Numerical instability in the element-free Galerkin method for bi-material modeling

Abstract

This paper presents numerical results from modeling of bi-material problems using the element-free Galerkin method. The conventional EFG shape functions do not pass through the nodal data, imposition of nodal constraints brings difficulties, thus some special techniques must be employed. In bi-material problems, connecting the two subdomains of different properties may still be possible via Lagrange multipliers, penalty function, Nitsche’s formulation, or direct imposition when using a regularized weighting function to transform the EFG shape functions. All these mentioned techniques are explored and compared in this paper. Some remarks about numerical instabilities are reported.