Data-driven experimental stress identification method and system for non-constitutive model materials

Abstract

The present invention provides a data-driven experimental stress identification method and system for materials without a constitutive model, comprising the following steps: obtaining the displacement field and load boundary conditions of the specimen measurement area through DIC; calculating the strain field according to the displacement field; dividing clusters according to the strain field and establishing an initial mapping between elements and data points; defining an energy deviation optimization objective function and node balance constraint conditions; establishing a linear equation system through the Lagrange multiplier method; solving the linear equation system according to the mapping relationship and updating the data points and element stresses; updating the mapping relationship according to the stress-strain states of the elements and data points; determining whether the mapping relationship reaches convergence; and outputting the stress-strain data points and element stresses. The present invention can directly obtain the stress field of the measurement area through the displacement field and load boundary conditions without a prior material constitutive model; at the same time, a large number of material stress-strain data points can be generated under simple experimental conditions to meet the requirements of data-driven algorithms.

Description

Technical Field

[0001] The present invention relates to the technical field of data-driven computing, and particularly to a method and system for identifying experimental stresses of materials without a constitutive model driven by data, especially a method for obtaining a stress field and simultaneously obtaining a large number of stress-strain data sets through the displacement field and load boundary conditions of DIC. Background Art

[0002] The finite element method is the most widely used numerical simulation method in the development of current technical sciences and engineering analysis, and is an important part of computer-aided engineering and numerical simulation. The constitutive model of materials is used to describe the relationship between stress and strain during the loading process, and is one of the key theoretical bases in the traditional finite element method. With the development of materials science, the microstructure of materials has become increasingly refined, and the mechanical behavior has become more and more complex. It is very difficult to establish a constitutive model that can accurately describe the mechanical behavior of materials. There are often inevitable differences between the traditional phenomenological constitutive models and the actual mechanical behavior of materials, which will bring certain systematic deviations to the simulation analysis of structures. On the other hand, the phenomenological constitutive model generally has multiple model parameters, and the model parameters need to be calibrated through experiments. The parameter calibration process will also cause new deviations, which further restricts the reliability of the simulation analysis results.

[0003] The data-driven computational mechanics method is a newly emerging numerical solution paradigm in recent years that does not rely on the constitutive model of materials and has received extensive attention in the field of computational mechanics. This method directly starts from the material data set obtained from experiments, combines constraint conditions such as compatibility conditions and equilibrium equations, and obtains the optimal solution of the system equilibrium state by minimizing the free energy of the system. The data-driven computational mechanics method has been rapidly developed and improved in recent years, and the relevant theoretical system has been extended to problems such as viscoelasticity, elastoplasticity, and dynamics. This method does not need to establish a phenomenological constitutive model of materials, and can directly solve the mechanical response of structures through the discrete stress-strain data points of materials, which can fundamentally avoid the systematic deviations caused by the phenomenological constitutive model and material parameter calibration. On the other hand, this method requires a large amount of material stress-strain data to ensure the solution accuracy, and the acquisition of the stress-strain data set has also become a key issue in the data-driven computational mechanics method.

[0004] Digital Image Correlation (DIC) technology is a method widely used in the field of materials to measure strain fields. Random speckles are sprayed on the surface of the specimen's deformation area, and real-time image acquisition of the speckle area is performed during the test. By comparing the speckle distribution states before and after deformation, the displacement field and strain field of the measurement area can be obtained. Through DIC technology, a large amount of strain data of materials can be obtained quickly. On the other hand, it is very difficult to obtain stress data. For test specimens with simple shapes, the stress within the measurement area is approximately uniformly distributed, so only the stress data of a very narrow range under a specific path can be obtained, which cannot meet the computational requirements driven by data. For test specimens with complex shapes, traditional methods cannot directly obtain the stress field distribution of the specimen during the test, and it is necessary to combine the finite element method to numerically simulate the loading process of the specimen. On the one hand, this method requires a prior constitutive model of the material, and the introduction of the constitutive model will lead to new systematic deviations; on the other hand, the method process is too cumbersome, and multiple parameter calibration processes are required to reproduce the strain field and stress field of the specimen, making it difficult to quickly generate a large amount of material data. Therefore, there is an urgent need for a method for identifying material stress that does not rely on a prior constitutive model, which can quickly generate a large amount of material data under simple experimental conditions to meet the requirements of data-driven computational methods.

