Simple and robust element-free Galerkin method with almost interpolating shape functions for finite deformation elasticity

In this paper, we present a meshless method belonging to the family of element-free Galerkin (EFG) methods. The presented meshless method allows accurate enforcement of essential boundary conditions. The method uses total Lagrangian formulation with explicit time integration to facilitate code simplicity and robust computations in applications that involve large deformations and non-linear materials. We use a regularized weight function, which closely approximates the Kronecker delta, to generate interpolating shape functions. The imposition of the prescribed displacements on the boundary becomes as straightforward as in the finite element method (FEM). The effectiveness and accuracy of the proposed method is demonstrated using 3D numerical examples that include cylinder indentation by 70% of its initial height, and indentation of the brain.