A method for calculating the energy release rate of delamination damage propagation in composite materials based on shell elements.

Abstract

This invention discloses a method for calculating the energy release rate of delamination damage propagation in composite materials based on shell elements, belonging to the field of composite material delamination damage modeling and efficient energy release rate calculation. The method includes: deriving an equivalent energy release rate calculation method based on energy differential, and proposing a simplified formula for calculating the structural energy release rate under the linear elasticity assumption of the material. Undamaged regions are established using multi-layered plate and shell elements after delamination, and structural damage analysis models are constructed under different damage sizes, structural load conditions, and displacement boundary conditions. The structural response under different damage sizes is calculated and a database is formed. The relationship between damage size and structural strain energy or overall flexibility and stiffness is fitted using a polynomial isofunction fitting method, establishing a reduced-order model for calculating the energy release rate of delamination damage propagation with damage size and external load as inputs. This invention is used to quickly calculate the energy release rate of delamination damage propagation in composite materials, supporting rapid online safety assessment of composite structures.

Description

Technical Field

[0001] This invention belongs to the field of composite material delamination damage modeling and efficient energy release rate calculation, specifically involving a method, device and storage medium for calculating the extended energy release rate of composite material delamination damage based on shell elements. Background Technology

[0002] The large-scale application of composite materials in aerospace structures began in the 1990s. In recent years, in particular, the use of carbon fiber reinforced polymer (CFRP) in the airframe structure of new-generation commercial aircraft, such as the Boeing 787 and Airbus A350, has increased to over 50%, marking the aerospace industry's entry into the "composite materials era." However, this has also brought with it safety concerns. Composite materials exhibit various damage types and failure modes. Because they are often made by layering different components, the interlayer bonding strength is often weaker than the intralayer properties. In practical engineering applications, delamination damage is a particularly common and threatening form of damage to composite materials compared to other damage modes. This type of damage not only affects the mechanical properties of the material, such as stiffness and strength, but can also significantly impact the durability and reliability of the composite material.

[0003] Delamination damage can originate at any stage of the composite structure's lifecycle, including manufacturing, assembly, service, and maintenance. Caused by internal defects, impacts, or extreme loads during extreme maneuvers, delamination damage can manifest as interlaminar debonding, intralaminar cracking, and peeling. It often begins with minute damage at the interlaminar interfaces, gradually expanding with subsequent loads or cyclical changes, and can easily lead to structural failure if left untreated. In most cases, delamination damage caused by factors such as impacts is almost invisible on the structural surface, yet it significantly impacts the strength and lifespan of the entire component.

[0004] From the perspective of current practical engineering applications in aircraft, both structural developers and users face the challenge of lacking mature and reliable theoretical support to assess the structural safety for future service after discovering internal delamination damage. This hinders the development of reasonable maintenance and inspection decisions for aircraft structures. In particular, with the increasing influence of the "damage tolerance" safety concept, strength verification of existing damaged structural areas and prediction of subsequent damage evolution and expansion require more accurate models of composite material delamination damage and precise calculation of energy release rates, placing higher demands on analytical efficiency.

[0005] Energy Realease Rate (ERR) is one of the most important concepts in fracture mechanics. Finite element methods (FEMs) are highly adaptable to crack propagation analysis of complex geometries or multi-irregular crack structures and have been widely used for ERR calculation. Currently, numerical simulation methods based on finite element models, such as Virtual Crack Closure Technology (VCCT), Cohesive Z-Mechanism (CZM), and Extended Finite Element Method (XFEM), can be used for relatively accurate fracture mechanics analysis, providing benchmark values ​​for evaluating the accuracy of the analytical expression for ERR. However, these methods suffer from cumbersome modeling and simulation processes. Some precise simulation methods may require regenerating new, detailed meshes after calculating the ERR over a certain crack length. The complexity of the models they rely on leads to difficulties and time consumption in practical implementation, making it difficult to meet real-time requirements in terms of analysis efficiency. Therefore, a more accurate method for modeling delamination damage in composite materials is urgently needed to calculate the ERR more accurately and quickly. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method for calculating the energy release rate of delamination damage propagation in composite materials based on shell elements. It also provides a comprehensive framework for calculating the energy release rate of delamination damage propagation in composite materials based on shell elements, enabling rapid calculation of the energy release rate of delamination damage propagation in composite materials to support online safety and rapid assessment of composite material structures.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for calculating the energy release rate of delamination damage propagation in composite materials based on shell elements, comprising the following steps:

