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

TL;DR

This paper introduces a simple, meshless element-free Galerkin method with interpolating shape functions that accurately enforces boundary conditions and handles large deformations in nonlinear elasticity.

Contribution

It presents a novel meshless EFG method using a regularized weight function for interpolating shape functions, improving boundary condition enforcement and robustness in large deformation problems.

Findings

Accurate boundary condition enforcement comparable to finite element methods.

Effective in large deformation and nonlinear material simulations.

Validated with 3D examples including cylinder and brain indentation.

Abstract

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.