[0005] The patent document with the publication number CN105740541A discloses a prestress identification method based on structural dynamics model modification, which involves the prestress identification of a pre-tightened structure, establishing a finite element model of the structure; converting boundary conditions such as fixed supports or simply supported supports into spring supports in three or two directions, and applying axial prestress at the same time; calculating the natural frequencies and natural vibration modes of the structure through commercial finite element software; testing and identifying the natural frequencies and natural vibration modes of the structure by experimental modal analysis technology; and simultaneously identifying the spring support stiffness and prestress at the boundary based on model modification technology. However, this patent document still has the defect of relying on a material constitutive model. Summary of the Invention

[0006] Aiming at the defects in the prior art, the purpose of the present invention is to provide a data-driven experimental stress identification method and system for materials without a constitutive model.

[0007] A data-driven experimental stress identification method for materials without a constitutive model provided by the present invention includes the following steps:

[0008] Step 1: Obtain the displacement field and load boundary conditions of the specimen measurement area through DIC;

[0009] Step 2: Calculate the strain field according to the displacement field;

[0010] Step 3: Divide clusters according to the strain field and establish an initial mapping between elements and data points;

[0011] Step 4: Define the energy deviation optimization objective function and the node balance constraint conditions;

[0012] Step 5: Establish a linear equation system by the Lagrange multiplier method;

[0013] Step 6: Solve the linear equation system according to the mapping relationship, and update the data points and the element stresses;

[0014] Step 7: Update the mapping relationship according to the stress and strain states of the elements and the data points;

[0015] Step 8: Determine whether the mapping relationship reaches convergence. If so, proceed to Step 9; if not, return to Step 6;

[0016] Step 9: Output the stress and strain data points and the element stresses.

[0017] Preferably, Step 1 is specifically: Obtain the displacement field distribution of the specimen measurement area at different moments during the loading process through DIC, and simultaneously record the load boundary conditions at the corresponding moments through a tensile testing machine.

[0018] Preferably, in Step 2, the element strain field ε e has the following calculation formula:

[0019]

[0020] where u j is the nodal displacement of all nodes in the measurement area, f j obtains the nodal forces of all nodes through the load boundary conditions of the tensile testing machine, and B ej is the strain differential matrix of element e at node j.

[0021] Preferably, Step 3 is specifically: Based on the element strain field, divide the elements in the specimen measurement area into clusters through the K-means clustering algorithm, and establish the initial mapping relationship between the elements and the data points.

[0022] Preferably, Step 4 is specifically: Take the minimum energy deviation between the element and the mapped data point as the optimization objective, and take the equilibrium equation of the node as the constraint condition, and convert the stress identification problem into an optimization problem of the objective function under the constraint conditions.

[0023] Preferably, Step 5 is specifically: Use the Lagrange multiplier method to solve the optimization problem of the objective function under the constraint conditions, and obtain a linear equation system about the strain data points, stress data points, element stresses, and nodal Lagrange multipliers by finding the extreme points of the Lagrangian function.

[0024] Preferably, step 6 is specifically as follows: According to the mapping relationship between elements and data points, solve the linear equations, and update the strain data points, stress data points, element stresses, and nodal Lagrange multipliers.

[0025] Preferably, step 7 is specifically as follows: According to the stress-strain states of elements and data points, update the mapping relationship between elements and data points, and remap the elements to the data points with the minimum energy deviation.

[0026] Preferably, step 8 is specifically as follows: Repeat steps 6-7 until the mapping relationship between elements and data points no longer changes, and obtain the final strain data points, stress data points, and element stresses.

