Virtual Element Method for Peridynamic Diffusion Problems
Please login to view abstract download link
Peridynamics is a nonlocal version of continuum mechanics theory able to incorporate singularities since it does not take into account spatial partial derivatives. As a consequence, it assumes long-range interactions among material particles and is able to describe the formation and the evolution of fractures. The discretization of such nonlocal model requires the use of raffinate numerical tools for approximating the solutions to the model. We propose a virtual element approach to obtain the solution. The main feature of the proposed technique is that we are able to construct a nonlocal counterpart for the divergence operator in order to obtain a weak formulation of the peridynamic model and exploiting the analogies with the known results in the context of Galerkin approximation. We prove the convergence of the proposed method and provide several simulations to validate our results.