be recorded as... The reference surface height obtained by fitting the undamaged region is denoted as... Then the residual deformation field of the pit can be expressed as: ; in, For the impact surface at position The residual indentation deformation at the location. When using a dial indicator or laser displacement sensor for discrete point measurement, the displacement value at each sampling point can be obtained first. The residual deformation distribution on the surface is then obtained through interpolation or fitting. The maximum depth of the pit can be expressed as: ; in, The maximum depth of the pit. The measurement area is defined by the contour of the pit, which meets a preset depth threshold. The equivalent boundary is determined, that is: ; Accordingly, the pitted area can be represented as: ; in, The outline of the pit boundary, This represents the projected area of ​​the pit.

[0078] Through the above processing, the depth distribution, boundary contour, and residual deformation field of the surface pits after impact can be obtained. The surface pit deformation information is not only used to characterize the surface damage state after impact, but also serves as the input for local initial geometric defects in subsequent post-impact compression analysis to characterize the influence of residual pit deformation on the buckling response and failure behavior of the structure.

[0079] Therefore, the process of obtaining surface pit deformation information can be described as follows: measuring the depth of the surface pit using a depth gauge; Discrete point measurements are performed using a dial gauge or laser displacement sensor to obtain displacement values ​​at each sampling point. The residual deformation distribution on the surface is then obtained through interpolation or fitting. Based on this distribution, the formula... The boundary contour of the surface pit is determined; the depth of the surface pit, the distribution of residual surface deformation, and the boundary contour of the surface pit are used together as the surface pit deformation information after impact of the composite laminate.

[0080] For example, in addition to using depth gauges, dial gauges, laser displacement sensors, or three-dimensional surface contour measurement equipment, surface pit deformation information can also be obtained using three-dimensional digital image correlation, structured light measurement, laser scanning, or contact contour measurement.

[0081] (3) Obtaining intralaminar damage information after impact of composite laminate Intralaminar damage includes matrix damage and fiber damage. When conditions permit, high-resolution detection methods such as X-ray computed tomography (CT) can be used to examine the impacted laminate to obtain information on the location, extent, and distribution of intralaminar damage.

[0082] In engineering applications, when intra-layer damage is difficult to obtain directly and completely, the influence range of intra-layer damage can be indirectly estimated or approximated based on the distribution characteristics of inter-layer damage and the residual deformation information of surface pits. The results can then be used as input information for subsequent finite element damage mapping. Therefore, the process of obtaining intra-layer damage information can be replaced by steps 301-303.

[0083] Step 301: When the intralayer damage is fiber damage, the inner region of the largest inscribed ellipse of the uppermost interlayer damage region is taken as the fiber damage region.

[0084] Based on step S21, the interlayer damage region at each interlayer interface is obtained, and denoted as the... The interlayer damage area at each interlayer interface is .

[0085] The fiber damage area can be approximated as the uppermost interlaminar damage area. The largest inscribed ellipse is denoted as . , can be represented as: ; in, ; ; In the formula, Center of the ellipse and These are the major and minor semi-axes of the approximately ellipse-like fiber damage. The direction of the principal axis of the ellipse is given. Since the fiber damage region is characterized using the same approximation in each layup, therefore the... The fiber damage area in the layup can be uniformly represented as: ; in, For the first Fiber damage areas in the layup.

[0086] Step 302: When the intralayer damage is matrix damage, the matrix damage area in each layup is characterized as the interlayer damage area of ​​the corresponding interlayer interface below each layup.

[0087] The area of ​​matrix damage varies depending on the layup location. Preferably, the first... Matrix damage area in layer layup This can be approximated as the interlaminar damage region at the corresponding interlaminar interface below it, i.e.: ; in, For the first Interlayer damage region at each interlayer interface For the first Damaged areas in the matrix during layer layup.

[0088] Step 303: Use the fiber damage area and the matrix damage area as the intralaminar damage information after impact of the composite laminate.

[0089] Through the above processing, the approximate location, range, and distribution information of fiber damage areas and matrix damage areas in each layup can be obtained, which can be used as the input basis for subsequent finite element damage mapping.

[0090] For example, in addition to X-ray CT, intralaminar damage information can also be obtained using digital radiography, acoustic emission monitoring, micro-ultrasound, or other high-resolution detection methods. Any detection method that can acquire one or more of the following information—interlaminar damage, intralaminar damage, and surface pits—after impact in composite laminates and use it for subsequent damage characterization and finite element mapping can be considered an alternative.

[0091] In another exemplary embodiment of this application, step 103 involves preprocessing, coordinate unification, spatial registration, unified characterization, and mesh mapping preparation of the acquired interlayer damage information, surface pit deformation information, and intralayer damage information to form a discrete damage description result that can be directly used for subsequent finite element model assignment. Step 103 can then be replaced by steps 401 to 406.

[0092] Step 401: Preprocess the interlayer damage information, surface pit deformation information, and intralayer damage information respectively to obtain preprocessed interlayer damage information, preprocessed surface pit deformation information, and preprocessed intralayer damage information.

[0093] The acquired interlayer damage information, surface pit deformation information, and intralayer damage information are preprocessed to improve the accuracy and stability of subsequent spatial registration and unified characterization.

