A Natural Neighbor Method Based on Fraeijs de Veubeke Variational Principle for Elastoplasticity and Fracture Mechanics

Abstract

The natural neighbor 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 is 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, a new approach based on the Fraeijs de Veubeke (FdV) functional (1) and initially developed for linear elasticity (2) is extended to the case of geometrically linear but materially nonlinear solids. Then, the extension to linear fracture mechanics, as a first step to the study of crack propagation, is briefly presented.