[0009] Step 1: Derive the method for calculating the equivalent energy release rate based on energy differential, and propose a simplified formula for calculating the structural energy release rate under the assumption of linear elasticity of materials;

[0010] Step 2: Establish undamaged regions using multi-layered plate and shell elements after layering, and construct structural damage analysis models under different damage sizes, structural load conditions, and displacement boundary conditions. Calculate the structural response under different damage sizes and form a database.

[0011] Step 3: Fit the relationship between damage size and structural strain energy or overall flexibility and stiffness using polynomial and other function fitting methods, and establish a reduced-order model for calculating the energy release rate of layered damage propagation with damage size and external load as input.

[0012] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the above-described method for calculating the energy release rate of composite material delamination damage propagation based on shell units.

[0013] The present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the above-described method for calculating the energy release rate of composite material delamination damage propagation based on shell elements.

[0014] Beneficial effects:

[0015] Unlike traditional single-layer shell modeling strategies for undamaged regions, this invention models undamaged regions using multi-layer shell elements, without restricting the rotational degrees of freedom of these regions. Based on energy differential derivation, this invention derives the energy release rate calculation formula under the assumption of structural linear elastic response and, using a parametric modeling method, calculates the energy release rate of layered damage propagation under different damage sizes. Based on the calculated energy release rate of layered damage propagation under different damage sizes, this invention fits a lightweight prediction model containing only a few model parameters, suitable for online simulation of layered damage propagation. This provides an efficient analytical and computational architecture for near real-time safety assessment of composite structures with layered damage. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method for calculating the energy release rate of delamination damage propagation in composite materials based on shell units according to the present invention;

[0017] Figure 2 A schematic diagram of layered damage modeling based on shell elements is shown; where (a) represents modeling method (I) and (b) represents modeling method (II).

[0018] Figure 3 The diagram shows the equivalent layered front deformation modes for different modeling methods; where (a) represents modeling method (I) and (b) represents modeling method (II).

[0019] Figure 4 A schematic diagram of parameterized modeling of layered damage is shown, where (a) is a schematic diagram of modeling and (b) is a cross-sectional view;

[0020] Figure 5 This is a schematic diagram of the layup dimensions of a woven laminate, where (a) is a cross-sectional view and (b) is a top view;

[0021] Figure 6 A schematic diagram of the layered test and equivalent plate-shell simulation model of the double cantilever beam;

[0022] Figure 7This is a schematic diagram comparing the calculated results of the energy release rate-layer size curve of the specimen in the double cantilever beam layered propagation test. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0024] like Figure 1 As shown, the method for calculating the energy release rate of composite material delamination damage propagation based on shell elements of the present invention includes the following steps:

[0025] Step 1: Based on the structural linear elastic response assumption, derive the formula for calculating the equivalent energy release rate based on energy differential.

[0026] Step 2: Establish multi-layered shell elements in the undamaged region, releasing rotational degrees of freedom, thereby establishing a novel shell modeling strategy with layered damage. Based on this modeling strategy, the layered energy release rate of shell structures with different damage sizes is calculated using the equivalent energy release rate calculation formula and the damage parameterization method.

[0027] Step 3: Based on structural response data under different damage sizes, establish a database of damage size and structural strain energy or overall flexibility and stiffness. Combined with the derived energy release rate calculation formula, establish a reduced-order model for calculating the energy release rate of layered damage propagation with damage size and external load as input.

[0028] Specifically, step 1 includes:

[0029] In fracture mechanics, the energy release rate represents the rate of energy conversion during material fracture. Based on the principle of energy conservation, the energy release rate in quasi-static fracture... This can be expressed as the decrease in total potential energy per unit increase in fracture surface area. It relates the energy released during fracture to the energy of the newly formed surface and other dissipated energy, characterizing the energy balance. According to the definition of energy release rate, it represents the total potential energy caused by the increase in unit fracture surface area. The amount of reduction:

[0030] (1)

[0031] in, This represents the area of ​​layered damage.