[0094] In this step, for the ultrasound C-scan results corresponding to interlaminar damage, based on the already completed acquisition of interlaminar damage regions and allocation of interlaminar interfaces, damage region identification is not repeated. Instead, the main focus is on performing anomaly correction, small region removal, local hole filling, boundary smoothing, and local consistency correction on the obtained interlaminar damage regions to improve the continuity of interlaminar damage boundaries and the integrity of region representation. Preferably, the first... Damage area at interlayer interfaces Morphological smoothing was performed to obtain the pre-processed interlaminar damage area. .

[0095] For surface pit deformation measurement data, based on the obtained residual deformation field, boundary contour, and pit region, further processing can be performed including outlier removal, discrete point smoothing, local contour correction, and local surface completion. This reduces the impact of measurement noise and local discrete errors on the pit morphology characterization, thereby obtaining more stable surface pit deformation results, denoted as . , and .

[0096] For intra-layer damage information, based on the direct acquisition or indirect inference already completed, further processing such as boundary smoothing, small region removal, local hole filling, and shape correction can be performed to improve the stability of the intra-layer damage region representation. After preprocessing, the following can be obtained: The stable expression results of fiber damage regions and matrix damage regions in the layer-by-layer layup are denoted as follows: and .

[0097] Through the above preprocessing, we can obtain interlayer damage information, surface pit deformation information, and intralayer damage information with less noise, more stable boundaries, and more complete regional representation, which provides a foundation for subsequent coordinate unification and spatial registration, as well as unified characterization of damage information.

[0098] Step 402: Perform coordinate unification and spatial registration on the preprocessed interlayer damage information, preprocessed surface pit deformation information, and preprocessed intralayer damage information to obtain the registered interlayer damage information, registered surface pit deformation information, and registered intralayer damage information.

[0099] Since interlayer damage information, surface pit deformation information, and intralayer damage information may come from different detection equipment or different measurement coordinate systems, it is necessary to unify the coordinates and spatially register the various types of damage information obtained after preprocessing to ensure that the correspondence between damage information from different sources in the laminate plane position and thickness direction is consistent.

[0100] Specifically, based on the obtained preprocessing results , , , , and As the object to be registered, a unified reference coordinate system for the laminate is first established based on the laminate's geometry, boundary features, reference holes, corner points, center points, impact point locations, or preset reference marks. .in, shaft and The axis is defined in the plane containing the mid-face or surface of the laminate. The axis is defined as the thickness direction of the laminate.

[0101] For any detection source Let its original measurement coordinate system be... Several reference points can be selected under the original measurement coordinate system, and the coordinates of the corresponding reference points can be determined in a unified reference coordinate system. Coordinate transformation relationships can be established through reference point matching. For planar damage information or surface measurement information, a two-dimensional rigid body transformation can be used for coordinate transformation, the general form of which can be expressed as: ; in, For the detection source The original plane coordinates below, To unify planar coordinates under a reference coordinate system, This is the two-dimensional coordinate transformation matrix determined by matching the reference point.

[0102] When rigid body transformation is used, the above equation can be further expressed as: ; in, Let be a rotation matrix. This is a translation vector; if necessary, a scale factor can be introduced to accommodate situations where different detection devices have inconsistent resolutions and scales. The coordinate transformation relationship can be determined by the correspondence of at least three non-collinear reference points.

[0103] For interlaminar damage information, if the output of the first... The pre-treatment damage area of ​​each interlayer interface is Then the coordinates of the sampling point in the ultrasound scanning plane can be obtained. Transform to a unified reference coordinate system to obtain the registered interlaminar damage region. : ; in, This is the coordinate transformation matrix from the ultrasonic C-scan coordinate system to the unified reference coordinate system. For thickness-direction locations, the defined interlayer interface number can be directly retained. Or based on the depth information of the corresponding interlayer interface. By assigning thickness direction coordinates, the spatial positional relationship of interlayer damage under a unified reference coordinate system is established.

[0104] For surface pit deformation information, if the output preprocessed residual deformation field is This allows the plane coordinates of the measurement points from surface profile measurement, laser displacement measurement, or dial indicator measurement results to be displayed. Transform to a unified reference coordinate system to obtain the residual deformation field in the unified reference coordinate system. ,Right now: ; in, and The corresponding coordinate transformation relationship is satisfied. Accordingly, the surface pit boundary profile... and pitted areas The same transformation can also be used to obtain the following results: and .

[0105] For intra-layer damage information, if the output of the first... The damaged areas of the layered fibers and the damaged areas of the matrix are respectively and If the intra-layer damage information originates from direct detection results such as CT scans, it can be transformed from the original detection coordinate system to a unified reference coordinate system through reference point matching. If the intra-layer damage information originates from indirect inferences based on inter-layer damage distribution and surface pit deformation information, the fiber damage area in the unified reference coordinate system can be obtained simultaneously after the inter-layer damage information and surface pit deformation information are spatially registered. and matrix damage area .

[0106] Based on this, spatial location matching and region alignment can be performed on various types of damage information to check whether the planar positions and thickness directions of interlayer damage, intralayer damage, and surface pits are consistent in a unified reference coordinate system. If local offsets exist, further corrections can be made based on the reference point position, the degree of overlap of boundary contours, the position of the impact center, or the degree of overlap of characteristic regions to improve the spatial consistency between various types of damage information.

[0107] Through the above processing, interlayer damage information in a unified reference coordinate system can be obtained. Surface pit deformation information , , and intralayer damage information and This provides a spatial basis for the unified characterization of subsequent damage information and finite element mapping.

