Numerical Methods for the Nonlocal Peridynamics Continuum Model of Mechanics

Abstract

In contrast to classical partial differential equation models, the recently devel- oped peridynamic nonlocal continuum model for solid mechanics is an integro- differential equation that does not involve spatial derivatives of the displacement field. As a result, the peridynamic model admits solutions having jump discon- tinuities so that it has been successfully applied to fracture problems. Based on a variational formulation, continuous and discontinuous Galerkin finite element methods are developed for the peridynamic model. Discontinuous discretizations are conforming for the model without the need to account for fluxes across ele- ment edges. Through a series of one & two-dimensional computational experi- ments, we investigate the convergence behavior of the finite element approxima- tions and compare the results with theoretical estimates.