Towards elasto-plastic continuum-kinematics-inspired peridynamics

Javili, A., McBride, A.T. , Mergheim, J. and Steinmann, P. (2021) Towards elasto-plastic continuum-kinematics-inspired peridynamics. Computer Methods in Applied Mechanics and Engineering, 380, 113809. (doi: 10.1016/j.cma.2021.113809)

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Abstract

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 three-neighbour 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.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:McBride, Professor Andrew
Authors: Javili, A., McBride, A.T., Mergheim, J., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Computer Methods in Applied Mechanics and Engineering
Publisher:Elsevier
ISSN:0045-7825
ISSN (Online):1879-2138
Published Online:03 April 2021

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
300129Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational MechanicsChristopher PearceEngineering and Physical Sciences Research Council (EPSRC)EP/R008531/1ENG - Infrastructure & Environment