A data-driven modeling method for thermoplastic polyester materials

Abstract

This invention discloses a data-driven modeling method for thermoplastic polyester materials, comprising: preparing standard uniaxial tensile and compression specimens using thermoplastic polyester materials, conducting physical experiments to obtain tensile and compression experimental data; processing the tensile and compression experimental data separately to obtain data sequences under tensile and compression states; determining whether the material point is in a tensile-dominant or compression-dominant state to determine the current strain state of the material point; selecting the data sequence under tensile or compression states based on the current strain state of the material point; retrieving the target equivalent stress and target spherical stress from the selected data sequence; and updating the stress of the thermoplastic polyester material based on the current strain state, target equivalent stress, and target spherical stress. This invention solves the problem that existing methods cannot directly drive simulation based on physical experimental data to achieve accurate characterization of the mechanical behavior of thermoplastic polyester materials throughout all stages.

Description

Technical Field

[0001] This invention relates to data-driven computing technology, specifically to a data-driven modeling method for thermoplastic polyester materials. Background Technology

[0002] In modern engineering, thermoplastic polyester materials, such as polyethylene terephthalate (PET) and polybutylene terephthalate (PBT), are widely used in manufacturing fields with high requirements for lightweight materials, fatigue resistance, and structural reliability, such as automotive parts, electronic and electrical structural components, high-performance packaging, and biomedical equipment, due to their significant nonlinear mechanical response differences under tensile and compressive loads (i.e., tension-compression asymmetry).

[0003] The most significant tensile-compressive asymmetry of thermoplastic polyester materials (taking PET as an example) is manifested in the fact that their stress-strain curves exhibit significant nonlinear response differences from the initial loading stage. That is, under tensile and compressive loads, the initial tangential modulus and yield behavior show different evolution paths from the outset, rather than an ideal linear relationship. To accurately characterize the mechanical properties of this type of material, its basic model often employs theories that can distinguish between tensile and compressive responses: in the elastic stage, a bimodulus theory is typically introduced, defining the tensile elastic modulus E separately. + With compressive elastic modulus E − Characteristic parameters; in the plastic stage, different initial yield stress thresholds under tensile and compressive loads, as well as significantly different subsequent hardening evolution laws, need to be considered simultaneously. However, the limitations of existing technical solutions directly restrict the accurate application of thermoplastic polyester materials in engineering simulation, specifically in three aspects:

[0004] (1) Traditional constitutive models based on explicit mathematical functions (such as the classical elastoplastic constitutive model) are difficult to fully cover the tensile and compressive asymmetric behavior in the entire elastic-plastic stage. Moreover, the parameter fitting process is cumbersome and highly dependent on the researcher's experience, which cannot meet the needs of rapid engineering of new materials.

[0005] (2) The higher-order constitutive model that partially considers the anisotropic yield surface focuses only on the asymmetric characteristics of the plastic stage and fails to take into account the modulus difference in the elastic stage. In addition, the number of parameters is huge and the calibration process is complicated. It has not yet been deeply integrated and widely promoted in mainstream commercial engineering simulation software, which greatly reduces its engineering practicality.

[0006] (3) The model-free data-driven calculation method developed in recent years has avoided the explicit constitutive equation construction process by directly calling stress-strain experimental data. However, the existing mainstream frameworks either have poor compatibility with the displacement-driven finite element solution format widely used in the engineering field, or have not systematically solved the problem of convenient integration and collaborative driving of experimental data under tension and compression load paths. In particular, in the process of compressing experimental data, there is a lack of effective data homogenization preprocessing methods, which makes it difficult to ensure the stability of data quality and calculation accuracy.

[0007] The aforementioned technical limitations prevent existing methods from directly driving simulations based on physical experimental data, thus hindering the accurate characterization of the mechanical behavior of thermoplastic polyester materials across all stages. This becomes a key bottleneck restricting the large-scale application of such new materials in the rapid design and performance prediction of industrial products. Therefore, there is an urgent need in this field for an efficient, accurate, and easily engineering-implementable technical solution to overcome the limitations of existing modeling methods. Summary of the Invention

[0008] Purpose of the invention: The purpose of this invention is to provide a data-driven modeling method for thermoplastic polyester materials, which can solve the problem that existing methods cannot directly drive simulation based on physical experimental data to achieve accurate characterization of the mechanical behavior of thermoplastic polyester materials at all stages.

