Application of a three-field natural neighbour method in elastoplasticity

The natural neighbour method can be considered as one of the many variants of the meshless
methods. Classically, the development of these methods is based on the virtual work
principle: a set of nodes are distributed over the domain to be studied and the displacement
field is discretized with the help of interpolation functions that are not based on the finite element concept but only based on the nodes. In the present paper, we use a new approach based on the Fraeijs de Veubeke (FdV) functional [1] and initially developed for linear elasticity [2]. It uses separate discretizations of the displacements, stresses and strains. The method of [2] is extended to the case of geometrically linear but materially non linear solids and it is shown that, in the absence of body forces, the calculation of integrals over the area of the domain is avoided and that the derivatives of the nodal shape functions are not required, which constitutes an advantage over classical meshless and finite elements methods.