Modeling method and system of hyperelastic model for simulating two-dimensional woven fabric wrinkles

Abstract

The invention belongs to the technical field of mechanical simulation and prediction of woven fabrics, and particularly discloses a modeling method and system of a hyperelastic model for simulating wrinkles of a two-dimensional woven fabric, and the method comprises the steps: building the hyperelastic model which comprehensively considers mechanical behaviors of the two-dimensional woven fabric, and the two-dimensional woven fabric is formed by overlapping and weaving warp yarns and weft yarns; determining a numerical value implementation method of the hyperelastic model in the finite element framework, wherein the numerical value implementation method is implemented through a subprogram interface; simulating a wrinkle defect generated in the deformation process of the two-dimensional woven fabric by adopting a finite element framework through a numerical value implementation method of the hyperelastic model; wherein the hyperelastic model is established by defining strain invariants of tensile deformation, shear deformation and bending deformation of the two-dimensional woven fabric, obtaining a corresponding strain energy function based on the strain invariants, and calculating membrane stress and bending moment based on the strain energy function. According to the invention, the wrinkle defect generated in the deformation process of the two-dimensional woven fabric can be accurately simulated.

Description

Technical Field

[0001] The present application belongs to the technical field of mechanical simulation and prediction of woven fabrics, and more specifically, to a modeling method and system for a hyperelastic model for simulating wrinkles of two-dimensional woven fabrics. Background Art

[0002] Two-dimensional woven fabrics are fabrics made of alternating warp and weft yarns. They do not require additional stitching lines and are suitable for fibers with greater bending stiffness. Due to their high specific strength and high specific stiffness, two-dimensional woven fabrics can meet the requirements of composite materials for directional mechanical properties in different service environments and have been widely used as reinforcements for fiber-reinforced composites. Liquid forming technology is currently one of the most widely used processes for manufacturing fiber-reinforced composites. During the pre-forming process of the liquid forming process, woven fabrics will undergo significant deformation and even defects. Therefore, it is necessary to develop a stable numerical simulation method to simulate the deformation and defects of woven fabrics.

[0003] Wrinkles are the most important defects in the deformation process of woven fabrics. The generation of wrinkles depends on the material properties of woven fabrics, including stretching, shearing and bending behaviors. However, the material properties of woven fabrics are different from those of traditional continuous materials, such as rubber and metal. Traditional continuous materials follow the Kirchhoff theory, that is, the membrane stiffness is coupled with the bending stiffness, and the bending stiffness can be directly calculated from the membrane stiffness. However, woven fabrics do not follow the Kirchhoff theory, and the bending stiffness is much lower than the value calculated based on the membrane stiffness. Therefore, the membrane behavior and bending behavior should be decoupled in the deformation model of modeling woven fabrics.

[0004] A large number of numerical models have been developed to try to simulate the wrinkle defects of woven fabrics, such as the stress composite shell method and the hybrid element method. The stress composite shell method introduces the microscopic characteristics of woven fabrics into the macroscopic scale analysis. This type of model assumes that each unit contains a specified number of woven fabric cells, calculates the strain energy based on the deformation mode of the cell, and derives the unit node load. This type of method is usually very complex and difficult to implement in the general finite element framework. The hybrid element method uses two units to model the mechanical behavior of woven fabrics, one unit (membrane unit) models the membrane behavior of woven fabrics, and one unit (beam / shell unit) models the bending behavior of woven fabrics. The hybrid element method still follows the Kirchhoff theory and still overestimates the bending stiffness of woven fabrics.

[0005] In general, the current methods for simulating woven fabric wrinkles are still unable to accurately evaluate the mechanical behavior of woven fabrics and cannot accurately simulate the wrinkle defects of woven fabrics. Summary of the invention

[0006] In view of the defects of the prior art, the purpose of this application is to provide a modeling method and system for a hyperelastic model for simulating two-dimensional woven fabric wrinkles, aiming to solve the problem that the current methods for simulating woven fabric wrinkles are still unable to 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, the present application provides a modeling method for a hyperelastic model for simulating wrinkles of a two-dimensional woven fabric, comprising: A hyperelastic model is established that fully considers the mechanical behavior of a two-dimensional woven fabric, wherein the two-dimensional woven fabric is composed of warp yarns and weft yarns overlapped and woven with each other; Determining a numerical implementation method of a hyperelastic model in a finite element framework, wherein the numerical implementation method is implemented through a subroutine interface; The hyperelastic model is used through the numerical realization method to simulate the wrinkle defects generated during the deformation of the two-dimensional woven fabric using a finite element framework; The hyperelastic model is established by defining the strain invariants of the tensile deformation, shear deformation and bending deformation of the 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.

