Finite Element Methods for a Peridynamic Model of Mechanics

Abstract

Peridynamic is a recently developed theory of solid mechanics that replaces the partial differential equations (PDE) of the classical continuum theory with integro-differential equations (IDE). We apply Finite Element Methods (FEM) to implement the peridynamic model. Since the integro-differential equations remain valid in the presence of discontinuities such as cracks, the method has the potential to model fracture and damage with great generality. We use piecewise constant functions in regions where discontinuities may appear and piecewise linear function in areas wherethesolutionsissmoothandinvestigatehowtocombinethesetwomethods.Wearealsointerestedinthe choice of the horizon radius to implement the peridynamic model more accurately. Theoretical analysis and numerical results for different cases are given.