Kinematically exact peridynamics

Abstract The main objective of this contribution is to present a kinematically exact peridynamics (PD) formulation. The proposed formulation accounts for large deformations and is variationally consistent. We distinguish between one, two, and three neighbor interactions. One-neighbor interactions recover the original (bond-based) PD formalism. Two and three-neighbor interactions are fundamentally different to state-based PD. We account for material frame indifference and provide a set of appropriate arguments for objective interaction potentials accordingly. From a computational perspective, the proposed strategy is fully implicit and the quadratic rate of convergence associated with the Newton–Raphson scheme is observed. The capability of the proposed framework is demonstrated via a series of numerical examples at large deformations.