Mesh-independent data point finite element method (MDP-FEM) for large deformation elastic-plastic problems - An application to the problems of diffused necking

Abstract

In this paper, a method to carry out the finite strain elastic-plastic analysis using a remeshing technique is presented. When the remeshing is performed, deformation history dependent physical quantities that are stored at the integration points of finite elements need to be transferred to those of the refined finite elements. Such operations are generally performed based on the shape functions of the finite elements. A typical procedures are that i) the strain history dependent quantities are assigned at the nodal points and ii) interpolations are performed by the shape functions. Such processes assume that the sizes and the arrangements of finite elements change moderately after the remesh. We are aiming at developing a methodology that allows drastic changes in mesh arrangements and sizes and in even kinds of finite elements when the remeshing is carried out. We propose a method that the deformation history dependent physical quantities are stored at points independent of the finite element mesh. They move along with the deformation of the solid. The physical quantities at the points evolve in a Lagrange manner. We name such points to be Mesh-independent Data Points (MDPs). The MDPs take the function to store the physical quantities whereas the finite element mesh takes that of performing the numerical integration. Necessary variables are mapped between the MDPs and the finite element. We call proposed technique to be MDP-Finite Element Method (MDP-FEM). This paper describes the concept of the MDP-FEM and numerical implementations are discussed first. Then, the analyses of diffused necking of tensile bars are presented for a demonstrative purpose.