[0108] Step 403: According to the interlayer interface number, perform unified characterization on the registered interlayer damage information to obtain a unified characterization of the interlayer damage information.

[0109] After coordinate unification and spatial registration are completed, various types of damage information are uniformly characterized, and damage data from different sources and in different forms are converted into a unified damage description form that can be used for subsequent finite element mesh correspondence and damage assignment.

[0110] For interlayer damage information, it can be uniformly represented according to the interlayer interface number. Specifically, the number of the interlayer interface will be... The interlaminar damage area after registration of the interlaminar interfaces is denoted as... This results in an interlayer damage description organized according to interlayer interface numbering: ; in, This represents the total number of interfaces between layers.

[0111] Step 404: Unify the registered surface pit deformation information as ;in, A unified representation of surface pit deformation information. This is a surface pit area. The outline of the surface pit boundary. To unify the surface residual deformation field under the reference coordinate system.

[0112] Step 405: Based on the ply number and damage type, uniformly characterize the registered intra-layer damage information as follows: ;in, For a unified representation of intralayer damage information, and The first Fiber damage area and matrix damage area after registration in the layer layup. , This represents the total number of plies. .

[0113] Step 406: Integrate the unified representation of interlayer damage information, the unified representation of surface pit deformation information, and the unified representation of intralayer damage information into a unified damage information set.

[0114] The set of damage information after unified characterization is as follows: The unified damage information set is used to establish a spatial correspondence between the subsequent plywood elements, interlayer interface elements and surface nodes of the reference finite element model, and to form corresponding element damage marks and initial node offset results.

[0115] In another exemplary embodiment of this application, step 104 above is based on the damage information set after unified characterization. The various damaged regions are spatially mapped and numbered to the plywood elements, interlayer interface elements, and surface nodes in the reference finite element model, thereby generating element damage markers and initial node offset results for assignment to the finite element model. Step 104 can then be replaced by steps 501-506.

[0116] Step 501: Determine the damage state of each ply element based on the spatial inclusion relationship between the center coordinates of each ply element on the reference finite element model and the damage region within the layer.

[0117] For in-layer ply elements, let the first ply element in the reference finite element model be... Any target element within a layer is denoted as The coordinates of its unit center in the plane of the laminate are as follows: According to the ply number of the unit. and its center coordinates and the first Fiber damage area in the layup and matrix damage area The spatial containment relationship can be used to determine the damage state of the target unit. Specifically, if the following conditions are met: ; Then the element is considered to be located within the matrix damage region; if the following conditions are met: ; The unit is then considered to be located within the fiber damage region.

[0118] Step 502: Based on the damage state of each ply unit, generate the intralayer damage mark and corresponding unit number for each ply unit.

[0119] Generate intra-layer element damage markers For example, it can be defined as: ; in, Indicates no damage. Indicates matrix damage. Indicates fiber damage. This indicates damage to the matrix and fiber composite. This allows for the creation of intralayer damage markers and corresponding element numbers for each layup unit.

[0120] Step 503: Determine the delamination damage state of each interlayer interface element based on the spatial inclusion relationship between the center coordinates of each interlayer interface element on the reference finite element model and the interlayer damage region of the corresponding interlayer interface.

[0121] For inter-layer interface units, let the first... Any target interface unit on the inter-layer interface is denoted as The coordinates of its unit center in the plane are as follows: Based on the inter-layer interface number to which this interface unit belongs. and its center coordinates and the first Delamination damage area at the interlayer interface The spatial inclusion relationship can be used to determine whether the interface unit is located within the delamination damage region. Specifically, if the following conditions are met: ; If the interface element is damaged, it is considered a layered damaged element; otherwise, it is considered a non-damaged interface element.

[0122] Step 504: Based on the layer damage state of each interlayer interface unit, form the layer damage mark of each interlayer interface unit and the corresponding interface unit number.

[0123] Define interlayer interface element damage markers for: ; in, Indicates the state of layered damage. This indicates a state of no damage. From this, layer damage markers and corresponding interface element numbers can be generated for each interlayer interface element.

[0124] Step 505: Express the initial offset of the surface nodes within the surface pit region as... The initial offset of surface nodes outside the surface pit area is set to zero, thus forming the initial offset result of each surface node and its corresponding node number; where, This represents the initial offset in the thickness direction. node position The residual deformation value at that location.

[0125] For information on surface pit deformation, let the set of surface nodes of the reference finite element model be... , of which surface nodes The plane coordinates are The initial thickness direction coordinates are First, based on the spatial location of the nodes on the laminate surface, areas located in surface pits are selected. The nodes within the set are the target nodes to which the initial offset needs to be applied. ,Right now: ; in, This refers to the set of target nodes. In other words, it refers to any node whose planar projection coordinates fall within the concave region. All surface nodes within the area are designated as target nodes; for planar projected coordinates located at... External surface nodes are not treated as target nodes.

[0126] After determining the target node, based on the surface residual deformation field Calculate the initial offset for each target node. For any target node... Its initial offset in the thickness direction can be expressed as: ; in, For the first The initial offset of each target node, with the negative sign indicating that the node is offset in the negative direction of the laminate thickness. When When given a discrete height field, the node positions can be obtained using nearest neighbor interpolation, bilinear interpolation, or surface fitting interpolation. The residual deformation value at the location; when When given as a continuous surface function, the offset at the node position can be calculated directly. Correspondingly, the... The coordinates of each target node after offset can be represented as: .