[0008] Optionally, the modeling method of the two-dimensional woven fabric hyperelastic model specifically includes: determining strain invariants for each deformation mode, the deformation mode comprising tensile deformation, shear deformation, and bending deformation; Determining the total strain energy of the two-dimensional woven fabric, decoupling the total strain energy to obtain tensile deformation strain energy, shear deformation strain energy and bending deformation strain energy; determining a membrane strain energy function corresponding to the membrane strain energy, calculating 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 calculating the bending moment based on the bending deformation strain energy and the bending strain invariant; The hyperelastic model is established based on the strain invariant, the decoupling result of the total strain energy and the calculation result of the membrane strain energy function.

[0009] Optionally, the method for obtaining the strain invariant of the deformation mode includes: Determine the curvature tensor to describe the curvature and torsion of the material particles in the current configuration; Determine a deformation gradient tensor according to the relationship between the current position of the material particle and the initial configuration position, and determine the right Cauchy Green strain tensor based on the deformation gradient tensor; Get 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; Determining the tensile strain invariants corresponding to the tensile deformation of the warp yarn and the weft yarn based on the initial unit vector, the initial unit vector and the right Cauchy Green strain tensor; Determine the shear strain invariants corresponding to the shear deformation of the warp yarn and the weft yarn based on the initial unit vector, the initial unit vector, the right Cauchy Green strain tensor and the tensile strain invariant; The tensile strain invariants corresponding to the tensile deformation of the warp yarn and the weft yarn are determined based on the initial unit vector, the initial unit vector and the curvature tensor.

[0010] Optionally, the total strain energy is decoupled to obtain tensile deformation strain energy, shear deformation strain energy and bending deformation strain energy, including: Decomposing the total strain energy into membrane deformation strain energy and bending deformation strain energy; Decomposing the membrane deformation strain energy into tensile deformation strain energy and shear deformation strain energy; The bending deformation strain energy is decomposed into the warp yarn bending deformation strain energy corresponding to the warp yarn bending deformation and the weft yarn bending deformation strain energy corresponding to the warp yarn bending deformation.

[0011] Optionally, the membrane strain energy function corresponding to the membrane strain energy is determined based on the membrane deformation strain energy and the right Cauchy Green strain tensor.

[0012] Optionally, the numerical realization process includes a membrane deformation calculation process and a bending deformation calculation process, and the membrane deformation calculation process includes: Reading the deformation gradient tensor from the subroutine interface of the finite element framework, and calculating the right Cauchy Green strain tensor, defining the unit vectors in the warp direction and the weft direction in the initial configuration, and the membrane strain invariant, and calculating the strain energy of the membrane deformation; Membrane stress is calculated based on the membrane strain energy and is returned to the main program of the finite element framework.

[0013] Optionally, the bending deformation calculation process includes: Reading the curvature tensor from the subroutine interface of the finite element framework, defining the bending strain invariant, and calculating the bending deformation strain energy; The bending moment is calculated according to the bending deformation strain energy, and the bending moment is returned to the main program of the finite element framework.

[0014] In a second aspect, the present application provides a modeling system for simulating a hyperelastic model of two-dimensional woven fabric wrinkles, comprising: A model building module, for building a hyperelastic model that fully considers the mechanical behavior of a two-dimensional woven fabric, wherein the two-dimensional woven fabric is composed of warp yarns and weft yarns that overlap and weave with each other; A numerical realization module, used for determining a numerical realization method of a hyperelastic model in a finite element framework, wherein the numerical realization method is realized through a subroutine interface; A wrinkle simulation module, used to simulate the wrinkle defects of the two-dimensional woven fabric during the deformation process by using the hyperelastic model through the numerical realization method and a finite element framework; The hyperelastic model is established by defining the strain invariants of the tensile deformation, shear deformation and bending deformation of the 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.

[0015] In a third aspect, the present application provides an electronic device comprising: at least one memory for storing programs; and at least one processor for executing the programs stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method described in the first aspect or any possible implementation of the first aspect.

[0016] In a fourth aspect, the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method described in the first aspect or any possible implementation of the first aspect.

[0017] In a fifth aspect, the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method described in the first aspect or any possible implementation of the first aspect.

