On solving large strain hyperelastic problems with the natural element method

In this paper, an extension of the natural element method (NEM) is presented to solve finite deformation problems. Since NEM is a meshless method, its implementation does not require an explicit connectivity definition. Consequently, it is quite adequate to simulate large strain problems with important mesh distortions, reducing the need for remeshing and projection of results (extremely important in three-dimensional problems). NEM has important advantages over other meshless methods, such as the interpolant character of its shape functions and the ability of exactly reproducing essential boundary conditions along convex boundaries. The -NEM extension generalizes this behaviour to non-convex boundaries. A total Lagrangian formulation has been employed to solve different problems with large strains, considering hyperelastic behaviour. Several examples are presented in two and three dimensions, comparing the results with the ones of the finite element method. NEM performs better showing its important capabilities in this kind of applications