CN-119761126-B - Modeling method and system for super-elastic model for simulating two-dimensional woven fabric wrinkles

CN119761126BCN 119761126 BCN119761126 BCN 119761126BCN-119761126-B

Abstract

The application belongs to the technical field of mechanical simulation and prediction of woven fabrics, and particularly discloses a modeling method and a system of a super-elastic model for simulating wrinkles of a two-dimensional woven fabric, wherein the method comprises the steps of establishing the super-elastic model which comprehensively considers the mechanical behavior of the two-dimensional woven fabric, and the two-dimensional woven fabric is formed by mutually overlapping and weaving warp yarns and weft yarns; the method comprises the steps of determining a numerical value implementation method of a super-elastic model in a finite element frame, implementing the numerical value implementation method through a subprogram interface, simulating fold defects generated in a deformation process of a two-dimensional woven fabric by the super-elastic model through the numerical value implementation method by adopting the finite element frame, wherein the super-elastic model is established by defining strain invariants of tensile deformation, shear deformation and bending deformation of the two-dimensional woven fabric, obtaining corresponding strain energy functions based on the strain invariants, and calculating film stress and bending moment based on the strain energy functions. The application can accurately simulate the fold defect generated in the deformation process of the two-dimensional woven fabric.

Inventors

Zhou Helezi
ZHOU HUAMIN
LU XING
HUANG ZHIGAO
PENG XIONGQI
HUANG WEI

Assignees

华中科技大学

Dates

Publication Date: 20260508
Application Date: 20241219

Claims (7)