[0018] It can be understood that the beneficial effects of the second to fifth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0019] In general, the above technical solutions conceived by this application have the following beneficial effects compared with the prior art: (1) The present application provides a method for establishing a hyperelastic model for simulating the wrinkles of two-dimensional woven fabrics. The total strain energy characterizing the deformation of the woven fabric is decomposed into membrane strain energy and bending deformation strain energy by means of energy decoupling. The membrane strain energy is further decomposed into tensile and shear deformation strain energy according to the membrane deformation mode. The membrane stress is calculated based on the membrane strain energy, and the bending moment is calculated based on the bending deformation strain energy. The hyperelastic model of the present application can fully consider the material behaviors of two-dimensional woven fabrics such as stretching, shearing and bending, and can therefore accurately simulate the wrinkle defects generated by two-dimensional woven fabrics during the deformation process.

[0020] (2) This application provides a method for numerically implementing a hyperelastic model for simulating wrinkles in two-dimensional woven fabrics. The hyperelastic model can be numerically implemented in the VUGENS subroutine interface of the general finite element program ABAQUS / Explicit. During the numerical implementation, membrane stress and bending moment are calculated independently, so the mechanical behavior of two-dimensional woven fabrics can be accurately characterized. At the same time, the model is compatible with any general finite element framework and can be used for wrinkle prediction of large-scale two-dimensional woven fabrics. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is a flow chart of a modeling method of a hyperelastic model for simulating wrinkles of a two-dimensional woven fabric provided in an embodiment of the present application; Figure 2 It is a flow chart of the numerical realization process of the two-dimensional woven fabric hyperelastic model constructed in the embodiment of the present application through the VUGENS subroutine interface of the general finite element software ABAQUS / Explicit; Figure 3 is a schematic diagram of a woven fabric off-axis stretch finite element model constructed according to a preferred embodiment of the present application; Figure 4 It is a deformation cloud diagram of eccentric stretching of woven fabric predicted by the hyperelastic model constructed according to the preferred embodiment of the present application; Figure 5 is a schematic diagram of a woven fabric cupping forming finite element model constructed according to a preferred embodiment of the present application; Figure 6 It is a deformation cloud diagram of woven fabric cupping formation predicted by the hyperelastic model constructed according to the preferred embodiment of the present application; Figure 7 It is a structural schematic diagram of a modeling device for a hyperelastic model simulating wrinkles of a two-dimensional woven fabric provided in an embodiment of the present application; Figure 8 It is a schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0023] The term "and / or" in this article is a description of the association relationship of associated objects, indicating that there can be three relationships. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. The symbol " / " in this article indicates that the associated objects are in an or relationship, for example, A / B means A or B.

[0024] The terms "first" and "second" in the specification and claims herein are used to distinguish different objects rather than to describe a specific order of the objects. For example, a first response message and a second response message are used to distinguish different response messages rather than to describe a specific order of the response messages.

[0025] In the embodiments of the present application, words such as "exemplary" or "for example" are used to indicate examples, illustrations or descriptions. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0026] In the description of the embodiments of the present application, unless otherwise specified, "multiple" means two or more than two. For example, multiple processing units refer to two or more processing units, etc.; multiple elements refer to two or more elements, etc.

[0027] The embodiments of the present application are described below in conjunction with the drawings in the embodiments of the present application.

[0028] Reference Figure 1 The present application provides a modeling method for a hyperelastic model for simulating wrinkles of a two-dimensional woven fabric, comprising: S101. Establishing a hyperelastic model that fully considers the mechanical behavior of a two-dimensional woven fabric, wherein the two-dimensional woven fabric is composed of warp yarns and weft yarns that overlap and weave each other; S102. Determine a numerical implementation method of a hyperelastic model in a finite element framework, wherein the numerical implementation method is implemented through a subroutine interface; S103. The hyperelastic model is implemented by the numerical method, using a finite element framework to simulate wrinkle defects generated during the deformation of a two-dimensional woven fabric; The hyperelastic model is established by defining the strain invariants of the tensile deformation, shear deformation and bending deformation of the 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.

[0029] Specifically, through the above step S101, a hyperelastic model capable of fully capturing the mechanical behavior of the two-dimensional woven fabric is created.

[0030] It should be noted that the mechanical behavior of two-dimensional woven fabrics, as an important engineering material, is affected by the complex structure of warp and weft yarns interwoven with each other. The hyperelastic model is selected to adapt to the nonlinear behavior of woven fabrics under large deformation conditions.

[0031] Tensile deformation: Defines the strain invariants along the warp and weft directions to describe the deformation of the material during stretching.

[0032] Shear deformation: defines the shear strain invariant involving the mutual shearing of the warp and weft yarns of the fabric, describing the change in yarn orientation of the fabric during the shearing process.