[0032] Total potential energy satisfy:

[0033] (2)

[0034] in, The total strain energy includes reversible elastic strain energy and irreversible energy related to plastic deformation. This indicates that work is done by an external force, which can be expressed as surface force. ,physical strength and displacement Give, , Let represent the integral elements of surface forces and volume forces on the material surface and volume, respectively. The boundary surface representing the action of surface forces. This represents the volume region of the integral.

[0035] definition , These represent the external force acting on the structure and the corresponding displacement of a material point under that force. Based on the definition of energy release rate, when the displacement remains constant, the change in work done by the external force is zero. The energy release rate is determined by the change in total strain energy.

[0036] (3)

[0037] When the load is fixed, the energy release rate is:

[0038] (4)

[0039] If the material is linearly elastic, the calculation of its energy release rate can be greatly simplified. In this case, the load-displacement curve at the point of application of the load is linear. Here, compliance is defined. Displacement when a unit external load is applied:

[0040] (5)

[0041] Correspondingly, strain energy Then it equals:

[0042] (6)

[0043] Based on the above formula, it can be deduced that when the load is fixed, the energy release rate is:

[0044] (7)

[0045] When the displacement is fixed, the energy release rate of structural damage propagation is:

[0046] (8)

[0047] In the subsequent discussion of this invention, the above formula will be applied to calculate the structural energy release rate, mainly based on the structural linear elastic response assumption.

[0048] Specifically, step 2 includes:

[0049] Step 2.1: Establish a layered damage model based on shell elements:

[0050] This invention combines plate and shell theory with the delamination problem of composite materials. Based on the derivation of the analytical expression of the energy release rate at the delamination front using the Kirchhoff-Lep hypothesis plate theory, and using the aforementioned energy differential correlation theory, a method for constructing a reduced-order model for calculating the energy release rate of delamination in plate and shell structures under different damage sizes is given.

[0051] First, two plate and shell modeling strategies with delamination damage are given (i.e., modeling method (I) and modeling method (II)). Figure 2 As shown.

[0052] Modeling Method (1): In the undamaged area, a single-layer shell element is used for modeling. In the damaged area, models are performed separately according to the number of layers. Only "hard contact" is applied between the layers to prevent them from penetrating each other. Figure 2 (a) Figure 2 (as shown by the blue dashed line in (b)), at the boundaries of the layers, the boundaries of each layered shell element are respectively bound to the boundaries of the unlayered elements. Figure 2 (a) Figure 2 As shown by the red solid line in (b), the nodes on both sides are forced to be in close contact, with the same translational and rotational displacements. This simulates the connection relationship between the layered and unlayered regions, ensuring that each unit connecting the layered and unlayered regions of the overall plate structure satisfies the continuous deformation required in a real structure.

[0053] Based on this, the present invention presents a second equivalent modeling strategy for plate and shell structures. Unlike modeling method (I), in modeling method (II), the undamaged region is modeled using multi-layered plate and shell elements, rather than a single-layered plate and shell element with undamaged structural cross-sectional properties. In the layered damaged region, the elements are also defined based on "hard contact," allowing only slippage and separation between them. In the undamaged region, binding constraints are applied between the elements, but these constraints only restrict the two elements to have the same translational displacement, without restricting their rotational degrees of freedom. Figure 2 (a) Figure 2 In (b), the blue dashed line represents hard contact constraints, and the red dashed line represents binding constraints.

[0054] like Figure 3 As shown, compared to modeling method (I) ( Figure 3 (a)), Modeling Method (II) Figure 3 (b) effectively relaxes the deformation constraints on the locally undamaged region connected to the end of the damaged region, allowing different rotation angles to occur at the delamination front positions of the upper and lower plates. The impact of this difference on the energy release rate calculation results will be discussed in comparison with existing analytical solutions in subsequent embodiments of the present invention. Figure 3 (a) Figure 3 The red-lined area in (b) is the contact point between the damaged area and the undamaged area.

