2-D large deformation analysis of nearly incompressible body by natural element method

Recently, the natural element method based on the Voronoi diagram and Delaunay triangulation has being intensively explored, as an advanced meshfree method. But, most of studies have been restricted to the linear elasticity problem. In this context, this study intends to explore its applicability to the non-linear solid mechanics, through the 2-D large deformation analysis of nearly incompressible bodies. The non-linear natural element approximation is implemented by the linearized total Lagrangian mixed u–p formulation incorporated with the penalty method. Numerical results illustrating the theoretical work are also presented.