[0027] The present invention also provides a data-driven experimental stress identification system for materials without a constitutive model, including the following modules:

[0028] Module M1: Obtain the displacement field and load boundary conditions of the specimen measurement area through DIC;

[0029] Module M2: Calculate the strain field according to the displacement field;

[0030] Module M3: Divide clusters according to the strain field and establish an initial mapping between elements and data points;

[0031] Module M4: Define the energy deviation optimization objective function and nodal equilibrium constraint conditions;

[0032] Module M5: Establish linear equations by the Lagrange multiplier method;

[0033] Module M6: Solve the linear equations according to the mapping relationship and update the data points and element stresses;

[0034] Module M7: Update the mapping relationship according to the stress-strain states of elements and data points;

[0035] Module M8: Determine whether the mapping relationship has converged. If so, proceed to Module M9. If not, return to Module M6;

[0036] Module M9: Output the stress-strain data points and element stresses.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] 1. The method of the present invention can quickly identify the stress field of the measurement area through the displacement field and load boundary conditions measured by DIC, without the need for a prior constitutive model;

[0039] 2. The method of the present invention can be applied to identify the non-uniform stress field distribution in specimens of various complex shapes, and at the same time, there is no need to perform numerical simulation on the loading process;

[0040] 3. The method of the present invention can quickly generate a large amount of material stress-strain data under various loading paths, meeting the requirements of data-driven calculation methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Other features, objects, and advantages of the present invention will become more apparent by reading the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0042] Figure 1 is a flow chart of the steps of the data-driven experimental stress identification method for materials without a constitutive model of the present invention;

[0043] Figure 2 is a schematic diagram of the displacement field of an open-hole plate structure generated by the finite element method;

[0044] Figure 3 is a schematic diagram of the stress field of an open-hole plate structure identified by the method of the present invention;

[0045] Figure 4 is a schematic diagram of the stress field of an open-hole plate structure obtained by the finite element method. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0046] The present invention will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that those of ordinary skill in the art can make several changes and improvements without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0047] Example 1:

[0048] As Figure 1 shown, this embodiment provides a data-driven experimental stress identification method for materials without a constitutive model, including the following steps:

[0049] Step 1: Obtain the displacement field of the specimen measurement area and the load boundary conditions through DIC; obtain the displacement field distribution of the specimen measurement area at different moments during the loading process through DIC, and at the same time record the load boundary conditions at the corresponding moments through a tensile testing machine.

[0050] Step 2: Calculate the strain field according to the displacement field; the calculation formula of the element strain field ε e is as follows:

[0051]

[0052] In the formula, u j is the nodal displacement of all nodes in the measurement area, f j obtains the nodal force of all nodes through the load boundary conditions of the tensile testing machine, Bej is the strain differential matrix of element e at node j.

[0053] Step 3: Divide the clusters according to the strain field and establish the initial mapping between elements and data points; based on the element strain field, divide the elements in the specimen measurement area into clusters by the K-means clustering algorithm, and establish the initial mapping relationship between elements and data points.

[0054] Step 4: Define the energy deviation optimization objective function and the node balance constraint conditions; take the minimum energy deviation between the element and the mapped data point as the optimization objective, and take the balance equation of the node as the constraint condition, and transform the stress identification problem into an optimization problem of the objective function under the constraint conditions.

[0055] Step 5: Establish a linear equation system by the Lagrange multiplier method; use the Lagrange multiplier method to solve the optimization problem of the objective function under the constraint conditions, and obtain a linear equation system about the strain data points, stress data points, element stresses, and node Lagrange multipliers by finding the extreme points of the Lagrange function.

[0056] Step 6: Solve the linear equation system according to the mapping relationship and update the data points and element stresses; according to the mapping relationship between the element and the data point, solve the linear equation system and update the strain data points, stress data points, element stresses, and node Lagrange multipliers.

[0057] Step 7: Update the mapping relationship according to the stress-strain states of the element and the data point; according to the stress-strain states of the element and the data point, update the mapping relationship between the element and the data point, and remap the element to the data point with the minimum energy deviation.

[0058] Step 8: Determine whether the mapping relationship has converged. If so, proceed to Step 9; if not, return to Step 6; repeat Steps 6-7 until the mapping relationship between the element and the data point no longer changes, and obtain the final strain data points, stress data points, and element stresses.

[0059] Step 9: Output the stress-strain data points and element stresses.

