Study On The Mechanical Behavior Of Visco-Hyperelastic Materials With Smoothed Finite Element Method

The viscoelastic model is a material constitutive model with both viscous fluid and elastic solid characteristics,and it is an import ant part of cont inuum mechanics.In recent years,with the development and progress of new building materials,composite materials,bio materials and other disciplines,the research on the viscoelastic behavior of materials has become more and more in-depth.Through the cont inuous enhancement of the understanding of viscoelasticit y theory,the nonlinear viscoelasticit y theory has been paid attent ion by researchers.With the improvement of computer software and hardware,advanced simulat ion technology has become an indispensable tool for product design and analysis in aerospace,civ il engineering and other related fields.With the development of technology and the refinement of research,higher requirements are placed on the accuracy,efficiency and robustness of numerical methods.As the most widely used and commercialized numerical algorithm,FEM has shown good applicabilit y in various fields,but it also has some limitations,such as poor calculation accuracy on linear elements,and cumbersome pre-processing of high-order elements;volumetric locking problems;mesh matching for discontinuit y problems,etc.The nonlinear viscoelast ic mechanical behavior is often accompanied by large geometric nonlinear deformat ion,which also has higher requirements on the mesh distortion tolerance of the calculat ion method.In this paper,using gradient smoothing technology and W~2 formulat ion,and considering mult iple element types,time-dependent nonlinear visco-hyperelastic materials,and geometric nonlinear large deformation,a nonlinear smoothed finite element method solver is proposed The calculat ion accuracy,efficiency and robustness are analyzed by mult i-material and mult i-component numerical examples.The main works are exhibited as follows:(1)An n-sided polygonal smoothed finite element method(n SFEM)is formulated for dynamic analyses of nonlinear problems of visco-hyperelast ic materials undergoing large deformations.By construct ing two types of smoothing domains in polygonal elements,using Gaussian divergence theorem and gradient smoothing technique,the element integrals in polygonal element are transformed into boundary integrals of smoothing domains,and the continuit y requirement o f the trial funct ion is reduced.The simple averaging point interpolation technique is used to calculate the values of the shape funct ions on the boundary of smoothing domains.The advantages of present method in computational accuracy,efficiency,and volumetric locking problems for finite-strain plane problems are demonstrated by typical numerical experiments.(2)Based on automatically generated tetrahedral elements,a Total Lagrangian Explicit Select ive S-FEM is formulated to analyze the dynamic behavior of 3D visco-hyperelastic large deformation problem undergoing extremely large deformat ion.Considering the discrete advantage of tetrahedral element in complex geometric models,and adopting selective integration scheme and gradient smoothing technique,a low-order element smoothed finite element algorithm for quasi-incompressible bio logical soft tissue is established.Combined with the features that the smooth ing domain informat ion in the TL format ion does not need iterative update,and the explicit calculat ion does not require tangent st iffness matrix,the accuracy and efficiency of soft tissue modeling and simulat ion are improved.Numerical experiments show that the present method significant ly improves the computat ional accuracy and efficiency of linear tetrahedral elements in simulat ion,exhibits robust mesh distort ion capabilit y and volumetric immunity,and is an efficient nonlinear solid mechanics solver.(3)The generalized Maxwell visco-hyperelastic solid model for convolut ion integration is coupled with the select ive S-FEM,which makes shear relaxat ion and bulk relaxat ion independent of each other,making the visco-hyperelast ic const itutive model more flexible.Different time-dependent visco-hyperelastic solid structure simulat ions are achieved by changing the type of hyperelast icit y model in the convolut ion integration,demonstrating goo d scalabilit y.Numerical experiments verify that the Maxwell visco-hyperelast ic solid model has the characterist ics of strain rate sensit ivit y and stress relaxation.(4)A unified-implementation of smoothed finite element method on tetrahedral elements(UI-SFEM-T4)is developed to simulate the mult i-material and mult i-component visco-hyperelast ic solid mechanics problems,and the stabilit y of the method is discussed theoretically.The basic idea is to construct or combine different smoothing domains in the S-FEM"family"based on the gradient smoothing technology according to the mechanical characterist ics of different parts to solve the numerical difficult ies of corresponding materials or components.The accuracy,efficiency,and rate of convergence of the method are verified by solving stat ic and finite-strain multi-material,mult i-component solid mechanics problems,and finally the simulat ion of crimped fiber-reinforced composites is effectively simulated.(5)A unified-implementation of smoothed finite element method(UI-SFEM)is established to solve the mechanical behavior of the complex bio logical tissues of arterial walls,orthodont ics,and the human spine.Considering the complex geometric structure of bio logical t issue,the opt imal discrete spat ial domain unit type can be selected according to the geometric model of the component.Considering different types of background meshes and gradient smoothing techniques,a cross-element unified-implementation of smoothed finite element method is established,so that UI-SFEM not only considers the material and numerical characterist ics,but also considers the geometric characterist ics,and can fully explo it the advantages of the S-FEM,making it more"free"to solve various complex biological systems.By establishing different smoothing domains on tetrahedral elements and triangular prism elements,UI-SFEM is used to simulate biological t issues with complex geometry and various materials.