[0055] Step 2.2, Parameterized Modeling and Simulation of Layered Damage Based on Shell Elements:

[0056] Building upon the established modeling strategy, this invention introduces parametric modeling and simulation methods to achieve efficient solutions for energy release rates under different damage sizes. This enables automated modeling and multi-condition simulation analysis of layered damage, such as... Figure 4 As shown in (b), The semi-major axis of the equivalent region for composite material delamination damage. The semi-minor axis is defined as the equivalent region for delamination damage in composite materials. Specifically, a Python script combined with finite element software is used for automatic modeling, enabling flexible adjustment of parameters such as delamination damage size and external load, and rapidly generating the corresponding structural analysis model. Figure 4 In (a), the gray area is the undamaged area, the blue area is the delamination damage area, and the dark green area is the initial impact area.

[0057] In each simulation case, a parametric layered structural analysis model is constructed by setting different layered areas and external load information. Each layered region is modeled using the aforementioned modeling method two: undamaged areas are modeled as multi-layered shell elements with bound translational degrees of freedom, while layered regions release the relative slippage and separation behavior between the upper and lower layer contact surfaces, simulating layered behavior through hard contact definition. The loading method uniformly employs concentrated force or equivalent boundary load, recording the overall strain energy change under structural response, and calculating it based on the equivalent energy release rate formula derived in step 1.

[0058] Step 2.3: Construct a structural response database based on damage parameterization modeling.

[0059] Through the aforementioned damage parameterization modeling process, parametric layered modeling and simulation calculations are completed, extracting key structural response indices at each damage size, including structural strain energy or overall flexibility and stiffness, and establishing a structural response database. The database takes layered dimensions and load conditions as input and outputs the corresponding structural response quantities and energy release rates, stored in a unified format. This database covers typical structural forms and various combinations of layered parameters, providing rich data support for subsequent lightweight reduction modeling and fitting analysis.

[0060] Specifically, step 3 includes establishing a reduced-order model for calculating the energy release rate of layered damage propagation:

[0061] Based on the completion of numerous finite element simulations under different delamination sizes and load conditions and the construction of a response database, this invention further constructs a reduced-order model for rapidly predicting the energy release rate of delamination expansion. This model aims to achieve an approximate prediction of the energy release rate with as few parameters as possible and with low computational cost, meeting the needs of online analysis and real-time assessment of delamination damage in composite structures.

[0062] Specifically, the model uses layer size and external load amplitude as input variables, and the equivalent energy release rate obtained by calculating the simulation results through formulas as the target output. It employs fitting methods such as multinomial regression and response surface methodology to construct a simplified and accurate reduced-order model.

[0063] Preferably, model reduction methods include, but are not limited to, principal component analysis (PCA), Krylove subspace method, multinomial regression, response surface methodology, and other model reduction methods.

[0064] Preferably, the applied structure includes, but is not limited to, multilayer composite material structures that can adopt the structural linear elastic response assumption.

[0065] Example:

[0066] In the embodiments, the method of the present invention is applied to a layered expansion test example of a double cantilever beam to verify the calculation accuracy of the present invention.

[0067] The example is a double cantilever beam (DCB) layered propagation test. The specimens used were made of woven prepreg (G0814 / 913), with materials consisting of T300 carbon fiber and an epoxy resin matrix. The layup adopted a multi-directional arrangement, with the weaving directions of each layer alternating between 0° / 90° and +45° / -45°, for a total of 15 layers. Figure 5 As shown, where This represents the principal direction of the fibers in the composite laminate. Indicates and The other main fiber direction is perpendicular to the direction of the main fiber. Indicates the thickness direction of the laminate.

[0068] The delamination occurs between the seventh and eighth layers of the laminate, with different ply directions on the upper and lower sides of the delamination interface: (e.g.) Figure 5 As shown ( Figure 5 (a) is a cross-sectional view. Figure 5(b) is a top view; the purple ply is the upper layer material with a weave direction of 0° / 90°, and the red ply is the lower layer material with a weave direction of +45° / -45°. The equivalent material properties of the un-delaminated area and the upper and lower delaminated layers of this sample are shown in Table 1:

[0069] Table 1. Equivalent stiffness performance parameters of layered and unlayered regions

[0070]

[0071] Where E11 and E22 represent the tensile modulus of elasticity in the principal directions within the laminate, E33 represents the modulus of elasticity in the thickness direction, G12 represents the in-plane shear modulus, and G31 and G32 represent the thickness-related shear moduli. 12 This represents the lateral contraction ratio in the second direction when the object is under tension in the first direction. 31 = 32 This indicates the lateral shrinkage ratio in the in-plane direction when the thickness is subjected to tension.