[0009] Technical solution: The present invention provides a data-driven modeling method for thermoplastic polyester materials, comprising:

[0010] Offline data generation stage: Standard uniaxial tensile and compression specimens were prepared using thermoplastic polyester material. Physical experiments were conducted on the tensile and compression specimens respectively, and load-displacement data were recorded synchronously. Digital image correlation technology was used to acquire full-field displacement information on the surface of the tensile and compression specimens respectively, to obtain tensile and compression experimental data. The tensile experimental data were processed to obtain the data sequence under tensile conditions; the compression experimental data were processed to obtain the data sequence under compression conditions.

[0011] Online data-driven calculation stage: Determine whether the upper, middle, and lower points of the thermoplastic polyester material are in a tensile-dominant or compression-dominant state. Select the data sequence under tensile or compression state based on the current strain state of the three points. Retrieve the target equivalent stress and target spherical stress from the selected data sequence. Update the stress of the thermoplastic polyester material based on the current strain state, target equivalent stress, and target spherical stress.

[0012] Furthermore, the processing of the compressed experimental data to obtain a data sequence under compressed conditions includes:

[0013] The equivalent strain-stress data sequence and spherical strain-stress data sequence under compression were calculated by using the volume average homogenization method on the compression test data.

[0014] Furthermore, the spherical strain-stress data sequence is calculated as follows:

[0015] Radial displacement of the side surface of the compression specimen in the compression test data The spherical radial strain in both the x and y directions is calculated by integrating along the axial direction. , ; axial displacement of the upper end face of the compression specimen in the compression test data Calculate the axial strain of the sphere .

[0016] Furthermore, the radial displacement of the compression specimen side surface in the compression test data... The spherical radial strain in both the x and y directions is calculated by integrating along the axial direction. , ,include:

[0017] The radial strain of the spherical specimen is calculated by measuring the radial displacement at three preset height positions (top, middle, and bottom) on the side surface of the compression specimen and applying Simpson's integral rule. , The specific formula is as follows:

[0018] ;

[0019] in, The radius of the cylindrical specimen; For height; These represent the radial displacements of the upper, middle, and lower points, respectively.

[0020] Furthermore, the spherical axial strain The calculation formula is as follows:

[0021] ;

[0022] in, For height.

[0023] Furthermore, the online data-driven computation phase includes the following steps:

[0024] Based on the sign of the spherical strain component of the current total strain, determine whether the three points are in a tensile-dominant or compressive-dominant state, thereby determining the current strain state of the three points.

[0025] Based on the current strain state at three points, select either the data sequence under tensile or compressive conditions;

[0026] The target equivalent stress is retrieved from the selected data sequence using the equivalent strain of the current elastic test strain as an index; the target spherical stress is retrieved from the selected data sequence using the current spherical strain as an index.

[0027] Based on the target equivalent stress, target spherical stress, and current strain state, and combined with the loading / unloading judgment criteria, the updated stress deviation and spherical stress are determined, and the stress update of the thermoplastic polyester material is completed.

[0028] Furthermore, the process of determining the updated stress deviation and spherical stress based on the target equivalent stress, target spherical stress, and current strain state, combined with loading / unloading criteria, to complete the stress update of the thermoplastic polyester material includes:

[0029] If the current equivalent test stress Greater than or equal to the target equivalent stress If so, it is determined to be a loading condition, and the updated stress bias is determined accordingly. Using formula Calculation, where , If the deviation is the elastic strain, then it is considered unloading. Using the deviator of the test stress .

[0030] Furthermore, the process of determining the updated stress deviation and spherical stress based on the target equivalent stress, target spherical stress, and current strain state, combined with loading / unloading criteria, to complete the stress update of the thermoplastic polyester material includes:

[0031] If the absolute value of the current spherical test stress Greater than or equal to the absolute value of the target spherical stress If so, it is determined to be a loading condition, and the updated spherical stress is determined. Using target spherical stress Otherwise, it is judged as unloading, and the updated spherical stress is determined. Spherical stress test .

[0032] Furthermore, the formula for calculating the spherical test stress is as follows:

[0033] ;

[0034] This represents the spherical stress of the previous time step; For the strain increment at the next time step; Let be the fourth elastic tensor of an isotropic material.