[0127] For surface nodes located outside the pit region, their initial offset can be set to zero, i.e.: .

[0128] This allows us to generate the initial offset results for each surface node and its corresponding node number.

[0129] Step 506: The damage assignment result is formed by combining the intralayer damage marker and corresponding element number of each ply element, the layer damage marker and corresponding interface element number of each interlayer interface element, and the initial offset result and corresponding node number of each surface node.

[0130] After the above processing, damage assignment results can be generated for the input of the finite element model. The damage assignment results include at least: intra-layer damage marking information for each ply element, layer damage marking information for each inter-layer interface element, initial offset of each surface target node, and element number and node number corresponding to the above information. The damage assignment results can be represented using an element marking matrix, node offset matrix, interface damage assignment table, discrete field file, or a combination thereof, and serve as direct input for subsequent finite element damage mapping and post-impact compression finite element analysis.

[0131] In another exemplary embodiment of this application, step 105 is used to write the formed damage assignment result into the reference finite element model, thereby constructing a post-impact compression analysis finite element model containing measured damage features such as interlaminar damage, intralaminar damage, and surface pits. For delaminated damage regions, interlaminar delamination damage is characterized by canceling interface element settings or deleting interface constraints; for undamaged regions, the original interface connection relationship is retained, and corresponding interface constitutive parameters are assigned. Intralaminar elements are divided into undamaged state, matrix damage state, fiber damage state, and matrix and fiber composite damage state, and are characterized using different material parameters, stiffness reduction schemes, or initial damage variables respectively. For surface nodes within the surface pit region, the node coordinates are corrected according to the initial offset; for surface nodes outside the surface pit region, the original position remains unchanged. A more detailed writing process is as follows: ① Mapping of interlaminar damage Based on the damage marking results of the interlayer interface elements, the layered damage information is mapped to the corresponding interlayer interface locations in the finite element model. Specifically, the program can automatically read the interlayer interface element numbers and their damage marking results, and apply corresponding interface processing methods to the corresponding interface regions.

[0132] As one implementation method, for interface regions marked as undamaged, the original interface connections can be preserved, and corresponding interface constitutive parameters can be assigned. For interface regions marked as delamination damage, the interlayer delamination damage can be characterized by canceling interface element settings, deleting interface constraints, or other equivalent methods. Through the above processing, the mapping of interlayer damage in the finite element model can be achieved.

[0133] ② Mapping of intralayer damage Based on the damage marking results of the generated in-layer elements, the in-layer damage information is mapped to the corresponding plywood elements in the finite element model. Specifically, the program can automatically read the number of each plywood element and its damage type marking, and apply corresponding material properties or damage parameters to the corresponding elements according to different damage states.

[0134] As one implementation method, intralayer elements can be categorized into undamaged, matrix-damaged, fiber-damaged, and matrix-fiber composite-damaged states. These are then characterized using different material parameters, stiffness reduction schemes, initial damage variables, or other equivalent methods to reflect the impact of different intralayer damage states on the structural response. Through this process, the mapping of intralayer damage into the finite element model can be achieved.

[0135] ③ Mapping of surface pits Based on the initial offset results of the nodes, the surface pit deformation information is mapped onto the surface of the finite element model to construct local initial geometric defects. Specifically, the program can automatically read the target node number and its corresponding initial offset, and update the initial coordinates of the corresponding surface nodes in the finite element model.

[0136] As one implementation method, for target nodes, the node coordinates can be corrected based on their corresponding initial offset, thereby forming a local residual depression morphology on the finite element model surface that corresponds to the measured pit; for non-target nodes, the original position remains unchanged. Through the above processing, the geometric information of surface pits can be mapped into the finite element model.

[0137] After the above-described interlaminar damage mapping, intralaminar damage mapping, and surface pit mapping processes, a finite element model for post-impact compression analysis containing measured damage characteristics can be obtained. The mapping process can be implemented using Python scripts, automatic input file generation programs, secondary development interfaces, or a combination thereof.

[0138] In another exemplary embodiment of this application, step 106 is used to perform post-impact compression finite element analysis and output prediction results: after completing the mapping of measured damage information to the finite element model, compression boundary conditions and loading conditions are applied to the constructed post-impact compression finite element model containing measured damage, and incremental solution analysis is performed to obtain the mechanical response and failure results of the composite laminate under compressive load.

[0139] During the solution process, results such as loading end reactions, displacements, stress-strain distributions, out-of-plane deformations, and inter-layer and intra-layer damage variables can be extracted. Among these, the first... The total reaction force corresponding to each loading increment step can be expressed as: ; in, For the set of loading end nodes, For the first In the increment step, the first The reaction force at each loading end node. Further, this can be determined based on the initial bearing cross-sectional area. Calculate the corresponding compressive stress: .

[0140] Based on the above analysis results, characteristic response parameters such as peak load, peak stress, initial buckling point, maximum out-of-plane displacement, damage propagation location, and final failure region can be extracted. The residual compressive strength of the composite laminate can be determined by the load or stress peak; the buckling initiation load or buckling load can be determined based on the load-displacement response, the location of abrupt changes in out-of-plane displacement, or the location of a significant decrease in stiffness; the local buckling mode and the overall buckling mode can be determined based on the deformation contour map and out-of-plane displacement distribution; the damage propagation path and key failure location can be determined based on the evolution results of interlaminar and intralaminar damage variables; the final failure behavior and failure mode can be determined based on the damage distribution and overall deformation morphology under the final increment step.