[0060] Example 2:

[0061] This embodiment provides a data-driven experimental stress identification system for materials without a constitutive model, including the following modules:

[0062] Module M1: Obtain the displacement field and load boundary conditions of the specimen measurement area through DIC;

[0063] Module M2: Calculate the strain field according to the displacement field;

[0064] Module M3: Divide the clusters according to the strain field and establish the initial mapping between elements and data points;

[0065] Module M4: Define the energy deviation optimization objective function and the node balance constraint conditions;

[0066] Module M5: Establish a linear equation system by the Lagrange multiplier method;

[0067] Module M6: Solve the linear equation system according to the mapping relationship, and update the data points and element stresses;

[0068] Module M7: Update the mapping relationship according to the stress and strain states of the elements and data points;

[0069] Module M8: Determine whether the mapping relationship has converged. If so, proceed to Module M9. If not, return to Module M6;

[0070] Module M9: Output the stress and strain data points and element stresses.

[0071] Example 3:

[0072] Those skilled in the art can understand this embodiment as a more specific illustration of Embodiment 1 and Embodiment 2.

[0073] This embodiment provides a data-driven experimental stress identification method for materials without a constitutive model, mainly including the following steps:

[0074] Step 1: Obtain the displacement field and load boundary conditions of the test area through DIC, and establish the initial mapping from elements to data points;

[0075] Step 2: Define the energy deviation objective function and the node balance constraint conditions, and minimize the objective function under the constraint conditions by the Lagrange multiplier method to establish a linear equation system;

[0076] Step 3: Solve the equation system according to the mapping relationship between elements and data points, update the mapping relationship according to the stress and strain states of elements and data points, and make the mapping relationship converge through iteration to obtain the final stress and strain data points and element stresses.

[0077] The method of this embodiment can directly obtain the stress field of the measurement area through the displacement field and load boundary conditions, without the need for a priori material constitutive model. At the same time, a large number of material stress and strain data points can be generated under simple experimental conditions to meet the requirements of data-driven algorithms.

[0078] Example 4:

[0079] Those skilled in the art can understand this embodiment as a more specific illustration of Embodiment 1 and Embodiment 2.

[0080] This embodiment provides a data-driven stress identification method. By using the displacement field measured by DIC and the load boundary conditions during the loading process, the stress field in the measurement area can be quickly identified, and a large amount of material stress-strain data can be generated to meet the requirements of data-driven calculation methods.

[0081] The method of this embodiment is implemented through the following technical solutions:

[0082] Step 1: Obtain the displacement field distribution of the specimen measurement area at different moments during the loading process through DIC, and simultaneously record the load boundary conditions at the corresponding moments through a tensile testing machine;

[0083] Step 2: Obtain the element strain field distribution based on the displacement field distribution;

[0084] Step 3: Based on the element strain field, divide the elements in the measurement area into clusters through the K-means clustering algorithm, and establish the initial mapping relationship between the elements and the data points;

[0085] Step 4: Take the minimum energy deviation between the element and the mapped data point as the optimization objective, and take the equilibrium equation of the node as the constraint condition, and convert the stress identification problem into an optimization problem of the objective function under the constraint condition;

[0086] Step 5: Use the Lagrange multiplier method to solve the optimization problem of the objective function under the constraint condition. By finding the extreme points of the Lagrangian function, obtain a linear equation system about the strain data points, stress data points, element stresses, and node Lagrange multipliers;

[0087] Step 6: According to the mapping relationship between the element and the data point, solve the above linear equation system, and update the strain data points, stress data points, element stresses, and node Lagrange multipliers;

[0088] Step 7: According to the stress-strain states of the element and the data point, update the mapping relationship between the element and the data point, and remap the element to the data point with the minimum energy deviation;

[0089] Step 8: Repeat Steps 6 to 7 until the mapping relationship between the element and the data point no longer changes, and obtain the final strain data points, stress data points, and element stresses.

[0090] Example 5:

[0091] Those skilled in the art can understand this embodiment as a more specific description of Embodiment 1 and Embodiment 2.

[0092] As Figure 1 shown, this embodiment provides a data-driven stress identification method, which mainly includes the following steps:

[0093] Step 1: Obtain the nodal displacement u of all nodes within the measurement area through DIC j , and obtain the nodal force f of all nodes through the load boundary conditions of the tensile testing machine j .