[0072] The length, width, and thickness of the sample are respectively , and ,like Figure 6 As shown. h represents half the thickness. Based on the experimental setup, the initial layer length is determined by the hinge-applied opening displacement. This is the distance from the right end of the hinge to the leading edge of the delamination. In the model construction of this embodiment, the specimen is also modeled starting from the right side of the hinge, with an initial delamination length. The experimental setup and simulation model are as follows: Figure 6 The figures show the layering of modeling method (I) and modeling method (II), respectively. The layered areas are located between the seventh and eighth layers of the laminate, while the unlayered areas do not include the layering between the seventh and eighth layers.

[0073] For this sample, the delamination damage area is rectangular. Therefore, based on equation (7) and the parametric modeling simulation results, the reduced-order model for calculating the energy release rate can be fitted as follows:

[0074] (9)

[0075] in, For the opening displacement under unit load, in this example, a cubic polynomial can be used to fit it well with the damage size. The relationship is shown in the fitted energy release rate-damage size curve results. Figure 7 As shown (the numerical values ​​in the illustration correspond to...) (load conditions).

[0076] Here, we will compare the correctness of the calculation results using the following two reference solutions as a reference. First, we will compare the energy release rate calculation expression derived based on beam theory:

[0077] (10)

[0078] in, For the applied load, The layer length is measured from the load line. The width of the sample. The longitudinal elastic modulus of the material. This represents a reference value for the energy release rate derived from classical mechanics. The expression takes into account the different thicknesses of each layer. and These are the thicknesses of the upper and lower plates, respectively. This analytical expression actually introduces the assumption that the deflection and rotation at the layer tip are zero.

[0079] To account for this deformation, the model was further modified, and the following modification factors were proposed. :

[0080] (11)

[0081] in, It is the out-of-plane shear modulus. The expression used to characterize the effect of the thickness-direction stiffness of the laminate on the crack tip field is as follows:

[0082] (12)

[0083] in, This is the out-of-plane elastic modulus. Parameter It is a stiffness constant; according to the data, the parameter K is set to K = 0.85. Type I energy release rate describes the energy release at the crack tip due to positive tensile opening displacement, and can be expressed as:

[0084] (13)

[0085] in, and These are the corresponding correction factors for the upper and lower plates calculated according to equation (11), respectively. and These are the equivalent longitudinal elastic moduli of the upper and lower plates, respectively. This is a reference value for the energy release rate based on the revised formula. This indicates the thickness of the laminates at the crack interface. This indicates the thickness of the laminate below the crack interface.

[0086] Based on the above formula and the energy release rate calculated by this invention under different layer sizes (all load sizes are P = 20N), the results are compared as follows: Figure 7 As shown, the black solid line is the curve of energy release rate as a function of layer size calculated by the flexibility differential method using modeling method (I), the red dots are the calculation results corresponding to formula (10), the purple dashed line is the curve of energy release rate as a function of layer size calculated by the flexibility differential method using modeling method (II), and the yellow dots are the calculation results corresponding to formula (13).

[0087] from Figure 7 The results clearly show that, according to the method proposed by the present invention, among the energy release rate results calculated by different modeling methods, the plate and shell model constructed based on method one is consistent with the prediction result of formula (10), and the plate and shell model constructed based on method two is consistent with the result calculated by formula (13). In fact, whether comparing the finite element simulation results based on J-integral or the results of layered extended actual experiments, the prediction of formula (13) is more accurate. Therefore, the results obtained by the present invention are in better agreement with the theoretical solution.

[0088] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the above-described method for calculating the energy release rate of composite material delamination damage propagation based on shell units.

