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An edge-based smoothed finite element method for visco-elastoplastic analyses of 2D solids using triangular mesh. (English) Zbl 1398.74382
Summary: An edge-based smoothed finite element method (ES-FEM) using triangular elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the elastic solid mechanics problems. In this paper, the ES-FEM is extended to more complicated visco-elastoplastic analyses using the von-Mises yield function and the Prandtl-Reuss flow rule. The material behavior includes perfect visco-elastoplasticity and visco-elastoplasticity with isotropic and linear kinematic hardening. The formulation shows that the bandwidth of stiffness matrix of the ES-FEM is larger than that of the FEM, and hence the computational cost of the ES-FEM in numerical examples is larger than that of the 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 ES-FEM is more efficient than the FEM.

##### MSC:
 74S05 Finite element methods applied to problems in solid mechanics 74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) 74D05 Linear constitutive equations for materials with memory 74S30 Other numerical methods in solid mechanics (MSC2010)
XFEM
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