Finite Element Simulation Of Surface Wrinkle Of Functionally Gradient Material Block Under Compression

Surface instability is a common problem in engineering.The applicability and safety of structures or materials are reduced because of instability.In some fields,new properties and functions of materials have emerged due to the change of morphology,and new applications have been obtained,such as biomedical engineering,flexible electronics and so on.The research results of surface instability at home and abroad include the study of instability morphology,numerical theoretical solutions,and the influence of structural shape on surface instability.The main research results are homogeneous flexible materials,while the research on surface wrinkling of functionally graded materials is less.In this paper,hyperelastic functionally gradient material is taken as the research object,and the UMAT subroutine of its constitutive model is completed.The finite element model of hyperelastic functionally gradient material block is established by ABAQUS software,and the mechanical behavior of its surface wrinkling is simulated.Functionally gradient material(FGM)is a new type of composite material.By continuously changing the composition and structure of the material at the interface,the material properties on both sides of the interface can be mitigated continuously and excessively,which can effectively solve the abrupt change of the interface of the composite material and improve the integrity of the material.By means of experiments,theoretical analysis and numerical simulation,scholars at home and abroad have made some achievements in the study of mechanical properties,material preparation methods,gradient design and numerical simulation of functionally graded materials.As one of the common materials,the mechanical properties of Hyperelastic Materials have particularity compared with linear elastic materials.Under external stimulus,the mechanical response of Hyperelastic Materials is larger,and the stress-strain relationship of materials is nonlinear.When describing the mechanical properties of hyperelastic functionally gradient materials,the constitutive model has a greater impact on the calculation results.However,there is no constitutive model of functionally graded materials in the common finite element software material library.In this paper,the UMAT subroutine in ABAQUS is used to define the constitutive model of hyperelastic functionally graded materials.Therefore,the research contents of this paper are as follows:(1)Neo-Hookean model is selected as the hyperelastic constitutive model according to the scope of application of the commonly used hyperelastic constitutive model and the research object of this subject.(2)Comparing the properties of Hyperelastic Materials defined in ABAQUS program,UAMT subroutine is chosen to define the constitutive relationship of NeoHookean model.Neo-Hookean constitutive model,Jacobian matrix and deformation gradient are defined by Fortran language.The UAMT subroutine for Hyperelastic Materials is developed.(3)The volume fraction theory of functionally graded materials is introduced into the hyperelastic constitutive model to complete the definition of UMAT subroutine for hyperelastic functionally graded materials.Based on this subroutine,a plane strain finite element model of superelastic functionally graded material(FGM)surface wrinkling is established in ABAQUS,and the stress distribution,critical strain and wrinkle waveform are studied.(4)The effects of material parameters and geometric parameters on wrinkling of hyperelastic functionally gradient materials are studied and compared with theoretical solutions and experimental results of homogeneous materials.The accuracy of UMAT subroutine of Neo-Hookean model for hyperelastic functionally graded materials is verified by the above research contents.It provides a method for defining the properties of hyperelastic functionally graded materials and expands the ABAQUS program material library.The results of numerical simulation based on UMAT subroutine show that there is a deviation between the critical strain of the model wrinkling and the theoretical and experimental values of homogeneous materials.Changing the geometrical size of the material will not affect the critical strain of wrinkling on the material surface,but the larger the aspect ratio is,the longer the wrinkle wavelength is,the smaller the aspect ratio is,and the smaller the wrinkle wavelength is.Changing the elastic modulus of material components will affect the critical strain of wrinkling.The greater the difference of elastic modulus of material components,the smaller the critical strain.On the contrary,the smaller the difference of elastic modulus,the larger the critical strain,and the closer to the critical strain value of homogeneous materials.The critical strain of wrinkling does not change with Poisson's ratio,but the closer the two surface Poisson's ratios are in the direction of gradient change,and the closer the Poisson's ratio is to 0.5,the more obvious the wrinkling effect is.