An implicit implementation of non-ordinary state-based peridynamics

Hashim, N.A.; Coombs, W.M.; Hattori, G.; Augarde, C.E.

Abstract

Peridynamics is a non-local continuum theory that was introduced by Silling. Its key advantage is its use of integral equation forms of the underlying physics, as compared to the partial differential equations in, say the finite element method and therefore does not need any extra assumptions to treat singularities. In this paper we present an implicit implementation of the non-ordinary state-based peridynamics formulation. Fracture is introduced into the peridynamic model by allowing bonds to break irreversibly. Bond breakage occurs when a damage criterion is satisfied, for instance, if the bond exceeds a critical stretch. This paper presents for the first time an implicit formulation of non-ordinary state-based peridynamic theory for finite deformation mechanics. An iterative procedure based on the Newton-Raphson method is used to solve the discretised problem.

Citation

Hashim, N., Coombs, W., Hattori, G., & Augarde, C. (2017, April). An implicit implementation of non-ordinary state-based peridynamics. Presented at 25th Conference on Computational Mechanics UKACM 2017., Birmingham, UK

• Presentation Conference Type: Conference Paper (published)
• Conference Name: 25th Conference on Computational Mechanics UKACM 2017.
• Start Date: Apr 11, 2017
• End Date: Apr 13, 2017
• Publication Date: Apr 13, 2017
• Deposit Date: Jun 7, 2017
• Publicly Available Date: Nov 22, 2024
• Publisher: University of Birmingham
• Pages: 134-137
• Book Title: Proceedings of the 25th Conference on Computational Mechanics (UKACM 2017) : 11th – 13th April 2017, School of Engineering, University of Birmingham, Birmingham, UK.
• Public URL: https://durham-repository.worktribe.com/output/1146897
• Publisher URL: http://ukacm2017.ukacm.org/wp-content/uploads/2017/04/Proceedings-UKACM2017-compressed.pdf