α-Finite Element Method for Frictionless and Frictional Contact Including Large Deformation

Abstract

In this paper, one of the variants of the smoothed finite element method, [Formula: see text]-FEM is adopted for hyperelastic material with large deformation and contact nonlinearity in two dimensions. The salient feature of the [Formula: see text]-FEM is that it is stable and this is accomplished by using the scale factor [Formula: see text] to combine the compatible finite element method and the node-based smoothed finite element method. The framework is implemented in the commercial software, Abaqus using the user element feature, UEL. The efficacy and robustness of the proposed work is demonstrated by several benchmark problems in both linear and nonlinear elasticity with and without contacts. The developed UEL and the associated files can be downloaded from https://github.com/nsundar/alphaFEM .