A Peridynamic Approach to Calculate the Elastoplastic Stress and Strain Fields

Resumo

The peridynamic theory is a new approach developed in recent years for the numerical solution of
elastodynamics problems. One of the advantages of the peridynamic theory is the natural capacity to simulate the
initiation and growth of cracks in solid materials, without the aid of numerical procedures commonly employed in
the conventional finite element formulation. This advantage is due to the peridynamic constitutive relations are
based on partial integral equations, rather than differential ones, where these equations keep definite even with a
geometrical discontinuity. This theory relies on the displacement fields of a given simulated problem, where the
stress and strain fields are not obtained natively. Within this context, a numerical approach to calculate the strain
and stress fields for a peridynamic elastoplastic simulation is presented, based on the developments published in
the literature. The accuracy of this approach is verified by comparing the results for the Von Mises stress field
obtained with the peridynamic theory, to those obtained with a commercial finite element code, and conclusions
are drawn.