[0035] Furthermore, the fourth-order elastic tensor of the isotropic material Different values ​​are taken under tensile and compressive conditions, and the specific determination method is as follows:

[0036] If spherical strain Then use the stretch tensor. Calculate the stress of the spherical test; if the spherical strain Then use the compressible elastic tensor. Calculate the stress of the spherical test.

[0037] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows: (1) The present invention breaks through the technical bottleneck of complex modeling and difficult parameter fitting of traditional constitutive models when describing the tensile and compressive asymmetry of thermoplastic polyester materials by directly driving simulation with experimental data; (2) The method adopts a dual-path data collaborative driving mechanism of tension and compression, combined with compression data processing technology based on volume average homogenization, to realize the complete characterization of the tensile and compressive asymmetric response of the material from elastic to plastic process; (3) The proposed stress update algorithm is naturally compatible with the displacement-driven finite element solution format, which significantly improves the simulation efficiency while ensuring the same calculation accuracy as commercial software, and provides an efficient and practical solution for the rapid and accurate engineering simulation of thermoplastic polyester materials. Attached Figure Description

[0038] Figure 1 This is a schematic diagram of the process of the present invention;

[0039] Figure 2 This is a schematic diagram of a standard dog bone-shaped specimen used for uniaxial tension in this invention.

[0040] Figure 3 This is a schematic diagram of a cylindrical specimen used for uniaxial compression in this invention;

[0041] Figure 4 This is a graph of the dataset generated from the uniaxial tensile-compression experiment of PET material used in online calculations in this invention;

[0042] Figure 5 This is a schematic diagram of a specimen under uniaxial tension with a central hole in an embodiment of the present invention.

[0043] Figure 6 This is a comparison chart of the calculation time for a centrally pored specimen using the method of this invention and commercial finite element software.

[0044] Figure 7 This is a topological diagram of the beam structure in an embodiment of the present invention;

[0045] Figure 8 This is a comparison chart showing the calculation time of the beam structure model using the method of this invention and commercial finite element software. Detailed Implementation

[0046] The technical solution of the present invention will now be described in detail with reference to specific embodiments and accompanying drawings.

[0047] like Figure 1 As shown, a data-driven modeling method for thermoplastic polyester materials according to the present invention includes the following steps:

[0048] S1. Offline Data Generation Stage: Standard uniaxial tensile and compression specimens are prepared using thermoplastic polyester material. Physical experiments are performed on the tensile and compression specimens respectively, and load-displacement data are recorded synchronously. Digital image correlation technology is used to acquire the full-field displacement information of the surface of the tensile and compression specimens respectively to obtain tensile test data and compression test data. The tensile test data is processed to obtain the data sequence under tensile conditions; the compression test data is processed to obtain the data sequence under compression conditions.

[0049] The specific implementation process of step S1 is as follows:

[0050] S1.1 Standard uniaxial tensile and compression specimens were prepared using thermoplastic polyester material.

[0051] Standard dog-bone shaped tensile specimens (T1, T2) and cylindrical compression specimens (C1, C2) were cut from the same PET sheet along different directions (0° and 90°), as follows: Figure 2 and Figure 3 As shown. Quasi-static uniaxial tensile and compression tests were performed on a universal testing machine.

[0052] S1.2. Physical experiments were conducted on the tensile and compression specimens respectively, and load-displacement data were recorded synchronously. Digital image correlation technology was used to collect the full-field displacement information of the surface of the tensile and compression specimens respectively, so as to obtain tensile test data and compression test data.

[0053] During the experiment, a digital image correlation system was used to synchronously acquire full-field displacement information of the sample surface to obtain tensile and compression test data.

[0054] S1.3 Process the tensile test data to obtain the data sequence under tensile conditions.