[0141] The process of determining the remaining compressive strength from the load or peak stress is as follows: Based on the finite element analysis results, the reaction forces at the loading end nodes are first extracted and summed to obtain the total compressive load corresponding to each loading increment step. for: ; in, For the set of loading end nodes, For the first In the first loading increment step The reaction forces at each loading end node. After plotting the load-displacement curve, the maximum load occurring during the loading process is determined as the residual compressive bearing capacity after impact: .

[0142] Further based on the initial load-bearing cross-sectional area of ​​the specimen Calculate the residual compressive strength after impact of the composite laminate: .in, This represents the remaining compressive strength after impact.

[0143] The process for determining the buckling initiation load or instability load is as follows: When the load-displacement curve transitions from an initial linear stage to a significantly nonlinear stage, the structural tangential stiffness decreases significantly, or the out-of-plane displacement increases rapidly with increasing load, the load at the corresponding increment step can be determined as the buckling initiation load or instability load. As one implementation method, the tangential stiffness can be calculated based on adjacent loading increment steps. : ;in, For the first The loading displacement corresponding to each incremental step. When Stiffness relative to the initial linear stage A significant decrease, or maximum out-of-plane displacement, was observed. When rapid growth occurs, the corresponding total compressive load can be... It is determined to be either the buckling initiation load or the instability load.

[0144] The process for determining the local buckling mode and the overall buckling mode is as follows: if the out-of-plane deformation is mainly concentrated in the impact damage area and its adjacent area, it is determined to be local buckling; if the out-of-plane deformation develops over a large area of ​​the specimen and forms an overall bending deformation that runs through the length or width direction, it is determined to be overall buckling; if both exist simultaneously, it is determined to be a local and overall coupled buckling mode.

[0145] The process for determining the damage propagation path and critical failure location is as follows: The cell locations where the damage variable reaches a preset threshold can be recorded in different loading increment steps, for example: ;in, Finite element element For the first The damage variable of the unit in each incremental step. Set a preset damage threshold. Track according to the loading order. By observing the spatial development process, the damage initiation location, propagation direction, and main failure area can be obtained. If a certain area is the first to show a rapid increase in damage variables, interface separation and propagation, or concentrated fiber damage, then that area can be identified as the critical failure location.

[0146] The process for determining the final failure behavior and failure mode is as follows: when interlaminar damage dominates, it can be determined as delamination-dominated failure; when fiber damage is concentrated and leads to a rapid decrease in load-bearing capacity, it can be determined as fiber fracture-dominated failure; when local buckling in the impact damage zone induces rapid propagation of interlaminar or intralaminar damage, it can be determined as damage-induced buckling failure; when the overall out-of-plane deformation is significant and accompanied by large-scale damage propagation, it can be determined as overall instability failure. Through the above process, a comprehensive prediction of the residual compressive strength, buckling instability characteristics, damage propagation path, and final failure mode of composite laminates after impact can be achieved.

[0147] The above analysis enables the prediction of the residual compressive bearing capacity, buckling instability characteristics, and failure behavior of composite laminates after impact, thus providing a basis for structural damage tolerance assessment, residual strength analysis, and service safety determination.

[0148] The execution process of step 106 above can be summarized as follows: apply compression boundary conditions and loading conditions to the finite element model of post-impact compression analysis containing measured damage characteristics to obtain the mechanical response and failure results of the composite laminate under compressive load; determine the remaining compressive strength of the composite laminate based on the load or stress peak value in the mechanical response; determine the local buckling mode and the overall buckling mode based on the deformation cloud map and out-of-plane displacement distribution in the mechanical response; and determine the failure behavior and failure mode based on the damage distribution and overall deformation morphology in the final incremental step in the failure results.

[0149] The principle block diagram of the method in this application is as follows: Figure 2As shown, the process mainly includes five steps, S1 to S5. S1. Establish the baseline finite element model for post-impact compression analysis of composite laminates; S2. Obtain the measured damage information of composite laminates after impact; S3. Preprocess, uniformly characterize, and prepare mesh mapping for the measured damage information; S4. Map the processed damage information into the finite element model; S5. Perform post-impact compression finite element analysis and output the prediction results.

[0150] This application proposes a method for predicting the residual compressive strength of composite laminates after impact based on measured damage mapping. This method establishes a benchmark finite element model for post-impact compression analysis, acquires and characterizes measured interlaminar damage, intralaminar damage, and surface pitting information of the composite laminate after impact, and maps this measured damage information into the finite element model to construct a post-impact compression analysis model containing the measured damage. This allows for the prediction of the residual compressive strength, buckling mode, and failure behavior of the composite laminate after impact.

[0151] The key points of this application are: 1. Overall Technical Approach for Predicting Residual Compressive Strength of Composite Laminates After Impact Based on Measured Damage Mapping: This invention does not rely on empirical damage parameters, regular geometric equivalent damage, or continuous impact simulation under known impact conditions for residual strength analysis. Instead, it establishes an overall technical approach where measured damage information after impact is directly input into the finite element model, and further post-impact compression analysis is conducted. This approach covers the entire process, including establishing the baseline finite element model, acquiring measured damage information, unified characterization of damage information, finite element damage mapping, and predicting residual compressive strength and failure behavior.

