A modeling method and system of a hyperelastic model simulating two-dimensional woven fabric wrinkles

Abstract

The application belongs to the technical field of mechanical simulation and prediction of woven fabrics, and specifically discloses a modeling method and system of a super-elastic model for simulating wrinkles of two-dimensional woven fabrics. The method comprises: establishing a super-elastic model that comprehensively considers the mechanical behavior of two-dimensional woven fabrics, wherein the two-dimensional woven fabrics are composed of warp yarns and weft yarns that are interlaced with each other; determining a numerical implementation method of the super-elastic model in a finite element framework, wherein the numerical implementation method is realized through a subroutine interface; and simulating the wrinkles defects generated in the deformation process of the two-dimensional woven fabrics by using the finite element framework and the numerical implementation method of the super-elastic model. The super-elastic model is established by defining the strain invariants of tensile deformation, shear deformation and bending deformation of the two-dimensional woven fabrics, obtaining the corresponding strain energy function based on the strain invariants, and calculating the membrane stress and bending moment. The application can accurately simulate the wrinkles defects generated in the deformation process of the two-dimensional woven fabrics.

Description

Technical Field

[0001] This application belongs to the field of mechanical simulation and prediction technology of woven fabrics, and more specifically, relates to a modeling method and system for simulating the hyperelasticity model of two-dimensional woven fabric folds. Background Technology

[0002] Two-dimensional woven fabrics are fabrics woven from alternating warp and weft yarns, requiring no additional stitching and suitable for fibers with high bending stiffness. Due to their high specific strength and high specific stiffness, two-dimensional woven fabrics can meet the directional mechanical property requirements of composite materials under different service environments and have been widely used as reinforcements in fiber-reinforced composites. Liquid forming is one of the most widely used processes for manufacturing fiber-reinforced composites. During the preforming process of liquid forming, the woven fabric undergoes significant deformation and may even develop defects. Therefore, it is necessary to develop stable numerical simulation methods to simulate the deformation and defects of woven fabrics.

[0003] Wrinkling is the most significant defect in the deformation process of woven fabrics. The formation of wrinkles depends on the material properties of the woven fabric, including its tensile, shear, and bending behaviors. However, the material properties of woven fabrics differ from those of traditional continuous materials such as rubber and metals. Traditional continuous materials follow Kirchhoff's theory, where membrane stiffness and bending stiffness are coupled, and the bending stiffness can be directly calculated from the membrane stiffness. However, woven fabrics do not follow Kirchhoff's theory, and their bending stiffness is much lower than the value calculated based on membrane stiffness. Therefore, in modeling the deformation of woven fabrics, membrane behavior and bending behavior should be decoupled.

[0004] Numerous numerical models have been developed to simulate wrinkling defects in woven fabrics, such as the stress-synthesized shell method and the hybrid element method. The stress-synthesized shell method introduces the microscopic properties of woven fabrics into macroscopic-scale analysis. These models assume that each element contains a specified number of woven fabric unit cells, calculates strain energy based on unit cell deformation modes, and derives element nodal loads. Such methods are typically very complex and difficult to implement in a general finite element framework. The hybrid element method uses two types of elements to model the mechanical behavior of woven fabrics: one element (membrane element) to model the membrane behavior, and another element (beam / shell element) to model the bending behavior. The hybrid element method still follows Kirchhoff's theory and still overestimates the bending stiffness of woven fabrics.

[0005] Overall, current methods for simulating woven fabric wrinkles are still unable to accurately assess the mechanical behavior of woven fabrics or accurately simulate wrinkle defects in woven fabrics. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this application is to provide a modeling method and system for simulating the hyperelastic model of two-dimensional woven fabric wrinkles, aiming to solve the problem that current methods for simulating woven fabric wrinkles still cannot accurately evaluate the mechanical behavior of woven fabrics and cannot accurately simulate the wrinkle defects of woven fabrics.

[0007] To achieve the above objectives, in a first aspect, this application provides a modeling method for simulating the hyperelasticity of two-dimensional woven fabric wrinkles, comprising:

[0008] A hyperelastic model is established that comprehensively considers the mechanical behavior of two-dimensional woven fabrics, which are composed of warp and weft yarns interwoven together.

[0009] A numerical implementation method for the hyperelastic model in a finite element framework is determined, and the numerical implementation method is implemented through a subroutine interface.

[0010] The hyperelastic model is simulated using the numerical implementation method and the finite element framework to simulate the wrinkle defects generated during the deformation of two-dimensional woven fabrics.

[0011] The hyperelastic model is established by defining strain invariants for tensile, shear, and bending deformation of a two-dimensional woven fabric, obtaining the corresponding strain energy function based on the strain invariants, and calculating the membrane stress and bending moment based on the strain energy function.

[0012] Optionally, the modeling method for the two-dimensional woven fabric hyperelasticity model specifically includes:

[0013] Determine the strain invariant for each deformation mode, which includes tensile deformation, shear deformation, and bending deformation;

[0014] The total strain energy of the two-dimensional woven fabric is determined, and the total strain energy is decoupled to obtain the tensile deformation strain energy, shear deformation strain energy, and bending deformation strain energy.

