FE-EFGM Coupling using maximum entropy shape functions and its application to small and finite deformation

The element-free Galerkin method (EFGM) is superior to its counterpart the finite element method (FEM) in terms of accuracy and convergence but is computationally expensive. Therefore it is more practical to use the EFGM only in a region, which is difficult to model using the FEM, while the FEM can be used in the remaining part of the problem domain. In the conventional EFGM, moving least squares (MLS) shape functions are used for the approximation of the field variables. These shape functions do not possess the Kronecker delta property and it is therefore not straightforward to couple the EFGM with the FEM. Local maximum entropy (max-ent) shape functions are an alternative way to couple the EFGM and FEM. These shape functions possess a weak Kronecker delta property at boundaries, which provides a natural way to couple the EFGM with the FEM as compared to the MLS basis functions, which need extra care to properly couple the two regions. This formulation removes the need for interface elements between the FEM and the EFGM, unlike the approach adopted by most researchers. This approach is verified using benchmark problems from small and finite deformation.