[0033] Bending deformation: Consider the bending behavior of the fabric under the action of external forces and define the corresponding bending strain invariants.

[0034] Secondly, the established hyperelastic model is implemented in the finite element framework through the above S102. Finite element framework selection: use finite element analysis software such as ABAQUS / Explicit. Subroutine interface implementation: use user-defined subroutines (such as VUGENS) to write the model so as to connect the stress-strain relationship and moment-curvature relationship of the hyperelastic model with the finite element solution process. The calculation logic of the strain invariant and strain energy function is implemented in the subroutine, including the calculation formulas of membrane stress and moment.

[0035] Finally, S103 is used to simulate the wrinkle defects of the two-dimensional woven fabric during the deformation process. By using the established hyperelastic model and subroutine interface, dynamic deformation simulation is performed to determine the deformation behavior of the fabric and the evolution of wrinkles under different conditions.

[0036] Optionally, the modeling method of the two-dimensional woven fabric hyperelastic model specifically includes: determining strain invariants for each deformation mode, the deformation mode comprising tensile deformation, shear deformation, and bending deformation; Determining the total strain energy of the two-dimensional woven fabric, decoupling the total strain energy to obtain tensile deformation strain energy, shear deformation strain energy and bending deformation strain energy; determining a membrane strain energy function corresponding to the membrane strain energy, calculating 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 calculating the bending moment based on the bending deformation strain energy and the bending strain invariant; The hyperelastic model is established based on the strain invariant, the decoupling result of the total strain energy and the calculation result of the membrane strain energy function.

[0037] Specifically, in this embodiment, three main deformation modes need to be identified and defined: tensile deformation, shear deformation and bending deformation. The strain invariant corresponding to each deformation mode is used to describe the characteristics of the object under these deformation states.

[0038] 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 yarns 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.

[0039] Then the total strain energy of the 2D woven fabric is determined and decoupled by constructing the total strain energy of the 2D woven fabric, which is composed of the energy contributions of the three deformation modes of tension, shear and bending.

[0040] In the process of determining the membrane strain energy, a strain energy function related to the membrane deformation is established based on the specific material behavior. After the membrane strain energy function is established, 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 the bending deformation and its strain invariant.

[0041] Finally, combining the results of the above parts, a hyperelastic model is established, which integrates the decoupling results of the strain invariant, the total strain energy, and the calculation results of the membrane strain energy function.

[0042] Optionally, the method for obtaining the strain invariant of the deformation mode includes: Determine the curvature tensor to describe the curvature and torsion of the material particles in the current configuration; Determine a deformation gradient tensor according to the relationship between the current position of the material particle and the initial configuration position, and determine the right Cauchy Green strain tensor based on the deformation gradient tensor; Get 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; Determining the tensile strain invariants corresponding to the tensile deformation of the warp yarn and the weft yarn based on the initial unit vector, the initial unit vector and the right Cauchy Green strain tensor; Determine the shear strain invariants corresponding to the shear deformation of the warp yarn and the weft yarn based on the initial unit vector, the initial unit vector, the right Cauchy Green strain tensor and the tensile strain invariant; The tensile strain invariants corresponding to the tensile deformation of the warp yarn and the weft yarn are determined based on the initial unit vector, the initial unit vector and the curvature tensor.

[0043] Specifically, the following is a specific method for obtaining the strain invariant: The strain invariant of the deformation mode is given by the following formula:

[0044]

[0045]

[0046]

[0047]

[0048] in, are the strain invariants associated with the tensile deformation of the warp and weft yarns, is the strain invariant related to the shear deformation between the warp and weft yarns, are the strain invariants associated with the bending deformation of warp and weft yarns, respectively; It is the curvature tensor in the current configuration, which is used to describe the curvature and torsion of material particles.

[0049] are the unit vectors in the warp and weft directions in the initial (undeformed) configuration, are the unit vectors in the warp and weft directions in the current (deformed) configuration, respectively.

[0050] is the right Cauchy Green strain tensor, defined as follows:

[0051] in, is the deformation gradient tensor, defined as follows:

[0052] in, are the positions of material particles in the current and initial configurations, respectively.

[0053] Optionally, the total strain energy is decoupled to obtain tensile deformation strain energy, shear deformation strain energy and bending deformation strain energy, including: Decomposing the total strain energy into membrane deformation strain energy and bending deformation strain energy; Decomposing the membrane deformation strain energy into tensile deformation strain energy and shear deformation strain energy; The bending deformation strain energy is decomposed into the warp yarn bending deformation strain energy corresponding to the warp yarn bending deformation and the weft yarn bending deformation strain energy corresponding to the warp yarn bending deformation.