[0015] Determine the membrane strain energy function corresponding to the membrane strain energy, calculate the membrane stress based on the membrane strain energy function combined with the determinant of the deformation gradient tensor and the transpose of the deformation gradient tensor, and calculate the bending moment based on the bending deformation strain energy and the bending strain invariant.

[0016] The hyperelastic model is established based on the decoupling results of the strain invariants, the total strain energy, and the calculation results of the membrane strain energy function.

[0017] Optionally, the method for obtaining the strain invariant of the deformation mode includes:

[0018] Determine the curvature tensor to describe the curvature and torsion of material particles in the current configuration;

[0019] The deformation gradient tensor is determined based on the relationship between the current position of the material particles and their initial configuration position, and the right Cauchy Green strain tensor is determined based on the deformation gradient tensor.

[0020] Obtain the initial unit vectors of the warp and weft directions in the initial configuration, and the current unit vectors of the warp and weft directions in the current configuration;

[0021] Based on the initial unit vector, the initial unit vector, and the right Cauchy Green strain tensor, determine the tensile strain invariants corresponding to the tensile deformation of the warp and weft yarns;

[0022] Based on the initial unit vector, the right Cauchy Green strain tensor, and the tensile strain invariant, the shear strain invariant corresponding to the warp and weft shear deformation is determined.

[0023] Based on the initial unit vector, the initial unit vector, and the curvature tensor, the tensile strain invariants corresponding to the tensile deformation of the warp and weft yarns are determined.

[0024] Optionally, the total strain energy is decoupled to obtain tensile strain energy, shear strain energy, and bending strain energy, including:

[0025] The total strain energy is decoupled and decomposed into membrane deformation strain energy and bending deformation strain energy;

[0026] The membrane deformation strain energy is decomposed into tensile deformation strain energy and shear deformation strain energy;

[0027] The bending deformation strain energy is decomposed into the warp bending deformation strain energy corresponding to the warp bending deformation and the weft bending deformation strain energy corresponding to the warp bending deformation.

[0028] Optionally, the membrane strain energy function corresponding to the determined membrane strain energy is determined based on the membrane deformation strain energy and the right Cauchy-Green strain tensor.

[0029] Optionally, the numerical implementation process includes a membrane deformation calculation process and a bending deformation calculation process, wherein the membrane deformation calculation process includes:

[0030] Read the deformation gradient tensor from the subroutine interface of the finite element framework, calculate the right Cauchy Green strain tensor, define the unit vectors of the warp and weft directions in the initial configuration, as well as the membrane strain invariant, and calculate the strain energy of the membrane deformation.

[0031] The membrane stress is calculated based on the membrane strain energy, and the membrane stress is returned to the main program of the finite element framework.

[0032] Optionally, the bending deformation calculation process includes:

[0033] Read the curvature tensor from the subroutine interface of the finite element framework, define the bending strain invariant, and calculate the bending deformation strain energy.

[0034] The bending moment is calculated based on the bending deformation strain energy, and the bending moment is returned to the main program of the finite element frame.

[0035] Secondly, this application provides a modeling system for simulating a hyperelastic model of two-dimensional woven fabric wrinkles, comprising:

[0036] The model building module establishes a hyperelastic model that comprehensively considers the mechanical behavior of two-dimensional woven fabrics, which are composed of warp and weft yarns interwoven together.

[0037] The numerical implementation module is used to determine the numerical implementation method of the hyperelastic model in the finite element framework, and the numerical implementation method is implemented through a subroutine interface.

[0038] The wrinkle simulation module is used to simulate the wrinkle defects generated by the two-dimensional woven fabric during deformation using the numerical implementation method and the finite element framework of the hyperelastic model.

[0039] The hyperelastic model is established by defining strain invariants for tensile, shear, and bending deformation of a two-dimensional woven fabric, obtaining the corresponding strain energy function based on the strain invariants, and calculating the membrane stress and bending moment based on the strain energy function.

[0040] Thirdly, this application provides an electronic device, comprising: at least one memory for storing a program; and at least one processor for executing the program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to execute the method described in the first aspect or any possible implementation thereof.

[0041] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0042] Fifthly, this application provides a computer program product that, when run on a processor, causes the processor to perform the method described in the first aspect or any possible implementation thereof.

[0043] It is understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0044] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art:

[0045] (1) This application provides a method for establishing a hyperelastic model to simulate wrinkles in two-dimensional woven fabrics. Through energy decoupling, the total strain energy characterizing the deformation of the woven fabric is decomposed into membrane strain energy and bending deformation strain energy. The membrane strain energy is further decomposed into tensile and shear deformation strain energies according to the membrane deformation mode. Membrane stress is calculated based on the membrane strain energy, and bending moment is calculated based on the bending deformation strain energy. The hyperelastic model of this application can comprehensively consider the tensile, shear, and bending material behaviors of two-dimensional woven fabrics, and therefore can accurately simulate wrinkle defects generated during the deformation process of two-dimensional woven fabrics.