[0089] The present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the above-described method for calculating the energy release rate of composite material delamination damage propagation based on shell elements.

[0090] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of the present invention can be implemented using various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0091] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0092] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0093] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0094] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0095] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for calculating the energy release rate of delamination damage propagation in composite materials based on shell elements, characterized in that, Includes the following steps: Step 1: Derive the method for calculating the equivalent energy release rate based on energy differential, and propose a simplified formula for calculating the structural energy release rate under the assumption of linear elasticity of materials; Step 2: Establish undamaged regions using multi-layered plate and shell elements after layering, and construct structural damage analysis models under different damage sizes, structural load conditions, and displacement boundary conditions. Calculate the structural response under different damage sizes and form a database. Step 3: Fit the relationship between damage size and structural strain energy or overall flexibility and stiffness using a polynomial function fitting method, and establish a reduced-order model for calculating the energy release rate of layered damage propagation with damage size and external load as input.

2. The method for calculating the energy release rate of delamination damage propagation in composite materials based on shell units according to claim 1, characterized in that, In step 1, the simplified formula is derived through energy differential. Under the assumption of linear elasticity of the material, the change in external force work is directly converted into the change in structural flexibility or stiffness based on the linear relationship between load and displacement, thereby establishing an explicit relationship between energy release rate and structural response, providing a basis for the rapid calculation of energy release rate in subsequent steps.

3. The method for calculating the energy release rate of delamination damage propagation in composite materials based on shell units according to claim 2, characterized in that, In step 2, when establishing the undamaged region, a multi-layer shell unit is used, and only the translational degrees of freedom between each layer are constrained in the undamaged region, without constraining the rotational degrees of freedom, so that different layers in the undamaged region can rotate independently.

4. The method for calculating the energy release rate of delamination damage propagation in composite materials based on shell elements according to claim 3, characterized in that, By setting contact relationships between layers in the layered region that allow only slippage and separation, a simulation consistent with the actual structural deformation is formed by releasing constraints, providing an accurate mechanical model for calculating the structural response under different damage sizes in subsequent steps.

5. The method for calculating the energy release rate of delamination damage propagation in composite materials based on shell elements according to claim 4, characterized in that, In step 2, the structural damage analysis model is implemented through parametric modeling. The layered damage size, structural load conditions and displacement boundary conditions are automatically adjusted by scripts to generate finite element models in batches and solve them to obtain structural response data covering different damage sizes. The correspondence between damage size and structural response stored in the database provides data support for the construction of the order reduction model in subsequent steps.

6. The method for calculating the energy release rate of delamination damage propagation in composite materials based on shell units according to claim 5, characterized in that, In step 3, the polynomial function fitting is based on the database obtained in step 2. The damage size and external load are used as input variables, and the overall strain energy or overall flexibility and stiffness of the structure are used as intermediate variables. The polynomial coefficients are determined by the least squares method to establish a continuous mapping relationship between the damage size, external load and structural response, so that the intermediate variables can be directly calculated from the input variables in subsequent steps.

7. The method for calculating the energy release rate of delamination damage propagation in composite materials based on shell units according to claim 6, characterized in that, In step 3, the reduced-order model takes the simplified formula of the energy release rate in step 1 as its core, and substitutes the continuous mapping relationship into the simplified formula to form an expression that depends only on the damage size and the external load. This expression enables rapid prediction of energy release rate by replacing the finite element solution process, thereby completing the model order reduction from offline library construction to online calculation.

8. The method for calculating the energy release rate of delamination damage propagation in composite materials based on shell units according to claim 1, characterized in that, When applied to multilayer composite structures with delamination damage, the modeling strategy of the multilayer plate and shell elements in step 2 works in conjunction with the reduced-order model in step 3. This allows for the online assessment of delamination damage propagation by directly outputting the energy release rate without remodeling after executing steps 1 to 3 in sequence, by inputting new damage dimensions and external loads.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method for calculating the energy release rate of composite material layered damage propagation based on shell units as described in any one of claims 1 to 8.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the computer program implements the steps of a method for calculating the energy release rate of composite material delamination damage propagation based on shell units, as described in any one of claims 1 to 8.

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