[0054] Specifically, based on the strain invariant, the strain energy functions related to deformation modes such as tension, shear and bending are calculated as follows: Decoupling membrane deformation from bending deformation, the total strain energy It can be decomposed into two parts: membrane deformation and bending deformation as follows:

[0055] in, is the strain energy of membrane deformation, is the strain energy of bending deformation.

[0056] Membrane strain energy It can be decomposed into two parts related to tensile and shear deformation as follows:

[0057] in, are the strain energies associated with the bending deformation of the warp and weft yarns, respectively. Furthermore, the bending deformation strain energy It can be considered as the corresponding strain invariant function.

[0058] Optionally, the membrane strain energy function corresponding to the membrane strain energy is determined based on the membrane deformation strain energy and the right Cauchy Green strain tensor.

[0059] Based on the strain energy function, the membrane stress and bending moment are calculated as follows: Based on the membrane strain energy, the membrane stress is calculated as follows:

[0060] in, is the determinant of the deformation gradient tensor, which is used to describe the volume change of the microelement before and after deformation; is the deformation gradient tensor The transpose of .

[0061] Based on the bending deformation strain energy, the bending moment is calculated as follows:

[0062] in, are the bending moments along the warp and weft directions, respectively. It is assumed that the bending behavior of the woven fabric depends mainly on the bending behavior of the warp and weft yarns. Therefore, the torque between the warp and weft yarns is Can be ignored.

[0063] Optionally, the numerical realization process includes a membrane deformation calculation process and a bending deformation calculation process, and the membrane deformation calculation process includes: Reading the deformation gradient tensor from the subroutine interface of the finite element framework, and calculating the right Cauchy Green strain tensor, defining the unit vectors in the warp direction and the weft direction in the initial configuration, and the membrane strain invariant, and calculating the strain energy of the membrane deformation; Membrane stress is calculated based on the membrane strain energy and is returned to the main program of the finite element framework.

[0064] Optionally, the bending deformation calculation process includes: Reading the curvature tensor from the subroutine interface of the finite element framework, defining the bending strain invariant, and calculating the bending deformation strain energy; The bending moment is calculated according to the bending deformation strain energy, and the bending moment is returned to the main program of the finite element framework.

[0065] Specifically, the numerical implementation process of the hyperelastic model in the VUGENS subroutine interface of the general finite element software ABAQUS / Explicit is as follows: Reference Figure 2 , the hyperelastic model calculates membrane deformation and bending deformation independently in the numerical implementation process as follows: Calculate membrane deformation: Read the deformation gradient tensor from the VUGENS subroutine interface of ABAQUS / Explicit, and then calculate the right Cauchy Green strain tensor. Define the unit vectors in the warp and weft directions in the initial configuration, and define the strain invariants related to the 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 main ABAQUS / Explicit program.

[0066] Calculate the bending deformation: Read the curvature tensor from the VUGENS subroutine interface of ABAQUS / Explicit. Then define the strain invariants related to the bending deformation. Then, based on the bending strain invariants, calculate the strain energy of the bending deformation. Finally, calculate the bending moment and return to the main ABAQUS / Explicit program.

[0067] The present application is described in detail below with reference to specific embodiments.

[0068] Embodiment 1: The off-axis stretching of a plain carbon fiber two-dimensional woven fabric is simulated by using the modeling method of the hyperelastic model for simulating the wrinkles of a two-dimensional woven fabric proposed in the present application.

[0069] like Figure 3 As shown in Figure 1, a finite element model of woven fabric eccentric stretching was established in ABAQUS software. The finite element model settings are consistent with the eccentric stretching experiment settings. In the eccentric stretching experiment, the loading direction is parallel to the warp and weft directions. Angle, to ensure that the central area of ​​the specimen is pure shear deformation. The warp direction vector is , the weft direction vector is The length of the specimen is L = 120 mm, and the width of the specimen is 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 4-node reduced integration shell element S4R was used to mesh the finite element model, and the mesh size was determined to be 1 mm based on mesh sensitivity analysis.

[0070] In order to illustrate the ability of the hyperelastic model proposed in this application to capture the wrinkles of woven fabrics, two types of units are used to simulate the eccentric tensile deformation of woven fabrics: membrane units and shell units. The membrane unit can only withstand in-plane deformation, so only the tensile and shear behaviors of the woven fabric can be considered. The shell unit can withstand both in-plane and out-of-plane deformations, so the tensile, shear and bending behaviors of the woven fabric are fully considered.