[0046] (2) This application provides a numerical implementation method for a hyperelastic model simulating the wrinkles of two-dimensional woven fabrics. This hyperelastic model can be numerically implemented using the VUGENS subroutine interface of the general-purpose finite element program ABAQUS / Explicit. Membrane stress and bending moment are calculated independently during the numerical implementation process, thus accurately characterizing the mechanical behavior of two-dimensional woven fabrics. Furthermore, this model is compatible with any general-purpose finite element framework and can be used for wrinkle prediction of large-scale two-dimensional woven fabrics. Attached Figure Description

[0047] Figure 1 This is a schematic flowchart of the modeling method for simulating the hyperelastic model of two-dimensional woven fabric wrinkles provided in the embodiments of this application;

[0048] Figure 2 This is a flowchart illustrating the process of numerically implementing the two-dimensional woven fabric hyperelastic model constructed in the embodiments of this application through the VUGENS subroutine interface of the general finite element software ABAQUS / Explicit.

[0049] Figure 3 This is a schematic diagram of an off-axis tensile finite element model of a woven fabric constructed according to a preferred embodiment of this application;

[0050] Figure 4 It is a deformation cloud map of the off-axis stretching of the woven fabric predicted by the hyperelastic model constructed according to the preferred embodiment of this application;

[0051] Figure 5 This is a schematic diagram of a finite element model of a cupped woven fabric constructed according to a preferred embodiment of this application;

[0052] Figure 6 It is a deformation cloud map of cupping formation of woven fabric predicted by the hyperelastic model constructed according to the preferred embodiment of this application;

[0053] Figure 7 This is a schematic diagram of the structure of the modeling device for simulating the hyperelastic model of two-dimensional woven fabric wrinkles provided in the embodiments of this application;

[0054] Figure 8This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0056] In this article, the term "and / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The symbol " / " in this article indicates that the related objects are in an "or" relationship; for example, A / B means A or B.

[0057] The terms "first" and "second," etc., used in the specification and claims herein are used to distinguish different objects, not to describe a specific order of objects. For example, "first response message" and "second response message," etc., are used to distinguish different response messages, not to describe a specific order of response messages.

[0058] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0059] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0060] The embodiments of this application are described below with reference to the accompanying drawings.

[0061] Reference Figure 1 This application provides a modeling method for simulating the hyperelasticity of two-dimensional woven fabric wrinkles, including:

[0062] S101. Establish a hyperelastic model that fully considers the mechanical behavior of two-dimensional woven fabrics, wherein the two-dimensional woven fabrics are composed of warp and weft yarns interlaced and woven together;

[0063] S102. Determine the numerical implementation method of the hyperelastic model in the finite element framework, wherein the numerical implementation method is implemented through a subroutine interface;

[0064] S103. The hyperelastic model is simulated using the numerical implementation method and the finite element framework to simulate the wrinkle defects generated during the deformation of two-dimensional woven fabrics;

[0065] The hyperelastic model is established by defining strain invariants for tensile, shear, and bending deformation of a two-dimensional woven fabric, obtaining the corresponding strain energy function based on the strain invariants, and calculating the membrane stress and bending moment based on the strain energy function.

[0066] Specifically, a hyperelastic model capable of comprehensively capturing the mechanical behavior of two-dimensional woven fabrics is created through the above step S101.

[0067] It should be noted that the mechanical behavior of two-dimensional woven fabrics, as an important engineering material, is influenced by the complex structure of the interlacing warp and weft yarns. A hyperelastic model is selected to accommodate the nonlinear behavior of woven fabrics under large deformation conditions.

[0068] Tensile deformation: Defines the strain invariant along the warp and weft directions, describing the deformation of a material during stretching.

[0069] Shear deformation: Defines the shear strain invariant involving the mutual shearing of warp and weft yarns in a fabric, describing the change in yarn orientation during the shearing process.

[0070] Bending deformation: Considering the bending behavior of the fabric under external force, the corresponding bending strain invariant is defined.

[0071] Secondly, the established hyperelastic model is implemented within the finite element framework using the aforementioned S102. Finite element framework selection: finite element analysis software such as ABAQUS / Explicit is used. Subroutine interface implementation: user-defined subroutines (such as VUGENS) are used to write the model, connecting the stress-strain and moment-curvature relationships of the hyperelastic model with the finite element solution process. The calculation logic for strain invariants and strain energy functions, including the formulas for calculating membrane stress and bending moment, is implemented within the subroutines.

[0072] Finally, the S103 simulation was used to model the wrinkling defects that occur in two-dimensional woven fabrics during deformation. By using the established hyperelastic model and subroutine interface, dynamic deformation simulation was performed to determine the deformation behavior of the fabric and the evolution of wrinkles under different conditions.

[0073] Optionally, the modeling method for the two-dimensional woven fabric hyperelasticity model specifically includes:

[0074] Determine the strain invariant for each deformation mode, which includes tensile deformation, shear deformation, and bending deformation;

[0075] The total strain energy of the two-dimensional woven fabric is determined, and the total strain energy is decoupled to obtain the tensile deformation strain energy, shear deformation strain energy, and bending deformation strain energy.