[0055] In this embodiment, the tensile test data are processed to calculate the equivalent strain-stress data sequence under tensile conditions ([ , ]) and spherical strain-stress data sequences ([ , The specific calculation method is as follows: For the tensile test, a uniform deformation zone in the middle of the dog bone specimen is selected. The displacement is calculated based on the value measured by the universal testing machine. and gauge length From the formula Calculate the three principal tensile strain components , , (in = Calculate the axial stress based on the axial force F recorded by the universal testing machine and the initial cross-sectional area A of the specimen. = F / A, and the remaining principal stresses are 0. For each load step, according to the definition:

[0056]

[0057]

[0058]

[0059]

[0060] Calculate equivalent strain Equivalent stress spherical strain and spherical stress This ultimately forms a data sequence under stretched conditions. ], [ ])and([ ], [ ]),like Figure 4 The curve is indicated by the "+" symbol. Figure 4 (a) is the equivalent strain-equivalent stress curve. Figure 4 (b) shows the spherical strain-spherical stress curves, where "+" and "-" indicate the data sequences under tensile and compressive conditions, respectively. These two sets of data sequences construct a "material database" for the material under different tensile and compressive load paths. By distinguishing between tensile and compressive dominant states, the corresponding stress values ​​are retrieved, providing accurate data support for subsequent updates of stress skewness and spherical stress.

[0061] S1.4 Process the compression experiment data to obtain the data sequence under compressed conditions.

[0062] In step S1.4, for compression test data, cylindrical compression specimens exhibit lateral bulging and uneven deformation. Therefore, the equivalent strain-stress data sequence under compression is calculated using the volume-averaged homogenization method of this invention. , ]) and spherical strain-stress data sequences ([ , The calculation method is as follows:

[0063] S1.4.1 Select three points on one side of the cylindrical surface: z = H, H / 2, and 0. Obtain the three heights (z = H, H / 2, and 0) of the side of the cylindrical compression specimen using DIC. H / 2 radial displacement of 0) and the axial displacement of the upper end face. .

[0064] S1.4.2 Calculate the radial strain of the sphere using Simpson's integral formula, as follows:

[0065] Radial displacement of the side surface of the compression specimen in the compression test data The spherical radial strain in both the x and y directions is calculated by integrating along the axial direction. , Cylindrical specimens exhibit the same radial displacement under compression, therefore... and The values ​​are the same, as detailed below:

[0066] The radial strain of the spherical specimen is calculated by measuring the radial displacement at three preset height positions (top, middle, and bottom) on the side surface of the compression specimen and applying Simpson's integral rule. , The specific formula is as follows:

[0067] ;

[0068] in, The radius of the cylindrical specimen; For height; These represent the radial displacements of the upper, middle, and lower points, respectively.

[0069] S1.4.3, Axial displacement of the upper end face of the compression specimen in the compression test data. Calculate the axial strain of the sphere The calculation formula is as follows:

[0070] ;

[0071] in, For height.

[0072] S1.4.4, will Recorded as Based on axial pressure and initial cross-sectional area calculate .

[0073] S1.4.5. For each load step, calculate the equivalent and spherical stress-strain to form the equivalent strain-stress data sequence under compression. ], [ ]) and spherical strain-stress data sequences ([ ], [ ]),like Figure 4 The curve is indicated by the "-" symbol.

[0074] Determination of elastic parameters: By fitting the initial linear segment of tensile and compressive experimental data, the elastic constants of the material are obtained: tensile Young's modulus. =100 GPa, Poisson's ratio =0.35; Young's modulus of compression =100.2 GPa, Poisson's ratio =0.35. Based on this, construct the elastic tensor. and .

[0075] S2. Online data-driven calculation stage: Determine whether the upper, middle, and lower points of the thermoplastic polyester material are in a tensile-dominant or compression-dominant state. Select the data sequence under tensile or compression state based on the current strain state of the three points. Retrieve the target equivalent stress and target spherical stress from the selected data sequence. Update the stress of the thermoplastic polyester material based on the current strain state, target equivalent stress, and target spherical stress.

[0076] In the data-driven approach, stress-strain data is generated offline to drive online calculations. The specific implementation process of step S2 is as follows:

[0077] S2.1, Based on the current total strain spherical strain components The sign of the value determines whether the three points are in a tensile-dominant or compression-dominant state, thereby determining the current strain state of the three points.

