A face-based smoothed finite element method (FS-FEM) for visco-elastoplastic analyses of 3D solids using tetrahedral mesh

A face-based smoothed finite element method (FS-FEM) using tetrahedral elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the solid mechanics problems. In this paper, the FS-FEM is further extended to more complicated visco-elastoplastic analyses of 3D solids using the von-Mises yield function and the Prandtl–Reuss flow rule. The material behavior includes perfect visco-elastoplasticity and visco-elastoplasticity with isotropic hardening and linear kinematic hardening. The formulation shows that the bandwidth of stiffness matrix of FS-FEM is larger than that of FEM, and hence the computational cost of FS-FEM in numerical examples is larger than that of FEM for the same mesh. However, when the efficiency of computation (computation time for the same accuracy) in terms of a posteriori error estimation is considered, the FS-FEM is more efficient than the FEM.