[0076] Determine the membrane strain energy function corresponding to the membrane strain energy, calculate the membrane stress based on the membrane strain energy function combined with the determinant of the deformation gradient tensor and the transpose of the deformation gradient tensor, and calculate the bending moment based on the bending deformation strain energy and the bending strain invariant.

[0077] The hyperelastic model is established based on the decoupling results of the strain invariants, the total strain energy, and the calculation results of the membrane strain energy function.

[0078] Specifically, this embodiment requires the identification and definition of three main deformation modes: tensile deformation, shear deformation, and bending deformation. The strain invariant corresponding to each deformation mode is used to describe the properties of the object under these deformation states.

[0079] The strain invariant of tensile deformation is related to the elongation of the fabric in the warp and weft directions, and mainly reflects the deformation characteristics of the material under tension; the strain invariant of shear deformation describes the relative shear deformation of the warp and weft of the fabric; the strain invariant of bending deformation is mainly related to the degree of bending of the material, especially the curvature change formed when the fabric is subjected to external force.

[0080] Then, the total strain energy of the two-dimensional woven fabric is determined and decoupled. By constructing the total strain energy of the two-dimensional woven fabric, the total strain energy is composed of the energy contributions of the three deformation modes of tension, shear and bending.

[0081] In determining the membrane strain energy, a strain energy function related to membrane deformation is established based on specific material behavior. After establishing the membrane strain energy function, the membrane stress is calculated using the function combined with the determinant and transpose of the deformation gradient tensor. On the other hand, the bending moment is calculated based on the strain energy of bending deformation and its strain invariants.

[0082] Finally, combining the results from the above sections, a hyperelastic model is established, which integrates the decoupling results of strain invariants, total strain energy, and the calculation results of the membrane strain energy function.

[0083] Optionally, the method for obtaining the strain invariant of the deformation mode includes:

[0084] Determine the curvature tensor to describe the curvature and torsion of material particles in the current configuration;

[0085] The deformation gradient tensor is determined based on the relationship between the current position of the material particles and the initial configuration position, and the right Cauchy Green strain tensor is determined based on the deformation gradient tensor.

[0086] Obtain the initial unit vectors of the warp and weft directions in the initial configuration, and the current unit vectors of the warp and weft directions in the current configuration;

[0087] Based on the initial unit vector, the initial unit vector, and the right Cauchy Green strain tensor, determine the tensile strain invariants corresponding to the tensile deformation of the warp and weft yarns;

[0088] Based on the initial unit vector, the right Cauchy Green strain tensor, and the tensile strain invariant, the shear strain invariant corresponding to the warp and weft shear deformation is determined.

[0089] Based on the initial unit vector, the initial unit vector, and the curvature tensor, the tensile strain invariants corresponding to the tensile deformation of the warp and weft yarns are determined.

[0090] Specifically, the following are the methods for obtaining strain invariants:

[0091] The strain invariants of the deformation mode are shown in the following formula:

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] in, These are the strain invariants related to the tensile deformation of the warp and weft yarns, respectively. It is the strain invariant related to the shear deformation between the warp and weft yarns. These are the strain invariants related to the bending deformation of the warp and weft yarns, respectively. This is the curvature tensor in the current configuration, used to describe the curvature and torsion of the material particles.

[0098] These are the unit vectors of the warp and weft directions in the initial (undeformed) configuration, respectively. These are the unit vectors for the warp and weft directions in the current (modified) configuration.

[0099] The right Cauchygreen strain tensor is defined as shown in the following formula:

[0100]

[0101] in, The deformation gradient tensor is defined as shown in the formula:

[0102]

[0103] in, These represent the positions of the material particles in the current and initial configurations, respectively.

[0104] Optionally, the total strain energy is decoupled to obtain tensile strain energy, shear strain energy, and bending strain energy, including:

[0105] The total strain energy is decoupled and decomposed into membrane deformation strain energy and bending deformation strain energy;

[0106] The membrane deformation strain energy is decomposed into tensile deformation strain energy and shear deformation strain energy;

[0107] The bending deformation strain energy is decomposed into the warp bending deformation strain energy corresponding to the warp bending deformation and the weft bending deformation strain energy corresponding to the warp bending deformation.

[0108] Specifically, based on strain invariants, the strain energy functions related to deformation modes such as tension, shear, and bending are calculated as follows:

[0109] Decoupling membrane deformation from bending deformation, total strain energy It can be decomposed into two parts: membrane deformation and bending deformation, as follows:

[0110]

[0111] in, It is the strain energy of membrane deformation. It is the strain energy of bending deformation.

[0112] Membrane strain energy It can be broken down into two parts related to tensile and shear deformation as follows:

[0113]

[0114] in, These are the strain energies related to the bending deformation of the warp and weft yarns, respectively. Further, the bending deformation strain energy... It can be considered as the corresponding strain invariant. The function.