[0152] 2. Unified Damage Characterization and Discretization Method for Interlaminar Damage, Intralaminar Damage, and Surface Pockmarks: This invention integrates information on interlaminar damage, intralaminar damage, and surface pits after impact in composite laminates into a unified damage description system. Through preprocessing, coordinate unification, spatial registration, and parametric characterization of measured damage information from different sources, element damage markers, interface damage markers, and initial node offset results are further generated for input to the finite element model.

[0153] 3. Mapping Method of Interlaminar Damage to Finite Element Interface Model: This invention maps delamination damage to the corresponding interlaminar interface location in the finite element model based on the damage marking results of the interlaminar interface elements. For interface regions without delamination damage, interface elements can be set and interface constitutive parameters can be assigned; for interface regions with delamination damage, the damage can be characterized by canceling the interface element settings, deleting interface constraints, or other equivalent methods, thereby realizing the mapping of measured interlaminar damage to the interface of the finite element model.

[0154] 4. Mapping Method of Intra-Layer Damage to Plyp Material Properties: This invention maps intra-layer damage to the corresponding plyp elements in the finite element model based on the damage marking results of the intra-layer elements. The intra-layer elements can be divided into undamaged states, matrix damaged states, fiber damaged states, and matrix-fiber composite damaged states, and different material parameters are assigned to each, thereby achieving the mapping of measured intra-layer damage to the finite element model.

[0155] 5. Mapping method of surface pits to local initial geometric defects: This invention maps the measured pit depth and residual deformation information after impact to the surface of the finite element model. By offsetting the node position, introducing the local geometric defect field or other equivalent methods, the local initial geometric defects in the post-impact compression analysis are constructed, thereby introducing the influence of surface pits on local buckling, overall instability and failure behavior into the finite element analysis.

[0156] The advantages of this application are as follows: 1. Improves the realism of the initial damage state in the finite element model, thereby enhancing the accuracy of residual compressive strength prediction: The main drawback of existing technologies is that they typically use empirical damage parameters, regular geometric regions, or material parameter reduction to simplify the characterization of impact damage. This makes it difficult to accurately reflect the actual damage state of composite laminates after impact, such as intralaminar damage, interlaminar damage, and surface pits, leading to a deviation between the initial damage state in the finite element model and the actual structure. This invention obtains measured interlaminar damage, intralaminar damage, and surface pit information, and maps them into the finite element model after unified characterization. This makes the post-impact compression analysis model closer to the actual damage state, thus improving the accuracy of residual compressive strength prediction results.

[0157] 2. It enables post-impact compression analysis under unknown impact conditions, resulting in greater engineering applicability: Existing methods based on continuous analysis of low-velocity impact and post-impact compression typically require accurate knowledge of parameters such as the impactor's mass, velocity, contact position, and contact posture. However, in real-world engineering scenarios, the impact process is often difficult to fully understand, and the current damage state is usually only obtained after the impact. This invention does not rely on specific impact conditions but directly constructs a finite element model based on the current measured damage state and performs post-impact compression analysis. Therefore, it is more suitable for engineering evaluation scenarios where "the current damage is known, but the specific impact process is unknown," thus exhibiting better engineering applicability.

[0158] 3. Improved predictive ability for buckling modes and failure behavior, providing a more reliable basis for damage tolerance assessment: Existing technologies do not adequately characterize the true damage state, making it difficult to accurately reflect the impact of impact damage on the local stiffness, local geometric defects, and stability characteristics of a structure. Therefore, their predictive ability for local instability locations, buckling propagation modes, and final failure behavior is limited. This invention maps measured interlaminar damage to interlaminar interfaces, measured intralaminar damage to ply material properties, and surface pits to local initial geometric defects. This allows the finite element model to more realistically reflect the impact of impact damage on buckling response and failure evolution, thus improving the predictive ability for buckling modes and failure behavior and providing a more reliable basis for damage tolerance assessment, residual strength analysis, and service safety determination of composite material structures.

[0159] Based on the same inventive concept, this application also provides a composite laminate post-impact compression response prediction device for implementing the aforementioned method for predicting the post-impact compression response of composite laminates. The solution provided by this device is similar to the solution described in the above method. Therefore, the specific limitations of one or more embodiments of the composite laminate post-impact compression response prediction device provided below can be found in the limitations of the composite laminate post-impact compression response prediction method described above, and will not be repeated here.

[0160] In one exemplary embodiment, a device for predicting the post-impact compression response of a composite laminate is provided, comprising: The model building module is used to build a baseline finite element model for post-impact compression analysis of composite laminates. The measured damage information acquisition module is used to acquire measured damage information of composite laminates after impact; the measured damage information includes interlaminar damage information, surface pit deformation information, and intralaminar damage information. The unified characterization module is used to perform unified characterization on the measured damage information to obtain a set of damage information after unified characterization. The spatial correspondence module is used to establish the spatial correspondence between the unified characterized damage information set and the plywood elements, interlayer interface elements and surface nodes of the benchmark finite element model, thus forming the damage assignment result. The mapping module is used to map the damage assignment results to the reference finite element model to obtain a finite element model for post-impact compression analysis that includes the measured damage characteristics. The finite element analysis module is used to perform post-impact compression finite element analysis using a post-impact compression analysis finite element model that includes measured damage characteristics, and outputs the predicted results of the post-impact compression response of composite laminates.