[0071] Reference Figure 4 , Figure 4 The eccentric tensile deformation behavior of woven fabrics predicted by membrane elements and shell elements is shown respectively. Obviously, the cross section of the woven fabric predicted by membrane elements has no deformation, so wrinkles cannot be simulated. However, the cross section of the woven fabric predicted by shell elements deforms significantly, which can capture the wrinkle behavior. The comparison shows that the proposed hyperelastic model has the ability to capture wrinkles in the deformation process of woven fabrics.

[0072] Embodiment 2: The cupping of plain carbon fiber two-dimensional woven fabric is simulated by using the modeling method of the hyperelastic model for simulating wrinkles of two-dimensional woven fabric proposed in the present application.

[0073] like Figure 5 As shown in the figure, a finite element model of woven fabric cupping forming is established in ABAQUS software. The finite element model of cupping forming includes a punch, an upper blank holder, a two-dimensional woven fabric, and a lower blank holder. Among them, the punch, the upper blank holder, and the lower blank holder are modeled as rigid bodies. Fixed constraints are imposed on the upper and lower blank holders. , the punch applies displacement loading , The two-dimensional woven fabric model is in the XOY plane, and the sample size is 100 mm × 100 mm. The warp direction vector is , the weft direction vector is The 4-node reduced integration shell element S4R was used to divide the two-dimensional woven fabric finite element model, and the mesh size was determined to be 1 mm based on mesh sensitivity analysis.

[0074] In order to illustrate the ability of the hyperelastic model proposed in this application to capture the wrinkles of woven fabrics, two types of elements are used to simulate the cupping of woven fabrics: membrane elements and shell elements. The membrane elements can only withstand in-plane deformation, so only the tensile and shear behaviors of the woven fabric can be considered. The shell elements can withstand both in-plane and out-of-plane deformations, so the tensile, shear and bending behaviors of the woven fabric are fully considered. Figure 6 The eccentric tensile deformation behavior of woven fabrics predicted by membrane elements and shell elements is shown respectively. Obviously, the cross section of the woven fabric predicted by membrane elements has no deformation, so wrinkles cannot be simulated. However, the cross section of the woven fabric predicted by shell elements deforms significantly, which can capture the wrinkle behavior. The comparison shows that the proposed hyperelastic model has the ability to capture wrinkles in the deformation process of woven fabrics.

[0075] The specific implementation of each module can refer to the description in the method embodiment, and the embodiments of this application will not be repeated.

[0076] The modeling system of the hyperelastic model for simulating two-dimensional woven fabric wrinkles provided in the present application is described below. The modeling system of the hyperelastic model for simulating two-dimensional woven fabric wrinkles described below and the modeling of the hyperelastic model for simulating two-dimensional woven fabric wrinkles described above can be referenced to each other.

[0077] Reference Figure 7 The present application provides a modeling system for simulating a hyperelastic model of two-dimensional woven fabric wrinkles, comprising: A model building module 710 is used to build a hyperelastic model that fully considers the mechanical behavior of a two-dimensional woven fabric, wherein the two-dimensional woven fabric is composed of warp yarns and weft yarns that are overlapped and woven with each other; A numerical realization module 720, for determining a numerical realization method of a hyperelastic model in a finite element framework, wherein the numerical realization method is realized through a subroutine interface; A wrinkle simulation module 730 is used to simulate the wrinkle defects generated by the two-dimensional woven fabric during the deformation process by using the hyperelastic model through the numerical realization method and a finite element framework; The hyperelastic model is established by defining the strain invariants of the tensile deformation, shear deformation and bending deformation of the 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.

[0078] Optionally, the modeling method of the two-dimensional woven fabric hyperelastic model specifically includes: determining strain invariants for each deformation mode, the deformation mode comprising tensile deformation, shear deformation, and bending deformation; Determining the total strain energy of the two-dimensional woven fabric, decoupling the total strain energy to obtain tensile deformation strain energy, shear deformation strain energy and bending deformation strain energy; determining a membrane strain energy function corresponding to the membrane strain energy, calculating 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 calculating the bending moment based on the bending deformation strain energy and the bending strain invariant; The hyperelastic model is established based on the strain invariant, the decoupling result of the total strain energy and the calculation result of the membrane strain energy function.