[0115] Optionally, the membrane strain energy function corresponding to the determined membrane strain energy is determined based on the membrane deformation strain energy and the right Cauchy-Green strain tensor.

[0116] Based on the strain energy function, the membrane stress and bending moment are calculated as follows:

[0117] Based on the membrane strain energy, the membrane stress is calculated as follows:

[0118]

[0119] in, The determinant of the deformation gradient tensor is used to describe the volume change of the infinitesimal element before and after deformation. For the deformation gradient tensor The transpose of .

[0120] Based on the bending deformation strain energy, the bending moment is calculated as follows:

[0121]

[0122] in, These are the bending moments along the warp and weft directions, respectively. It is assumed that the bending behavior of the woven fabric mainly depends on the bending behavior of the warp and weft yarns. Therefore, the torque between the warp and weft yarns... It can be ignored.

[0123] Optionally, the numerical implementation process includes a membrane deformation calculation process and a bending deformation calculation process, wherein the membrane deformation calculation process includes:

[0124] Read the deformation gradient tensor from the subroutine interface of the finite element framework, calculate the right Cauchy Green strain tensor, define the unit vectors of the warp and weft directions in the initial configuration, as well as the membrane strain invariant, and calculate the strain energy of the membrane deformation.

[0125] The membrane stress is calculated based on the membrane strain energy, and the membrane stress is returned to the main program of the finite element framework.

[0126] Optionally, the bending deformation calculation process includes:

[0127] Read the curvature tensor from the subroutine interface of the finite element framework, define the bending strain invariant, and calculate the bending deformation strain energy.

[0128] The bending moment is calculated based on the bending deformation strain energy, and the bending moment is returned to the main program of the finite element frame.

[0129] Specifically, the numerical implementation process of the hyperelastic model in the VUGENS subroutine interface of the general-purpose finite element software ABAQUS / Explicit is as follows:

[0130] Reference Figure 2 The hyperelastic model independently calculates membrane deformation and bending deformation in the numerical implementation process, as follows:

[0131] Calculate membrane deformation: Read the deformation gradient tensor from the VUGENS subroutine interface of ABAQUS / Explicit, and then calculate the right Cauchygreen strain tensor. Define unit vectors for the warp and weft directions in the initial configuration, and define strain invariants related to membrane deformation. Then, based on the membrane strain invariants, calculate the strain energy of the membrane deformation. Finally, calculate the membrane stress and return to the ABAQUS / Explicit main program.

[0132] Calculate bending deformation: Read the curvature tensor from the VUGENS subroutine interface of ABAQUS / Explicit. Then define the strain invariant associated with the bending deformation. Then, based on the bending strain invariant, calculate the strain energy of the bending deformation. Finally, calculate the bending moment and return to the ABAQUS / Explicit main program.

[0133] The present application will be described in detail below with reference to specific embodiments.

[0134] Example 1:

[0135] The modeling method of the hyperelastic model for simulating the wrinkles of two-dimensional woven fabrics proposed in this application is used to simulate the off-axis stretching of plain weave carbon fiber two-dimensional woven fabrics.

[0136] like Figure 3 As shown, an off-axis tensile finite element model of the woven fabric was established in ABAQUS software. The finite element model settings were consistent with the off-axis tensile test settings. In the off-axis tensile test, the loading direction was perpendicular to the warp and weft directions respectively. The included angle is used to ensure that the central region of the sample undergoes pure shear deformation. The warp direction vector is... The weft direction vector is The specimen length L = 120 mm and the specimen width W = 50 mm. A fixed constraint is applied to one end of the specimen. Displacement loading is applied to the other end of the specimen. , The finite element model was meshed using 4-node reduced integral shell elements (S4R), and the mesh size was determined to be 1 mm based on mesh sensitivity analysis.

[0137] To demonstrate the ability of the proposed hyperelastic model to capture wrinkles in woven fabrics, two types of elements are used to simulate the off-axis tensile deformation of woven fabrics: membrane elements and shell elements. Membrane elements can only withstand in-plane deformation, thus only considering the tensile and shear behaviors of woven fabrics. Shell elements, on the other hand, can withstand both in-plane and out-of-plane deformations simultaneously, thus comprehensively considering the tensile, shear, and bending behaviors of woven fabrics.

[0138] Reference Figure 4 , Figure 4The off-axis tensile deformation behavior of woven fabrics predicted using membrane elements and shell elements are presented separately. Clearly, the cross-section of the woven fabric predicted using membrane elements shows no deformation, thus failing to simulate wrinkles. In contrast, the cross-section of the woven fabric predicted using shell elements exhibits significant deformation, thus capturing wrinkle behavior. This comparison demonstrates that the proposed hyperelastic model has the ability to capture wrinkles during the deformation process of woven fabrics.

[0139] Example 2:

[0140] The cupping formation of plain weave carbon fiber two-dimensional woven fabric is simulated using the modeling method of the hyperelastic model of simulating the wrinkles of two-dimensional woven fabrics proposed in this application.