[0161] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 3 As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs in the non-volatile storage media. The database stores the predicted results of the post-impact compression response of composite laminates. The I / O interfaces are used for information exchange between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a method for predicting the post-impact compression response of composite laminates.

[0162] Those skilled in the art will understand that Figure 3 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer equipment to which the present application is applied. Specific computer equipment may include, for example, [the following is a list of possible additional structures]. Figure 3 The embodiments show more or fewer components, combinations of certain components, or different component arrangements. In one exemplary embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, which the processor executes to implement the steps in the above-described method embodiments.

[0163] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0164] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0165] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties.

[0166] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0167] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0168] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0169] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method of predicting the compressive response of a composite laminate after impact, characterized by, include: Establish a benchmark finite element model for post-impact compression analysis of composite laminates; Obtain measured damage information of composite laminates after impact; The measured damage information includes interlayer damage information, surface pit deformation information, and intralayer damage information; The measured damage information is uniformly characterized to obtain a set of damage information after uniform characterization. Establish the spatial correspondence between the unified damage information set and the plywood elements, interlayer interface elements and surface nodes of the benchmark finite element model to form the damage assignment result; The damage assignment results are mapped to the benchmark finite element model to obtain a finite element model for post-impact compression analysis that includes the measured damage characteristics. A finite element model for post-impact compression analysis, incorporating measured damage characteristics, was used to perform post-impact compression finite element analysis, and the predicted results of the post-impact compression response of the composite laminate were output.

2. The method of predicting the post-impact compressive response of a composite laminate according to claim 1, wherein, A baseline finite element model for post-impact compression analysis of composite laminates was established, including: Establish a geometric model of the composite laminate; Determine the finite element mesh generation rules for the geometric model; Determine the material constitutive model for intralayer damage and the interface constitutive model for interlayer damage; Set the compression boundary conditions after impact; The geometric model, finite element mesh generation rules, material constitutive model of intralaminar damage, interface constitutive model of interlaminar damage, and post-impact compression boundary conditions are combined to form the benchmark finite element model for post-impact compression analysis of composite laminates.

3. The method of predicting the post-impact compressive response of a composite laminate according to claim 2, wherein, Determine the finite element mesh generation rules for the geometric model, including: According to the envelope range of the measured damage area in the plane of the laminate after impact, the local reinforcement area is determined by using the formula and ; wherein, and are the dimensions of the local reinforcement area in the two in-plane directions, and are the dimensions of the measured damage area in the two in-plane directions after impact, is the buffer extension distance. According to , determining the grid characteristic length in the local encryption area; wherein, is the grid characteristic length, and respectively are the main direction and transverse elastic modulus of the fiber, 、 、 and respectively are the strength parameters corresponding to fiber tension, fiber compression, matrix tension and matrix compression, 、 、 and respectively are the fracture toughness parameters under the damage mode corresponding to fiber tension, fiber compression, matrix tension and matrix compression; The local encrypted region is divided into grids according to the grid feature length, and the global region is divided into grids according to twice the grid feature length. A transition grid is set between the local encrypted region and the global region. The global region refers to the region where the distance to the local encrypted region is greater than a preset distance threshold. The grid length of the transition grid is greater than the grid feature length but less than twice the grid feature length.

4. The method for predicting the post-impact compressive response of composite laminates according to claim 1, characterized in that, Obtain interlaminar damage information after impact on composite laminates, including: The composite laminate after impact was subjected to non-destructive testing using ultrasonic C-scan equipment to obtain the original flight time data. The raw flight time data is subjected to effective detection region extraction, outlier correction, noise suppression and smoothing to obtain preprocessed flight time data; Based on the preprocessed time-of-flight data, the background and non-background regions are determined, and the non-background regions are regarded as the projection regions of interlayer damage in the scanning plane. The location of the interlayer damage in the planar direction is determined based on the coordinates of each sampling point in the non-background area in the scanning plane coordinate system. The extent of interlayer damage in the planar direction is determined based on the boundary contour of the non-background area, the projection length of the projection area, and the projection width. According to the formula and For inter-layer damage with a known location and extent in the planar direction, inter-layer interfaces are assigned, and the inter-layer interface number to which each sampling point in the non-background area belongs is determined; among which, Sampling points The corresponding inter-layer interface number, Sampling points in non-background areas The measured flight time For the first Reference flight time of each interlayer interface For the first The depth of the interface between each layer from the front surface The equivalent propagation velocity of ultrasound in composite laminates; Based on the interlayer interface number to which each sampling point belongs, cluster analysis and regional consistency correction are performed in combination with the planar coordinate information and flight time information of the sampling points to obtain the preliminary allocation results of the damage areas of each interlayer interface. Based on the preliminary allocation of damage regions at the interlayer interfaces, and assuming that the damage in the next layer continuously fills the projection range of the damage in the upper layer, the final damage regions at each interlayer interface are represented as follows: The final damage area at each interlayer interface is used as the interlayer damage information of the composite laminate after impact; among which, For the first The final damaged area of ​​the interlayer interface, For the first Preliminary allocation results of interlayer interface damage regions For the first The final damaged area at the interlayer interface.