[0079] Optionally, the method for obtaining the strain invariant of the deformation mode includes: Determine the curvature tensor to describe the curvature and torsion of the material particles in the current configuration; Determine a deformation gradient tensor according to the relationship between the current position of the material particle and the initial configuration position, and determine the right Cauchy Green strain tensor based on the deformation gradient tensor; Get 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; Determining the tensile strain invariants corresponding to the tensile deformation of the warp yarn and the weft yarn based on the initial unit vector, the initial unit vector and the right Cauchy Green strain tensor; Determine the shear strain invariants corresponding to the shear deformation of the warp yarn and the weft yarn based on the initial unit vector, the initial unit vector, the right Cauchy Green strain tensor and the tensile strain invariant; The tensile strain invariants corresponding to the tensile deformation of the warp yarn and the weft yarn are determined based on the initial unit vector, the initial unit vector and the curvature tensor.

[0080] Optionally, the total strain energy is decoupled to obtain tensile deformation strain energy, shear deformation strain energy and bending deformation strain energy, including: Decomposing the total strain energy into membrane deformation strain energy and bending deformation strain energy; Decomposing the membrane deformation strain energy into tensile deformation strain energy and shear deformation strain energy; The bending deformation strain energy is decomposed into the warp yarn bending deformation strain energy corresponding to the warp yarn bending deformation and the weft yarn bending deformation strain energy corresponding to the warp yarn bending deformation.

[0081] Optionally, the membrane strain energy function corresponding to the membrane strain energy is determined based on the membrane deformation strain energy and the right Cauchy Green strain tensor.

[0082] Optionally, the numerical realization process includes a membrane deformation calculation process and a bending deformation calculation process, and the membrane deformation calculation process includes: Reading the deformation gradient tensor from the subroutine interface of the finite element framework, and calculating the right Cauchy Green strain tensor, defining the unit vectors in the warp direction and the weft direction in the initial configuration, and the membrane strain invariant, and calculating the strain energy of the membrane deformation; Membrane stress is calculated based on the membrane strain energy and is returned to the main program of the finite element framework.

[0083] Optionally, the bending deformation calculation process includes: Reading the curvature tensor from the subroutine interface of the finite element framework, defining the bending strain invariant, and calculating the bending deformation strain energy; The bending moment is calculated according to the bending deformation strain energy, and the bending moment is returned to the main program of the finite element framework.

[0084] It can be understood that the detailed functional implementation of each of the above-mentioned units / modules can be found in the introduction of the aforementioned method embodiment, and will not be repeated here.

[0085] It should be understood that the above-mentioned device is used to execute the method in the above-mentioned embodiment. The implementation principle and technical effect of the corresponding program module in the device are similar to those described in the above-mentioned method. The working process of the device can refer to the corresponding process in the above-mentioned method, which will not be repeated here.

[0086] Based on the method in the above embodiment, the embodiment of the present application provides an electronic device / image signal generator / network device / transmitter / terminal / base station / industrial computer, which may include: a processor (Processor) 810, a communication interface (CommunicationsInterface) 820, a memory (Memory) 830 and a communication bus 840, wherein the processor 810, the communication interface 820, and the memory 830 communicate with each other through the communication bus 840. The processor 810 may call the logic instructions in the memory 830 to execute the method in the above embodiment.

[0087] In addition, the logic instructions in the above-mentioned memory 830 can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product, which is stored in a storage medium and includes a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present application.

[0088] Based on the method in the above embodiment, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program runs on a processor, the processor executes the method in the above embodiment.

[0089] Based on the method in the above embodiment, an embodiment of the present application provides a computer program product. When the computer program product runs on a processor, the processor executes the method in the above embodiment.

[0090] It is understandable that the processor in the embodiment of the present application may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field programmable gate arrays (FPGA) or other programmable logic devices, transistor logic devices, hardware components or any combination thereof. The general-purpose processor may be a microprocessor or any conventional processor.

[0091] The method steps in the embodiments of the present application can be implemented by hardware or by a processor executing software instructions. The software instructions can be composed of corresponding software modules, and the software modules 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, mobile hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor so that the processor can read information from the storage medium 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 be located in an ASIC.

[0092] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented by software, it can be implemented in whole or in part in the form of 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, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions may be transmitted from a website site, computer, server or data center to another website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive (SSD)), etc.

[0093] It should be understood that the various numerical numbers involved in the embodiments of the present application are only used for the convenience of description and are not used to limit the scope of the embodiments of the present application.