[0141] like Figure 5 As shown, a finite element model of cupping forming of woven fabric is established in ABAQUS software. The finite element model of cupping forming includes a punch, an upper pressure ring, a two-dimensional woven fabric, and a lower pressure ring. The punch, upper pressure ring, and lower pressure ring are modeled as rigid bodies. The upper and lower pressure rings are subject to fixed constraints. The punch applies displacement loading. , The two-dimensional woven fabric was modeled in the XOY plane, with a sample size of 100 mm × 100 mm. The warp direction vector is... The weft direction vector is A two-dimensional woven fabric finite element model was generated using 4-node reduced integral shell elements (S4R), and the mesh size was determined to be 1 mm based on mesh sensitivity analysis.

[0142] To demonstrate the ability of the proposed hyperelastic model to capture wrinkles in woven fabrics, two types of elements are used to simulate the cupping formation of woven fabrics: membrane elements and shell elements. Membrane elements can only withstand in-plane deformation, thus only considering the tensile and shear behaviors of woven fabrics. Shell elements, on the other hand, can withstand both in-plane and out-of-plane deformations simultaneously, thus comprehensively considering the tensile, shear, and bending behaviors of woven fabrics. Figure 6 The off-axis tensile deformation behavior of woven fabrics predicted using membrane elements and shell elements are presented separately. Clearly, the cross-section of the woven fabric predicted using membrane elements shows no deformation, thus failing to simulate wrinkles. In contrast, the cross-section of the woven fabric predicted using shell elements exhibits significant deformation, thus capturing wrinkle behavior. This comparison demonstrates that the proposed hyperelastic model has the ability to capture wrinkles during the deformation process of woven fabrics.

[0143] The specific implementation methods of each module can be found in the descriptions in the method embodiments, and will not be repeated in the embodiments of this application.

[0144] The modeling system for the hyperelastic model of simulated two-dimensional woven fabric folds provided in this application is described below. The modeling system for the hyperelastic model of simulated two-dimensional woven fabric folds described below can be referred to in correspondence with the modeling system for the hyperelastic model of simulated two-dimensional woven fabric folds described above.

[0145] Reference Figure 7 This application provides a modeling system for simulating the hyperelasticity of two-dimensional woven fabric wrinkles, comprising:

[0146] Model building module 710 establishes a hyperelastic model that fully considers the mechanical behavior of two-dimensional woven fabrics, which are composed of warp and weft yarns interwoven together.

[0147] The numerical implementation module 720 is used to determine the numerical implementation method of the hyperelastic model in the finite element framework, and the numerical implementation method is implemented through a subroutine interface.

[0148] The wrinkle simulation module 730 is used to simulate the wrinkle defects generated by the two-dimensional woven fabric during deformation using the numerical implementation method and the finite element framework of the hyperelastic model.

[0149] The hyperelastic model is established by defining strain invariants for tensile, shear, and bending deformation of a two-dimensional woven fabric, obtaining the corresponding strain energy function based on the strain invariants, and calculating the membrane stress and bending moment based on the strain energy function.

[0150] Optionally, the modeling method for the two-dimensional woven fabric hyperelasticity model specifically includes:

[0151] Determine the strain invariant for each deformation mode, which includes tensile deformation, shear deformation, and bending deformation;

[0152] The total strain energy of the two-dimensional woven fabric is determined, and the total strain energy is decoupled to obtain the tensile deformation strain energy, shear deformation strain energy, and bending deformation strain energy.

[0153] Determine the membrane strain energy function corresponding to the membrane strain energy, calculate the membrane stress based on the membrane strain energy function combined with the determinant of the deformation gradient tensor and the transpose of the deformation gradient tensor, and calculate the bending moment based on the bending deformation strain energy and the bending strain invariant.

[0154] The hyperelastic model is established based on the decoupling results of the strain invariants, the total strain energy, and the calculation results of the membrane strain energy function.

[0155] Optionally, the method for obtaining the strain invariant of the deformation mode includes:

[0156] Determine the curvature tensor to describe the curvature and torsion of material particles in the current configuration;

[0157] The deformation gradient tensor is determined based on the relationship between the current position of the material particles and the initial configuration position, and the right Cauchy Green strain tensor is determined based on the deformation gradient tensor.

[0158] Obtain the initial unit vectors of the warp and weft directions in the initial configuration, and the current unit vectors of the warp and weft directions in the current configuration;

[0159] Based on the initial unit vector, the initial unit vector, and the right Cauchy Green strain tensor, determine the tensile strain invariants corresponding to the tensile deformation of the warp and weft yarns;

[0160] Based on the initial unit vector, the right Cauchy Green strain tensor, and the tensile strain invariant, the shear strain invariant corresponding to the warp and weft shear deformation is determined.

[0161] Based on the initial unit vector, the initial unit vector, and the curvature tensor, the tensile strain invariants corresponding to the tensile deformation of the warp and weft yarns are determined.