[0078] S2.2 Based on the current strain state at three points, select either the data sequence under tensile or compressive conditions;

[0079] S2.3, Equivalent strain of the current elastic test strain The target equivalent stress is retrieved from the selected data sequence using an index. ; with current spherical strain The target spherical stress is retrieved from the selected data sequence using an index. ;

[0080] S2.4, Based on target equivalent stress Target spherical stress Based on the current strain state and the loading / unloading criteria, the updated stress deviator is determined. and spherical stress This involves completing stress updates for the thermoplastic polyester material. Specifically:

[0081] (1) Determining the bias: If the current equivalent test stress Greater than or equal to the target equivalent stress If so, it is determined to be a loading condition, and the updated stress bias is determined accordingly. Using formula Calculation, where , If the deviation is the elastic strain, then it is considered unloading. Using the deviator of the test stress .

[0082] (2) Judgment of spherical stress: If the absolute value of the current spherical test stress is... Greater than or equal to the absolute value of the target spherical stress If so, it is determined to be a loading condition, and the updated spherical stress is determined. Using target spherical stress Otherwise, it is judged as unloading, and the updated spherical stress is determined. Spherical stress test .

[0083] Among them, spherical stress test It can be calculated as:

[0084]

[0085] The spherical stress of the previous time step, For the strain increment of the next time step, It is the fourth elastic tensor of isotropic materials, taking different values ​​under tensile and compressive conditions. The specific choices are as follows:

[0086] If spherical strain Then use the stretch tensor. Calculate the stress of the spherical test; if the spherical strain Then use the compressible elastic tensor. Calculate the stress in the spherical test. Where the tensile elastic tensor is... With compressive elastic tension The elastic constants are determined by fitting the initial linear phase of the tensile and compression experiments in step S1.

[0087] In this embodiment, the stress update of the thermoplastic polyester material is completed according to the following formula:

[0088] ;

[0089] To integrate this data-driven constitutive model into the finite element solution framework, a consistent tangent stiffness matrix for material points needs to be derived and provided. This matrix represents the linearized response of stress increments to strain increments and is a necessary component of the global stiffness matrix assembly. The following is the tangent stiffness matrix for stress updates:

[0090]

[0091]

[0092] in,

[0093]

[0094] Online data-driven calculation and verification: The generated data sequence is integrated into the finite element program to implement an online stress update algorithm.

[0095] (1) Calculation verification of single-hole structure: Tensile test was performed on a plate-shaped specimen with a central hole, as follows: Figure 5 As shown, the simulation is performed using the data-driven method of this invention. Figure 6 As shown, the simulated force-displacement curve (UMAT) is in high agreement with the calculation results of commercial finite element software, with calculation times of 5s and 4s respectively, which confirms that the method of the present invention has high reliability and computational efficiency.

[0096] (2) Beam structure calculation verification: The cantilever beam structure is topologically modified, such as... Figure 7 As shown, a downward displacement is applied at the top. Figure 8 As shown, the results of the data-driven method proposed in this invention are compared with those calculated by Abaqus. Even for this type of topology, the proposed method can still make accurate predictions.

[0097] This invention bypasses the traditional elastoplastic model's reliance on explicit mathematical functions for construction and parameter fitting. Instead, it directly drives the stress-strain calculation process in numerical simulation by collecting full stress-strain data from uniaxial tensile and compressive physical experiments, achieving accurate prediction of the material's mechanical response. Example calculations show that the force-displacement curves simulated using this method highly match the calculation results from the finite element software Abaqus, and the method exhibits superior computational efficiency while maintaining equivalent accuracy. This method is applicable to thermoplastic polyester materials with tensile-compressive asymmetric properties within a small deformation range. It provides an efficient and practical technical solution for rapidly constructing high-precision material models based on physical experimental data, and has significant application value in mechanical property analysis and numerical simulation modeling.

Claims

1. A data-driven modeling method for thermoplastic polyester materials, characterized in that, include: Offline data generation stage: Standard uniaxial tensile and compression specimens were prepared using thermoplastic polyester material. Physical experiments were conducted on the tensile and compression specimens respectively, and load-displacement data were recorded synchronously. Digital image correlation technology was used to acquire full-field displacement information on the surface of the tensile and compression specimens respectively, to obtain tensile and compression experimental data. The tensile experimental data were processed to obtain the data sequence under tensile conditions; the compression experimental data were processed to obtain the data sequence under compression conditions. Online data-driven calculation stage: Determine whether the upper, middle, and lower points of the thermoplastic polyester material are in a tensile-dominant or compression-dominant state. Select the data sequence under tensile or compression state based on the current strain state of the three points. Retrieve the target equivalent stress and target spherical stress from the selected data sequence. Update the stress of the thermoplastic polyester material based on the current strain state, target equivalent stress, and target spherical stress.

