An Element-Free Galerkin Analysis of Hyperelastic Materials

Nonlinear formulations of the Element-Free Galerkin Method (EFGM) are presented for the large deformation analysis of Ogden’s hyperelastic materials, which are considered incompressible. The EFGM requires no explicit mesh in computation and therefore avoids mesh distortion difficulties. In this study, the implementation of the Moving Least Squares (MLS) approximation with the quartic spline weight function is used to obtain the shape function and the transformation method is proposed to impose the essential boundary conditions. Numerical results for a typical example show that the present method is effective in dealing with large deformation hyperelastic materials problems.