A meshless local natural neighbor interpolation method for two-dimension incompressible large deformation analysis

A meshless local natural neighbor interpolation method (MLNNIM) is utilized to build shape functions for solving elastoplastic problems in this paper. This method searches natural neighbor nodes of the given point and defines local Delaunay triangles. Total Lagrangian (TL) and Updated Lagrangian (UL) formulae have been derived and analyzed. Consideration of the constitutive law and numerical efficiency indicates that the UL formulation is more expedient and attractive in practical problems of solid mechanics. Combined with the linearized UL formulation, the MLNNIM was used to solve problems of two-dimension elastoplastic large deformation. Finally, two representative numerical examples are given to demonstrate the effectiveness and superiority of the MLNNIM combined with the UL formulation for two-dimension incompressible large deformation problems.