[0162] Optionally, the total strain energy is decoupled to obtain tensile strain energy, shear strain energy, and bending strain energy, including:

[0163] The total strain energy is decoupled and decomposed into membrane deformation strain energy and bending deformation strain energy;

[0164] The membrane deformation strain energy is decomposed into tensile deformation strain energy and shear deformation strain energy;

[0165] The bending deformation strain energy is decomposed into the warp bending deformation strain energy corresponding to the warp bending deformation and the weft bending deformation strain energy corresponding to the warp bending deformation.

[0166] Optionally, the membrane strain energy function corresponding to the determined membrane strain energy is determined based on the membrane deformation strain energy and the right Cauchy-Green strain tensor.

[0167] Optionally, the numerical implementation process includes a membrane deformation calculation process and a bending deformation calculation process, wherein the membrane deformation calculation process includes:

[0168] Read the deformation gradient tensor from the subroutine interface of the finite element framework, calculate the right Cauchy Green strain tensor, define the unit vectors of the warp and weft directions in the initial configuration, as well as the membrane strain invariant, and calculate the strain energy of the membrane deformation.

[0169] The membrane stress is calculated based on the membrane strain energy, and the membrane stress is returned to the main program of the finite element framework.

[0170] Optionally, the bending deformation calculation process includes:

[0171] Read the curvature tensor from the subroutine interface of the finite element framework, define the bending strain invariant, and calculate the bending deformation strain energy.

[0172] The bending moment is calculated based on the bending deformation strain energy, and the bending moment is returned to the main program of the finite element frame.

[0173] It is understood that the detailed functional implementation of each of the above units / modules can be found in the description in the aforementioned method embodiments, and will not be repeated here.

[0174] It should be understood that the above-described device is used to execute the methods in the above embodiments. The implementation principle and technical effect of the corresponding program modules in the device are similar to those described in the above methods. The working process of the device can be referred to the corresponding process in the above methods, and will not be repeated here.

[0175] Based on the methods in the above embodiments, this application provides an electronic device / image signal generator / network device / transmitter / terminal / base station / industrial control computer. This electronic device / image signal generator / network device / transmitter / terminal / base station / industrial control computer may include: a processor 810, a communication interface 820, a memory 830, and a communication bus 840. The processor 810, communication interface 820, and memory 830 communicate with each other via the communication bus 840. The processor 810 can call logical instructions in the memory 830 to execute the methods in the above embodiments.

[0176] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0177] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0178] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0179] It is understood that the processor in the embodiments of this application can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0180] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0181] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0182] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0183] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A modeling method for simulating the hyperelasticity of two-dimensional woven fabric folds, characterized in that, include: A hyperelastic model is established that comprehensively considers the mechanical behavior of two-dimensional woven fabrics, which are composed of warp and weft yarns interwoven together. A numerical implementation method for the hyperelastic model in a finite element framework is determined, and the numerical implementation method is implemented through a subroutine interface. The hyperelastic model is simulated using the numerical implementation method and the finite element framework to simulate the wrinkle defects generated during the deformation of two-dimensional woven fabrics. The hyperelastic model is established by defining strain invariants for tensile deformation, shear deformation, and bending deformation of a two-dimensional woven fabric, obtaining the corresponding strain energy function based on the strain invariants, and calculating the membrane stress and bending moment based on the strain energy function. The modeling method for the hyperelastic model of the two-dimensional woven fabric specifically includes: Determine the strain invariant for each deformation mode, which includes tensile deformation, shear deformation, and bending deformation; The total strain energy of the two-dimensional woven fabric is determined, and the total strain energy is decoupled and decomposed into membrane deformation strain energy and bending deformation strain energy; the membrane deformation strain energy is decomposed into tensile deformation strain energy and shear deformation strain energy; the bending deformation strain energy is decomposed into warp bending deformation strain energy corresponding to warp bending deformation and weft bending deformation strain energy corresponding to warp bending deformation. Determine the membrane strain energy function corresponding to the membrane strain energy, calculate the membrane stress based on the membrane strain energy function combined with the determinant of the deformation gradient tensor and the transpose of the deformation gradient tensor, and calculate the bending moment based on the bending deformation strain energy and the bending strain invariant. The hyperelastic model is established based on the decoupling results of the strain invariants and total strain energy, as well as the calculation results of the membrane strain energy function, as shown in the following formula: in, These are the strain invariants related to the tensile deformation of the warp and weft yarns, respectively. It is the strain invariant related to the shear deformation between the warp and weft yarns. These are the strain invariants related to the bending deformation of the warp and weft yarns, respectively. This is the curvature tensor in the current configuration, used to describe the curvature and torsion of the material particles; These are the initial unit vectors in the warp and weft directions of the initial configuration, which is an undeformed configuration. These are the current unit vectors in the warp and weft directions of the current configuration, where the current configuration is the modified configuration; The right Cauchygreen strain tensor is defined as shown in the following formula: in, The deformation gradient tensor is defined as shown in the formula: in, These represent the positions of the material particles in the current and initial configurations, respectively. The decoupling process of the total strain energy is shown in the following formula: in, It is the strain energy of membrane deformation. It is the strain energy of bending deformation; Membrane strain energy It can be broken down into two parts related to tensile and shear deformation as follows: in, These are the bending strain energies related to the bending deformation of the warp and weft yarns, respectively. Based on membrane strain energy, membrane stress is calculated as shown in the following formula: in, Let be the determinant of the deformation gradient tensor, used to describe the volume change of the infinitesimal element before and after deformation. For the deformation gradient tensor transpose; Based on the bending deformation strain energy, the bending moment is calculated as follows: in, These are the bending moments along the warp and weft directions, respectively.

