Finite Element Simulation Of Wrinkling In The Soft FG Tube

Functionally graded materials belong to the category of composite materials.They combine a variety of materials in accordance with a certain law,so their structure and mechanical properties are changed according to a certain law,so as to achieve comprehensive utilization of the advantages of each component material,and to avoid the defects traditional simple material.In the existing studies on the mechanical properties of functionally graded materials,linear elastic materials are mostly used as their component materials.The mechanical properties of the functionally graded materials are studied through finite element software,experiments,and theoretical calculations.However,Few studies have used hyperelastic materials as component materials of functionally graded materials at home and abroad.Therefore,hyperelastic materials are used as component materials of functionally graded materials in this study,and a two-dimensional planar model of functionally graded tube is established based on this FGM.Then the finite element simulation of the wrinkling behavior is performed.In this paper,we use the secondary development interface provided by ABAQUS to expand the material library of the software.The Neo-Hookean material is used as the component material of the functionally graded material to realize the definition of its constitutive model in UMAT.Then based on the UMT subroutine,the wrinkling of the functionally graded hose is simulated in ABAQUS,and the influence of the material and model parameters on the wrinkling of the free surface of the inner wall of the hose is explored.The main research content of this paper is as follows:(1)The constitutive theory of hyperelastic materials are reviewed,and the commonly used hyperelastic material constitutive models are summarized.The strain energy density function and stress calculation theory for commonly used hyperelastic materials are briefly introduced;(2)The implementation of hyperelastic materials in ABAQUS are summarized to compare the advantages and disadvantages of various methods.The Neo-Hookean model is selected as the research object of this paper.Based on the Neo-Hookean model constitutive relationship,the UMAT subroutine is developed and the correctness of the developed subroutine is verified.Based on the developed subroutines,the UMAT subroutine for hyperelastic functional gradient material is developed and the material library of ABAQUS is improved.(3)The wrinkling phenomenon of functionally graded tube is simulated based on functional gradient material UMAT subroutine,and the effects of material parameters and model parameters to the wrinkling phenomenon of functionally graded tube is discussed.The critical strain of the free surface of the tube’s inner wall which leads to wrinkle is found.At the same time,qualitative analysis of the influence of changes in material parameters and model parameters on the wrinkling appearance of the inner wall of the FGM tube is performed.This paper develops the UMAT subroutine of Neo-Hookean material based on the constitutive theory of hyperelastic materials and verifies its correctness.Based on this,UMAT subroutine of hyper-elastic functional gradient material is developed and ABAQUS software library is extended.The wrinkling of the inner wall of a functionally graded tube is simulated under given conditions and based on the UMAT subroutine developed.The radial critical strain value and the circumferencial critical strain value of the free surface wrinkling of the inner wall of the functionally graded tube are obtained through fitting.At the same time,it is found that the change of the elastic modulus ratio of the component material of the functional gradient tube will not affect the radial critical strain value and the critical ring strain value,but the change of the Poisson’s ratio of the component material will lead to the change.Changes in the radius,thickness,and displacement boundary conditions of functionally graded tube also significantly affect the wrinkling of the inner wall,resulting in no wrinkling of the inner wall or non-convergence of finite element calculations.