Peridynamics via finite element analysis

Abstract

Peridynamics is a recently developed theory of solid mechanics that replaces the partial differential equations of the classical continuum theory with integral equations. Since the integral equations remain valid in the presence of discontinuities such as cracks, the method has the potential to model fracture and damage with great generality and without the complications of mathematical singularities that plague conventional continuum approaches. Although a discretized form of the peridynamic integral equations has been implemented in a meshless code called EMU, the objective of the present paper is to describe how the peridynamic model can also be implemented in a conventional finite element analysis (FEA) code using truss elements. Since FEA is arguably the most widely used tool for structural analysis, this implementation may hasten the verification of peridynamics and significantly broaden the range of problems that the practicing analyst might attempt. Also, the present work demonstrates that different subregions of a model can be solved with either the classical partial differential equations or the peridynamic equations in the same calculation thus combining the efficiency of FEA with the generality of peridynamics. Several example problems show the equivalency of the FEA and the meshless peridynamic approach as well as demonstrate the utility and robustness of the method for problems involving fracture, damage and penetration.