5. The method for predicting the post-impact compression response of composite laminates according to claim 1, characterized in that, Obtain surface pitting deformation information of composite laminates after impact, including: The depth of surface pits is measured using a depth gauge; Discrete point measurements are performed using a dial gauge or laser displacement sensor to obtain displacement values ​​at each sampling point, and the distribution of residual deformation on the surface is obtained through interpolation or fitting. Based on the distribution of residual deformation on the surface, using the formula Determine the boundary contour of the surface pits; where, The outline of the pit boundary, For the impact surface at the sampling point Residual depression deformation at the location, The preset depth threshold; The depth of the surface pit, the distribution of residual surface deformation, and the boundary contour of the surface pit are used together as surface pit deformation information after impact of the composite laminate.

6. The method for predicting the post-impact compressive response of composite laminates according to claim 1, characterized in that, Obtain intralaminar damage information after impact on composite laminates, including: When the intralayer damage is fiber damage, the area inside the largest inscribed ellipse of the uppermost interlayer damage region is taken as the fiber damage region. When the intralayer damage is matrix damage, the matrix damage region in each ply is characterized as the interlayer damage region of the corresponding interlayer interface below each ply. The fiber damage area and the matrix damage area are used as the intralaminar damage information after impact of the composite laminate.

7. The method for predicting the post-impact compressive response of composite laminates according to claim 1, characterized in that, The measured damage information is uniformly characterized to obtain a unified damage information set, including: Interlayer damage information, surface pit deformation information, and intralayer damage information are preprocessed to obtain preprocessed interlayer damage information, preprocessed surface pit deformation information, and preprocessed intralayer damage information. The pre-processed interlayer damage information, pre-processed surface pit deformation information, and pre-processed intralayer damage information are coordinate unified and spatially registered to obtain the registered interlayer damage information, registered surface pit deformation information, and registered intralayer damage information. Based on the interlayer interface number, the registered interlayer damage information is uniformly characterized to obtain a unified representation of the interlayer damage information. The registered surface pit deformation information is uniformly characterized. ;in, A unified representation of surface pit deformation information. This is a surface pit area. The outline of the surface pit boundary. To unify the surface residual deformation field under a reference coordinate system; According to the ply number and damage type, the registered intra-layer damage information is uniformly characterized as follows: ;in, For a unified representation of intralayer damage information, and The first Fiber damage area and matrix damage area after registration in the layer layup. , This represents the total number of plies. The unified representation of interlayer damage information, the unified representation of surface pit deformation information, and the unified representation of intralayer damage information are integrated into a unified damage information set.

8. The method for predicting the post-impact compression response of composite laminates according to claim 1, characterized in that, Establish the spatial correspondence between the unified damage information set and the plywood elements, interlayer interface elements, and surface nodes of the benchmark finite element model to form the damage assignment results, including: Based on the spatial inclusion relationship between the center coordinates of each ply element on the benchmark finite element model and the damage region within the layer, the damage state of each ply element is determined. Based on the damage state of each ply unit, an intralayer damage marker and corresponding unit number are generated for each ply unit. Based on the spatial inclusion relationship between the center coordinates of each interlayer interface element on the benchmark finite element model and the interlayer damage region of the corresponding interlayer interface, the delamination damage state of each interlayer interface element is determined. Based on the delamination damage state of each interlayer interface unit, a delamination damage mark and corresponding interface unit number are generated for each interlayer interface unit. The initial offset of the surface nodes within the surface pit region is expressed as: The initial offset of surface nodes outside the surface pit area is set to zero, thus forming the initial offset result of each surface node and its corresponding node number; where, This represents the initial offset in the thickness direction. node position The residual deformation value at the location; The damage assignment result is formed by combining the intralayer damage marker and corresponding element number of each ply element, the layer damage marker and corresponding interface element number of each interlayer interface element, and the initial offset result and corresponding node number of each surface node.

9. The method for predicting the post-impact compressive response of composite laminates according to claim 1, characterized in that, The damage assignment results are mapped to the baseline finite element model to obtain a post-impact compression analysis finite element model containing measured damage characteristics, including: For delamination damage regions, the delamination damage between layers is characterized by canceling the interface element settings or deleting the interface constraints; for undamaged regions, the original interface connection relationships are retained and the corresponding interface constitutive parameters are assigned. The intralayer elements are divided into undamaged state, matrix damaged state, fiber damaged state, and matrix and fiber composite damaged state, and are characterized by different material parameters, stiffness reduction schemes or initial damage variables respectively. For surface nodes within the surface pit area, the node coordinates are corrected based on the initial offset; for surface nodes outside the surface pit area, the original position remains unchanged.

10. The method for predicting the post-impact compression response of composite laminates according to claim 1, characterized in that, A finite element model for post-impact compression analysis incorporating measured damage characteristics was used to perform post-impact compression finite element analysis, outputting predicted results of the post-impact compression response of the composite laminate, including: Compression boundary conditions and loading conditions were applied to the finite element model of post-impact compression analysis containing measured damage characteristics to obtain the mechanical response and failure results of composite laminates under compressive load. The remaining compressive strength of the composite laminate is determined based on the load or stress peak value in the mechanical response. Based on the deformation contour map and out-of-plane displacement distribution in the mechanical response, the local buckling mode and the overall buckling mode are determined; Based on the damage distribution and overall deformation morphology at the final incremental step in the failure results, the damage behavior and failure mode are determined.

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