Configurational peridynamics

Abstract

Configurational forces that drive the evolution of material structures such as defects are introduced into a geometrically-exact peridynamics framework. The concept of bond-number double-density facilitates the definition of a peridynamic potential energy functional that inherits the key features of its conventional (local) continuum and discrete counterparts. The spatial and material variations of the peridynamic potential energy functional give rise to familiar Piola- and Cauchy-type bond-wise interaction forces that enter the point-wise force balance in the spatial and material setting, respectively. It is shown that the point-wise material body force density is a result of a non-local pull-back of the bond-wise spatial interaction force, and thereby captures non-local contributions. Several key features of configurational peridynamics are demonstrated via a computational example and a comparison to conventional configurational continuum mechanics.