Three-dimensional variable-node elements based upon CS-FEM for elastic-plastic analysis

In this paper, variable-node elements (VNEs) based on the cell-based smoothed finite element method (CS-FEM) are proposed with emphasis on their applications for elasto-plastic finite deformation. The formulation of CS-FEM is extended to cover elastic-plastic deformations beyond the classical linear theory of elasticity, which has been the major application domain of smoothed finite elements. The finite strain deformations are treated with the aid of the formulation based on the hyperelastic constitutive equation. The volumetric locking originating from the nearly incompressible behavior of elasto-plastic deformations is remedied by relaxing volumetric strain through its mean value. In addition, the existing VNEs limited to linear elastic analysis is extended to analysis of elasto-plastic deformations with the aid of CS-FEM. The comparison with the conventional finite elements and Abaqus demonstrates the effectiveness and accuracy of the present approach.