1. A method of modeling a superelastic model simulating two-dimensional woven fabric wrinkles, comprising: Establishing a super-elastic model comprehensively considering the mechanical behavior of a two-dimensional woven fabric, wherein the two-dimensional woven fabric is formed by mutually overlapping and weaving warp yarns and weft yarns; Determining a numerical value implementation method of the super-elastic model in the finite element frame, wherein the numerical value implementation method is implemented through a subroutine interface; simulating fold defects generated in the deformation process of the two-dimensional woven fabric by using the super-elastic model through the numerical value implementation method by adopting a finite element frame; the super-elastic model is established by defining strain invariants of tensile deformation, shear deformation and bending deformation of a two-dimensional woven fabric, obtaining corresponding strain energy functions based on the strain invariants, and calculating film stress and bending moment based on the strain energy functions; the modeling method of the two-dimensional woven fabric super-elastic model specifically comprises the following steps: Determining a strain invariant for each deformation mode, the deformation modes including tensile deformation, shear deformation, and bending deformation; The method comprises the steps of determining total strain energy of a two-dimensional woven fabric, decoupling and decomposing the total strain energy into film deformation strain energy and bending deformation strain energy, decomposing the film deformation strain energy into warp bending deformation strain energy corresponding to warp bending deformation and weft bending deformation strain energy corresponding to warp bending deformation; Determining a membrane strain energy function corresponding to the membrane strain energy, calculating membrane stress based on a determinant of the membrane strain energy function combined with a deformation gradient tensor and a transpose of the deformation gradient tensor, and calculating bending moment based on bending deformation strain energy and bending strain invariants; The superelastic model is established based on the strain invariants, the decoupling result of the total strain energy and the calculation result of the membrane strain energy function, and the superelastic model is specifically shown as the following formula: Wherein, the The strain invariants associated with warp and weft tensile deformation respectively, Is the strain invariant associated with shear deformation between warp and weft yarns, The strain invariants are respectively related to warp and weft bending deformation; is a curvature tensor in the current configuration, describing the curvature and flexibility of the material particles; The initial unit vectors in the warp and weft directions, respectively, in an initial configuration, which is an undeformed configuration, The current unit vectors of warp yarn and weft yarn directions in the current configuration are respectively, and the current configuration is a deformed configuration; for the right Ke Xige Lin Yingbian tensor, the following formula is defined: Wherein, the For the deformation gradient tensor, the formula is defined as: Wherein, the The position 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: Wherein, the Is the strain energy of the deformation of the membrane, Is the strain energy of bending deformation; Film strain energy The decomposition into two parts related to tensile and shear deformation is as follows: Wherein, the Bending strain energy associated with warp and weft bending deformations, respectively; based on the film strain energy, the film stress is calculated as shown in the following formula: Wherein, the For the determinant of deformation gradient tensor, for describing the volume change of the infinitesimal before and after deformation, For deformation gradient tensor Is a transpose of (2); Based on the bending deformation strain energy, the bending moment is calculated as follows: Wherein, the Bending moments along the warp and weft directions, respectively.
2. The modeling method of claim 1, wherein the determining a membrane strain energy function for a membrane strain energy is determined from a membrane deformation strain energy and a right Ke Xige Lin Yingbian tensor.
3. The modeling method of claim 1, wherein the numerical implementation procedure includes a membrane deformation calculation procedure and a bending deformation calculation procedure, the membrane deformation calculation procedure including: Reading deformation gradient tensors from a subroutine interface of the finite element frame, calculating right cauchy strain tensors, defining unit vectors of warp direction and weft direction in an initial configuration, and calculating strain energy of film deformation; And calculating the membrane stress according to the membrane strain energy, and returning the membrane stress to the main program of the finite element frame.
4. A modeling method in accordance with claim 3, wherein the bending deformation calculation procedure comprises: Reading curvature tensors from a subroutine interface of the finite element frame, defining bending strain invariants, and calculating bending deformation strain energy; And calculating a bending moment according to the bending deformation strain energy, and returning the bending moment to the main program of the finite element frame.
5. A modeling system for simulating a superelastic model of a two-dimensional woven fabric fold, comprising: the model building module is used for building a super-elastic model comprehensively considering the mechanical behavior of a two-dimensional woven fabric, wherein the two-dimensional woven fabric is formed by mutually overlapping and weaving warp yarns and weft yarns; The numerical value implementation module is used for determining a numerical value implementation method of the super-elastic model in the finite element frame, and the numerical value implementation method is implemented through a subroutine interface; The fold simulation module is used for simulating fold defects generated in the deformation process of the two-dimensional woven fabric by adopting a finite element frame through the numerical value implementation method; the super-elastic model is established by defining strain invariants of tensile deformation, shear deformation and bending deformation of a two-dimensional woven fabric, obtaining corresponding strain energy functions based on the strain invariants, and calculating film stress and bending moment based on the strain energy functions; the modeling method of the two-dimensional woven fabric super-elastic model specifically comprises the following steps: Determining a strain invariant for each deformation mode, the deformation modes including tensile deformation, shear deformation, and bending deformation; The method comprises the steps of determining total strain energy of a two-dimensional woven fabric, decoupling and decomposing the total strain energy into film deformation strain energy and bending deformation strain energy, decomposing the film deformation strain energy into warp bending deformation strain energy corresponding to warp bending deformation and weft bending deformation strain energy corresponding to warp bending deformation; Determining a membrane strain energy function corresponding to the membrane strain energy, calculating membrane stress based on a determinant of the membrane strain energy function combined with a deformation gradient tensor and a transpose of the deformation gradient tensor, and calculating bending moment based on bending deformation strain energy and bending strain invariants; Establishing the superelastic model based on the strain invariants, decoupling results of total strain energy and calculation results of a membrane strain energy function; Specifically, the method is shown in the following formula: Wherein, the The strain invariants associated with warp and weft tensile deformation respectively, Is the strain invariant associated with shear deformation between warp and weft yarns, The strain invariants are respectively related to warp and weft bending deformation; is a curvature tensor in the current configuration, describing the curvature and flexibility of the material particles; The initial unit vectors in the warp and weft directions, respectively, in an initial configuration, which is an undeformed configuration, The current unit vectors of warp yarn and weft yarn directions in the current configuration are respectively, and the current configuration is a deformed configuration; for the right Ke Xige Lin Yingbian tensor, the following formula is defined: Wherein, the For the deformation gradient tensor, the formula is defined as: Wherein, the The position 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: Wherein, the Is the strain energy of the deformation of the membrane, Is the strain energy of bending deformation; Film strain energy The decomposition into two parts related to tensile and shear deformation is as follows: Wherein, the Bending strain energy associated with warp and weft bending deformations, respectively; based on the film strain energy, the film stress is calculated as shown in the following formula: Wherein, the For the determinant of deformation gradient tensor, for describing the volume change of the infinitesimal before and after deformation, For deformation gradient tensor Is a transpose of (2); Based on the bending deformation strain energy, the bending moment is calculated as follows: Wherein, the Bending moments along the warp and weft directions, respectively.
6. An electronic device, comprising: At least one memory for storing a computer program; At least one processor for executing the memory-stored program, which processor is adapted to perform the method according to any of claims 1-4 when the memory-stored program is executed.
7. A computer readable storage medium storing a computer program, characterized in that the computer program, when run on a processor, causes the processor to perform the method according to any one of claims 1-4.

