An implicit implementation of non-ordinary state-based peridynamics.

Peridynamics is a non-local continuum theory that was introduced by Silling. Its key advantage is its use of integral equation forms of the underlying physics, as compared to the partial differential equations in, say the finite element method and therefore does not need any extra assumptions to treat singularities. In this paper we present an implicit implementation of the non-ordinary state-based peridynamics formulation. Fracture is introduced into the peridynamic model by allowing bonds to break irreversibly. Bond breakage occurs when a damage criterion is satisfied, for instance, if the bond exceeds a critical stretch. This paper presents for the first time an implicit formulation of non-ordinary state-based peridynamic theory for finite deformation mechanics. An iterative procedure based on the Newton-Raphson method is used to solve the discretised problem