The computational framework for continuum-kinematics-inspired peridynamics

Javilia, A., Firooza, S., McBride, A.T. and Steinmann, P. (2020) The computational framework for continuum-kinematics-inspired peridynamics. Computational Mechanics, 66(4), pp. 795-824. (doi: 10.1007/s00466-020-01885-3)

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Abstract

Peridynamics (PD) is a non-local continuum formulation. The original version of PD was restricted to bond-based interactions. Bond-based PD is geometrically exact and its kinematics are similar to classical continuum mechanics (CCM). However, it cannot capture the Poisson effect correctly. This shortcoming was addressed via state-based PD, but the kinematics are not accurately preserved. Continuum-kinematics-inspired peridynamics (CPD) provides a geometrically exact framework whose underlying kinematics coincide with that of CCM and captures the Poisson effect correctly. In CPD, one distinguishes between one-, two- 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 from state-based interactions as the basic elements of continuum kinematics are preserved precisely. The objective of this contribution is to elaborate on computational aspects of CPD and present detailed derivations that are essential for its implementation. Key features of the resulting computational CPD are elucidated via a series of numerical examples. These include three-dimensional problems at large deformations. The proposed strategy is robust and the quadratic rate of convergence associated with the Newton–Raphson scheme is observed.

Item Type:Articles
Additional Information:AJ and SF gratefully acknowledge the support provided by Scientific and Technological Research Council of Turkey (TU¨ BITAK) Career Development Program, grant number 218M700. PS and AM gratefully acknowledge the support provided by the EPSRC Strategic Support Package: Engineering of Active Materials by Multiscale/Multiphysics Computational Mechanics - EP/R008531/1.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:McBride, Professor Andrew and Steinmann, Professor Paul
Authors: Javilia, A., Firooza, S., McBride, A.T., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Computational Mechanics
Publisher:Springer
ISSN:0178-7675
ISSN (Online):1432-0924
Published Online:30 July 2020
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in Computational Mechanics 66(4): 795-824
Publisher Policy:Reproduced under a Creative Commons License

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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