  In this paper, we present a meshless method belonging to the family of
element-free Galerkin (EFG) methods. The distinguishing feature of the
presented meshless method is that it 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 (FE) method. 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.