2. The modeling method according to claim 1, characterized in that, The membrane strain energy function corresponding to the determined membrane strain energy is determined based on the membrane deformation strain energy and the right Cauchy-Green strain tensor.

3. The modeling method according to claim 1, characterized in that, The numerical implementation process includes a membrane deformation calculation process and a bending deformation calculation process. The membrane deformation calculation process includes: Read the deformation gradient tensor from the subroutine interface of the finite element framework, calculate the right Cauchy Green strain tensor, define the unit vectors of the warp and weft directions in the initial configuration, as well as the membrane strain invariant, and calculate the strain energy of the membrane deformation. The membrane stress is calculated based on the membrane strain energy, and the membrane stress is returned to the main program of the finite element framework.

4. The modeling method according to claim 3, characterized in that, The bending deformation calculation process includes: Read the curvature tensor from the subroutine interface of the finite element framework, define the bending strain invariant, and calculate the bending deformation strain energy. The bending moment is calculated based on the bending deformation strain energy, and the bending moment is returned to the main program of the finite element frame.

5. A modeling system for simulating the hyperelasticity of two-dimensional woven fabric folds, characterized in that, include: The model building module establishes a hyperelastic model that comprehensively considers the mechanical behavior of two-dimensional woven fabrics, which are composed of warp and weft yarns interwoven together. The numerical implementation module is used to determine the numerical implementation method of the hyperelastic model in the finite element framework, and the numerical implementation method is implemented through a subroutine interface. The wrinkle simulation module is used to simulate the wrinkle defects generated during the deformation of two-dimensional woven fabrics using the numerical implementation method and the finite element framework. The hyperelastic model is established by defining strain invariants for tensile deformation, shear deformation, and bending deformation of a two-dimensional woven fabric, obtaining the corresponding strain energy function based on the strain invariants, and calculating the membrane stress and bending moment based on the strain energy function. The modeling method for the hyperelastic model of the two-dimensional woven fabric specifically includes: Determine the strain invariant for each deformation mode, which includes tensile deformation, shear deformation, and bending deformation; The total strain energy of the two-dimensional woven fabric is determined, and the total strain energy is decoupled and decomposed into membrane deformation strain energy and bending deformation strain energy; the membrane deformation strain energy is decomposed into tensile deformation strain energy and shear deformation strain energy; the bending deformation strain energy is decomposed into warp bending deformation strain energy corresponding to warp bending deformation and weft bending deformation strain energy corresponding to warp bending deformation. Determine the membrane strain energy function corresponding to the membrane strain energy, calculate the membrane stress based on the membrane strain energy function combined with the determinant of the deformation gradient tensor and the transpose of the deformation gradient tensor, and calculate the bending moment based on the bending deformation strain energy and the bending strain invariant. The hyperelastic model is established based on the decoupling results of the strain invariants, the total strain energy, and the calculation results of the membrane strain energy function. The specific formula is shown below: in, These are the strain invariants related to the tensile deformation of the warp and weft yarns, respectively. It is the strain invariant related to the shear deformation between the warp and weft yarns. These are the strain invariants related to the bending deformation of the warp and weft yarns, respectively. This is the curvature tensor in the current configuration, used to describe the curvature and torsion of the material particles; These are the initial unit vectors in the warp and weft directions of the initial configuration, which is an undeformed configuration. These are the current unit vectors in the warp and weft directions of the current configuration, where the current configuration is the modified configuration; The right Cauchygreen strain tensor is defined as shown in the following formula: in, The deformation gradient tensor is defined as shown in the formula: in, These represent the positions of the material particles in the current and initial configurations, respectively. The decoupling process of the total strain energy is shown in the following formula: in, It is the strain energy of membrane deformation. It is the strain energy of bending deformation; Membrane strain energy It can be broken down into two parts related to tensile and shear deformation as follows: in, These are the bending strain energies related to the bending deformation of the warp and weft yarns, respectively. Based on membrane strain energy, membrane stress is calculated as shown in the following formula: in, Let be the determinant of the deformation gradient tensor, used to describe the volume change of the infinitesimal element before and after deformation. For the deformation gradient tensor transpose; Based on the bending deformation strain energy, the bending moment is calculated as follows: in, These are the bending moments along the warp and weft directions, respectively.

6. An electronic device, characterized in that, include: At least one memory for storing computer programs; At least one processor is configured to execute a program stored in the memory, wherein when the program stored in the memory is executed, the processor is configured to perform the method as described in any one of claims 1-4.

7. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is run on the processor, it causes the processor to perform the method as described in any one of claims 1-4.

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