2. The data-driven modeling method for thermoplastic polyester materials according to claim 1, characterized in that, The process of processing the compression experiment data to obtain a data sequence under compressed conditions includes: The equivalent strain-stress data sequence and spherical strain-stress data sequence under compression were calculated by using the volume average homogenization method on the compression test data.

3. The data-driven modeling method for thermoplastic polyester materials according to claim 2, characterized in that, The spherical strain-stress data sequence is calculated as follows: Radial displacement of the side surface of the compression specimen in the compression test data The spherical radial strain in both the x and y directions is calculated by integrating along the axial direction. , ; axial displacement of the upper end face of the compression specimen in the compression test data Calculate the axial strain of the sphere .

4. The data-driven modeling method for thermoplastic polyester materials according to claim 3, characterized in that, The radial displacement of the side surface of the compressed specimen in the compression test data The spherical radial strain in both the x and y directions is calculated by integrating along the axial direction. , ,include: The radial strain of the spherical specimen is calculated by measuring the radial displacement at three preset height positions (top, middle, and bottom) on the side surface of the compression specimen and applying Simpson's integral rule. , The specific formula is as follows: ； in, The radius of the cylindrical specimen; For height; These represent the radial displacements of the upper, middle, and lower points, respectively.

5. The data-driven modeling method for thermoplastic polyester materials according to claim 3, characterized in that, The spherical axial strain The calculation formula is as follows: ； in, For height.

6. The data-driven modeling method for thermoplastic polyester materials according to claim 1, characterized in that, The online data-driven computation phase includes the following steps: Based on the sign of the spherical strain component of the current total strain, determine whether the three points are in a tensile-dominant or compressive-dominant state, thereby determining the current strain state of the three points. Based on the current strain state at three points, select either the data sequence under tensile or compressive conditions; The target equivalent stress is retrieved from the selected data sequence using the equivalent strain of the current elastic test strain as an index; the target spherical stress is retrieved from the selected data sequence using the current spherical strain as an index. Based on the target equivalent stress, target spherical stress, and current strain state, and combined with the loading / unloading judgment criteria, the updated stress deviation and spherical stress are determined, and the stress update of the thermoplastic polyester material is completed.

7. The data-driven modeling method for thermoplastic polyester materials according to claim 6, characterized in that: The process involves determining the updated stress deviation and spherical stress based on the target equivalent stress, target spherical stress, and current strain state, combined with loading / unloading criteria, to complete the stress update of the thermoplastic polyester material. This includes: If the current equivalent test stress Greater than or equal to the target equivalent stress If so, it is determined to be a loading condition, and the updated stress bias is determined accordingly. Using formula Calculation, where , If the deviation is the elastic strain, then it is considered unloading. Using the deviator of the test stress .

8. The data-driven modeling method for thermoplastic polyester materials according to claim 6, characterized in that: The process involves determining the updated stress deviation and spherical stress based on the target equivalent stress, target spherical stress, and current strain state, combined with loading / unloading criteria, to complete the stress update of the thermoplastic polyester material. This includes: If the absolute value of the current spherical test stress Greater than or equal to the absolute value of the target spherical stress If so, it is determined to be a loading condition, and the updated spherical stress is determined. Using target spherical stress Otherwise, it is judged as unloading, and the updated spherical stress is determined. Spherical stress test .

9. The data-driven modeling method for thermoplastic polyester materials according to claim 8, characterized in that, The formula for calculating the spherical test stress is as follows: ； This represents the spherical stress of the previous time step; For the strain increment at the next time step; Let be the fourth elastic tensor of an isotropic material.

10. The data-driven modeling method for thermoplastic polyester materials according to claim 9, characterized in that: The fourth elastic tensor of the isotropic material Different values ​​are taken under tensile and compressive conditions, and the specific determination method is as follows: If spherical strain Then use the stretch tensor. Calculate the stress of the spherical test; if the spherical strain Then use the compressible elastic tensor. Calculate the stress of the spherical test.

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