Damage and Failure Analysis based on Peridynamics - Theory and Applications

Abstract

In this paper we give an overview over a recent non-local formulation of continuum mechanics called the Peridynamic theory in contrast to related non-local theories in the literature. The Peridynamic approach is fundamentally different as it avoids using any spatial derivatives which arise naturally when formulating balance laws in the classical, local theory. Motivated by molecular dynamics the differential operator in the equation of motion is replaced with an integral operator which can be applied to both continuous and discontinuous fields. By comparing the elastic energy density associated with homogeneous deformations in Peridynamics to the corresponding energy in classical elasticity we show how the connection to experimentally measurable material properties such as the Young’s modulus and the Poisson ratio can be established. This is done by expressing the elastic energy in Peridynamics as a function of the invariants of the strain tensor, a rigorously approach not previously published. The paper concludes with an example of a crack turning in a 3D isotropic material, illustrating the strength of the Peridynamic formulation in problems where the crack path is not known in advance.