A geometrically exact formulation of peridynamics

Javili, A., McBride, A. T. and Steinmann, P. (2021) A geometrically exact formulation of peridynamics. Theoretical and Applied Fracture Mechanics, 111, 102850. (doi: 10.1016/j.tafmec.2020.102850)

Abstract

The main objective of this contribution is to develop a geometrically exact peridynamics (PD) formulation wherein the basic elements of continuum kinematics are preserved. The proposed formulation accounts for large deformations and is variationally consistent. We distinguish between one-, two- and three-neighbour interactions. One-neighbour interactions recover the original (bond-based) PD formalism. Two- and three-neighbour 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. This contribution is presented in a manner such that the established theory is immediately suitable for computational implementation. From a computational perspective, the proposed strategy is fully implicit and the quadratic rate of convergence associated with the Newton–Raphson scheme is observed. Finally, we demonstrate the capability of our proposed framework via a series of numerical examples at large deformations.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Steinmann, Professor Paul and McBride, Professor Andrew
• Authors: Javili, A., McBride, A. T., and Steinmann, P.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Theoretical and Applied Fracture Mechanics
• Publisher: Elsevier
• ISSN: 0167-8442
• ISSN (Online): 1872-7638
• Published Online: 03 December 2020
• Copyright Holders: Copyright © 2020 Elsevier Ltd.
• First Published: First published in Theoretical and Applied Fracture Mechanics 111: 102850
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
300129		Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational Mechanics	Christopher Pearce	Engineering and Physical Sciences Research Council (EPSRC)	EP/R008531/1	ENG - Infrastructure & Environment