Towards elasto-plastic continuum-kinematics-inspired peridynamics

The main objective of this contribution is to develop a dissipation-consistent elasto-plastic peridynamic (PD) formulation that is also geometrically exact. We distinguish between one-neighbour, two-neighbour and three-neighbour interactions. One-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism. However, two- and threeneighbour interactions are fundamentally different to state-based interactions, as the basic elements of continuum kinematics are preserved exactly. We investigate the consequences of the angular momentum balance and provide a set of appropriate arguments for the interaction potentials accordingly. Furthermore, we elaborate on restrictions on the interaction energies and derive dissipation-consistent constitutive laws through a Coleman-Noll-like procedure. Although the framework is suitable for finite deformations, an additive decomposition of the kinematic quantities into elastic and plastic parts is rigorously proven to be a correct choice. Crucially, in our proposed scheme, the elasto-plastic framework resembles standard one-dimensional plasticity, for all interactions. Finally, we demonstrate the capability of our proposed framework via a series of numerical examples. (C) 2021 ElsevierB.V. All rights reserved.

Automated summary

The objective is to develop a dissipation-consistent elasto-plastic peridynamic formulation. The study distinguishes between different interaction types, investigates the consequences of angular momentum balance, provides appropriate interaction potentials and constitutive laws, and demonstrates the capability of the proposed framework through numerical examples. The framework resembles standard one-dimensional plasticity for all interactions.