Description

Modeling method and system for super-elastic model for simulating two-dimensional woven fabric wrinkles Technical Field The application belongs to the technical field of mechanical simulation prediction of woven fabrics, and particularly relates to a modeling method and a system for a super-elastic model for simulating wrinkles of a two-dimensional woven fabric. Background The two-dimensional woven fabric is formed by alternately weaving warp yarns and weft yarns, does not need additional suture lines, and is suitable for fibers with larger bending rigidity. Two-dimensional woven fabrics can meet the requirements of composite materials on directional mechanical properties under different service environments due to high specific strength and high specific rigidity, and have been widely used for reinforcing bodies of fiber reinforced composite materials. The liquid forming process is one of the most widely used processes for manufacturing fiber reinforced composites at present. During the preforming of the liquid forming process, the woven fabric can deform significantly and even become defective. Therefore, it is necessary to develop a stable numerical simulation method to simulate the deformation and defects of the woven fabric. Wrinkles are the predominant defect in the deformation process of woven fabrics. The generation of wrinkles depends on the material properties of the woven fabric, including stretching, shearing and bending behaviour. However, the material properties of woven fabrics differ from conventional continuous materials such as rubber, metal, etc. The traditional continuity material follows Kirchhoff theory, i.e. the membrane stiffness is coupled with the bending stiffness, which can be calculated directly from the membrane stiffness. However, the woven fabric does not follow Kirchhoff theory, and the bending stiffness is much lower than the value calculated based on the membrane stiffness. The film behaviour should be decoupled from the bending behaviour in modeling the deformation model of the woven fabric. Numerous numerical models have been developed to attempt to simulate the wrinkling defects of woven fabrics, such as the stress-shell synthesis method, the hybrid cell method, and the like. The stress synthesis shell method introduces the mesoscopic properties of woven fabrics into a macro-scale analysis, such models assuming that each cell contains a specified number of woven cells, calculates strain energy based on the cell deformation mode and derives cell node loads. Such methods are often very complex and difficult to implement in a general finite element framework. The hybrid cell method uses two cells to model the mechanical behavior of the woven fabric, one cell (membrane cell) to model the membrane behavior of the woven fabric and one cell (beam/shell cell) to model the bending behavior of the woven fabric. The hybrid cell method still follows Kirchhoff theory and still overestimates the bending stiffness of the woven fabric. In general, the existing method for simulating the folds of the woven fabric still cannot accurately evaluate the mechanical behavior of the woven fabric, and cannot accurately simulate the fold defects of the woven fabric. Disclosure of Invention Aiming at the defects of the prior art, the application aims to provide a modeling method and a modeling system for a super-elastic model for simulating wrinkles of a two-dimensional woven fabric, and aims to solve the problems that the existing method for simulating the wrinkles of the woven fabric still cannot accurately evaluate the mechanical behavior of the woven fabric and cannot accurately simulate the wrinkles of the woven fabric. To achieve the above object, in a first aspect, the present application provides a modeling method of a super elastic model for simulating wrinkles of a two-dimensional woven fabric, including: Establishing a super-elastic model comprehensively considering the mechanical behavior of a two-dimensional woven fabric, wherein the two-dimensional woven fabric is formed by mutually overlapping and weaving warp yarns and weft yarns; Determining a numerical value implementation method of the super-elastic model in the finite element frame, wherein the numerical value implementation method is implemented through a subroutine interface; simulating fold defects generated in the deformation process of the two-dimensional woven fabric by using the super-elastic model through the numerical value implementation method by adopting a finite element frame; the super-elastic model is established by defining strain invariants of tensile deformation, shear deformation and bending deformation of the two-dimensional woven fabric, obtaining corresponding strain energy functions based on the strain invariants, and calculating film stress and bending moment based on the strain energy functions. Optionally, the modeling method of the two-dimensional woven fabric super-elasticity model specifically compr