[0094] Step 2: Calculate the element strain field ε according to the nodal displacement field u j : e where B

[0095]

[0096] is the strain differential matrix of element e at node j ej .

[0097] Step 3: Based on the element strain field ε e , use the K-means clustering algorithm to divide the initial clusters for the elements in the measurement area. Each cluster corresponds to a data point, and establish the initial mapping between the elements and the data set:

[0098] s(e) = i(2)

[0099] where e represents the e-th element in the measurement area, i represents the i-th data point in the data set, and s represents the mapping relationship from the element to the data point

[0100] Step 4: Regard the stress identification problem as an optimization problem under constraints. The optimization goal is to make the strain-stress state (ε e , σ e ) of the element closest to the strain-stress state of the mapped data point ;

[0101] Define the objective function as the energy deviation between the element and the mapped data point. The objective function E can be expressed in the following form:

[0102]

[0103] where ω e is the area of the element, C e and are the user-defined stiffness matrix and flexibility matrix respectively;

[0104] The constraint condition is the equilibrium equation of the nodes:

[0105]

[0106] Step 5: Solve the optimization problem under the above constraints by the Lagrange multiplier method to establish a linear equation system

[0107] The Lagrangian function containing the constraint conditions can be expressed as:

[0108]

[0109] In the Lagrangian function F, the optimization variables include strain data points stress data points element stress σ e and nodal Lagrange multipliers η j ;

[0110] By finding the minimum point of the Lagrangian function F and setting the partial derivatives of F with respect to each variable to zero, a system of linear equations regarding the strain data points stress data points element stress σ e and nodal Lagrange multipliers η j can be obtained:

[0111]

[0112]

[0113]

[0114]

[0115] Step 6: Solve the above system of linear equations to update the strain data points stress data points element stress σ e and nodal Lagrange multipliers η j ;

[0116] The strain data points can be expressed as:

[0117]

[0118] where N i is the number of elements that satisfy the condition {e|s(e) = i};

[0119] Equations (7) - (9) can be further simplified to:

[0120]

[0121]

[0122] By simultaneously solving Equations (11) and (12), the nodal Lagrange multiplier η j and stress data points

[0123] element stress σ e can be expressed as:

[0124]

[0125] Step 7: According to the unit stress-strain state (ε e , σ e ) and the stress-strain state of the data points Update the mapping relationship s between the unit and the data points to minimize the energy deviation between the unit and the data points, that is:

[0126]

[0127] Step 8: Repeat Steps 6-7 until the mapping relationship s between the unit and the data points no longer changes, and obtain the final unit stress σ e and the material stress-strain data points

[0128] Taking the perforated plate structure as an example, the stress identification method in this embodiment is verified:

[0129] As Figure 2 shown, the displacement field of the perforated plate structure is generated by the finite element method instead of the DIC method. The length of the perforated plate in the x direction is 50 mm, the length in the y direction is 36 mm, the diameter of the central circular hole is 10 mm, all nodes on the left edge are fixed, and a concentrated force of 500 N in the X direction is applied to all nodes on the right edge. The perforated plate is in a plane stress state. The displacement field of the perforated plate generated by the finite element method is as Figure 2 shown.

[0130] Based on the method in this embodiment, relevant programs are written, and using the displacement field of the nodes and the load boundary conditions, the stress identification of the perforated plate structure and the generation process of the stress-strain data points are realized on the MATLAB platform. The distributions of the X-direction stress field S11 and the Y-direction stress field S22 identified by the method of this embodiment are as Figure 3 shown. It can be found that for the X-direction stress field, obvious stress concentration phenomena occur on both sides of the circular hole in the Y direction, while low stress areas appear on both sides in the X direction. For the Y-direction stress field, the average stress level is significantly lower than that of the X-direction stress field, and the high stress areas are concentrated on both sides of the circular hole in the Y direction and near the constraint positions of the left and right edges, which is consistent with the stress distribution characteristics of a general perforated plate under unidirectional tension conditions.