[0094] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A method for modeling a hyperelastic model for simulating wrinkles in a two-dimensional woven fabric, characterized in that: include: A hyperelastic model is established that fully considers the mechanical behavior of a two-dimensional woven fabric, wherein the two-dimensional woven fabric is composed of warp yarns and weft yarns overlapped and woven with each other; Determining a numerical implementation method of a hyperelastic model in a finite element framework, wherein the numerical implementation method is implemented through a subroutine interface; The hyperelastic model is used through the numerical realization method to simulate the wrinkle defects generated during the deformation of the two-dimensional woven fabric using a finite element framework; The hyperelastic model is established by defining the strain invariants of the tensile deformation, shear deformation and bending deformation of the 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.

2. The modeling method according to claim 1, characterized in that: The modeling method of the two-dimensional woven fabric hyperelastic model specifically includes: determining strain invariants for each deformation mode, the deformation mode comprising tensile deformation, shear deformation, and bending deformation; Determining the total strain energy of the two-dimensional woven fabric, decoupling the total strain energy to obtain tensile deformation strain energy, shear deformation strain energy and bending deformation strain energy; determining a membrane strain energy function corresponding to the membrane strain energy, calculating 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 calculating the bending moment based on the bending deformation strain energy and the bending strain invariant; The hyperelastic model is established based on the strain invariant, the decoupling result of the total strain energy and the calculation result of the membrane strain energy function.

3. The modeling method according to claim 2, characterized in that: The method for obtaining the strain invariant of the deformation mode includes: Determine the curvature tensor to describe the curvature and torsion of the material particles in the current configuration; Determine a deformation gradient tensor according to the relationship between the current position of the material particle and the initial configuration position, and determine the right Cauchy Green strain tensor based on the deformation gradient tensor; Get 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; Determining the tensile strain invariants corresponding to the tensile deformation of the warp yarn and the weft yarn based on the initial unit vector, the initial unit vector and the right Cauchy Green strain tensor; Determine the shear strain invariants corresponding to the shear deformation of the warp yarn and the weft yarn based on the initial unit vector, the initial unit vector, the right Cauchy Green strain tensor and the tensile strain invariant; The tensile strain invariants corresponding to the tensile deformation of the warp yarn and the weft yarn are determined based on the initial unit vector, the initial unit vector and the curvature tensor.

4. The modeling method according to claim 2, characterized in that: The total strain energy is decoupled to obtain tensile deformation strain energy, shear deformation strain energy and bending deformation strain energy, including: Decomposing the total strain energy into membrane deformation strain energy and bending deformation strain energy; Decomposing the membrane deformation strain energy into tensile deformation strain energy and shear deformation strain energy; The bending deformation strain energy is decomposed into the warp yarn bending deformation strain energy corresponding to the warp yarn bending deformation and the weft yarn bending deformation strain energy corresponding to the warp yarn bending deformation.

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

6. The modeling method according to claim 2, characterized in that: The numerical realization process includes a membrane deformation calculation process and a bending deformation calculation process, and the membrane deformation calculation process includes: Reading the deformation gradient tensor from the subroutine interface of the finite element framework, and calculating the right Cauchy Green strain tensor, defining the unit vectors in the warp direction and the weft direction in the initial configuration, and the membrane strain invariant, and calculating the strain energy of the membrane deformation; Membrane stress is calculated based on the membrane strain energy and is returned to the main program of the finite element framework.

7. The modeling method according to claim 6, characterized in that: The bending deformation calculation process includes: Reading the curvature tensor from the subroutine interface of the finite element framework, defining the bending strain invariant, and calculating the bending deformation strain energy; The bending moment is calculated according to the bending deformation strain energy, and the bending moment is returned to the main program of the finite element framework.

8. A modeling system for simulating a hyperelastic model of two-dimensional woven fabric wrinkles, characterized in that: include: A model building module, for building a hyperelastic model that fully considers the mechanical behavior of a two-dimensional woven fabric, wherein the two-dimensional woven fabric is composed of warp yarns and weft yarns that overlap and weave with each other; A numerical realization module, used for determining a numerical realization method of a hyperelastic model in a finite element framework, wherein the numerical realization method is realized through a subroutine interface; A wrinkle simulation module, used to simulate the wrinkle defects generated in the deformation process of the two-dimensional woven fabric by using the hyperelastic model through the numerical realization method and a finite element framework; The hyperelastic model is established by defining the strain invariants of the tensile deformation, shear deformation and bending deformation of the 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.

9. An electronic device, characterized in that: include: at least one memory for storing a computer program; At least one processor is used to execute the program stored in the memory. When the program stored in the memory is executed, the processor is used to execute the method according to any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program runs on a processor, the processor is caused to execute the method according to any one of claims 1 to 7.

Images