[0131] To further verify the accuracy of the stress identification method, the stress distribution of the perforated plate is simulated by the finite element method under the same constraint conditions. The stress field distribution of the perforated plate obtained by the finite element method is as Figure 4 shown. It can be seen that the distribution characteristics of the stress field identified by the method of this embodiment are consistent with those of the stress field simulated by the finite element method, and the stress levels are also basically the same, which further verifies the accuracy of the stress identification method of this patent.

[0132] The present invention can directly obtain the stress field of the measurement area through the displacement field and load boundary conditions without a prior material constitutive model; at the same time, a large number of material stress-strain data points can be generated under simple experimental conditions to meet the requirements of data-driven algorithms.

[0133] As known to those skilled in the art, in addition to implementing the system and its various devices, modules, and units provided by the present invention in the form of pure computer-readable program code, the method steps can be logically programmed to enable the system and its various devices, modules, and units provided by the present invention to be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers, etc. to achieve the same functions. Therefore, the system and its various devices, modules, and units provided by the present invention can be regarded as a kind of hardware component, and the devices, modules, and units included therein for implementing various functions can also be regarded as the structures within the hardware component; the devices, modules, and units for implementing various functions can also be regarded as either software modules for implementing the method or structures within the hardware component.

[0134] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A data-driven experimental stress identification method for non-constitutive model materials, characterized in that, it includes the following steps: Step 1: Obtain the displacement field and load boundary conditions of the specimen measurement area through DIC; Step 2: Calculate the strain field according to the displacement field; Step 3: Divide clusters based on the strain field and establish the initial mapping between elements and data points; Step 4: Define the energy deviation optimization objective function and the node balance constraint condition; Step 5: Establish a linear equation system by the Lagrange multiplier method; Step 6: Solve the linear equation system according to the mapping relationship and update the data points and element stresses; Step 7: Update the mapping relationship according to the stress-strain states of the elements and data points; Step 8: Determine whether the mapping relationship reaches convergence. If so, proceed to Step 9; if not, return to Step 6; Step 9: Output the stress-strain data points and element stresses; The specific content of Step 4 is: Taking the minimum energy deviation between the element and the mapped data point as the optimization objective and the node balance equation as the constraint condition, convert the stress identification problem into an optimization problem of the objective function under the constraint condition; The specific content of Step 5 is: Use the Lagrange multiplier method to solve the optimization problem of the objective function under the constraint condition, and obtain a linear equation system about the strain data points, stress data points, element stresses and node Lagrange multipliers by finding the extreme points of the Lagrange function.

2. The data-driven experimental stress identification method for non-constitutive model materials according to Claim 1, characterized in that, the specific content of Step 1 is: Obtain the displacement field distribution of the specimen measurement area at different moments during the loading process through DIC, and record the load boundary conditions at the corresponding moments through a tensile testing machine.

3. The data-driven experimental stress identification method for non-constitutive model materials according to Claim 2, characterized in that, In the said step 2, the unit strain field ε e has the following calculation formula: where u j is the nodal displacement of all nodes in the measurement area, and B ej is the strain differential matrix of element e at node j.

4. The data-driven experimental stress identification method for non-constitutive model materials according to Claim 3, characterized in that, the specific content of Step 3 is: Based on the element strain field, divide the clusters of the elements in the specimen measurement area through the K-means clustering algorithm and establish the initial mapping relationship between the elements and data points.

5. The data-driven experimental stress identification method for non-constitutive model materials according to Claim 1, characterized in that, the specific content of Step 6 is: Solve the linear equation system according to the mapping relationship between the element and the data point, and update the strain data point, stress data point, element stress and node Lagrange multiplier.

6. The data-driven experimental stress identification method for non-constitutive model materials according to Claim 5, characterized in that, the specific content of Step 7 is: Update the mapping relationship between the element and the data point according to the stress-strain states of the element and the data point, and remap the element to the data point with the minimum energy deviation.

7. The data-driven experimental stress identification method for non-constitutive model materials according to Claim 6, characterized in that, the specific content of Step 8 is: Repeat Steps 6 - 7 until the mapping relationship between the element and the data point no longer changes, and obtain the final strain data points, stress data points and element stresses.

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