A mathematical model for plasticity and damage: A discrete calculus formulation

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Title: A mathematical model for plasticity and damage: A discrete calculus formulation
Authors: Dassios, Ioannis K.
Jivkov, Andrey P.
Abu-Muharib, Andrew
James, Peter
Permanent link: http://hdl.handle.net/10197/10648
Date: 1-Mar-2017
Online since: 2019-05-23T13:57:31Z
Abstract: In this article we propose a discrete lattice model to simulate the elastic, plastic and failure behaviour of isotropic materials. Focus is given on the mathematical derivation of the lattice elements, nodes and edges, in the presence of plastic deformations and damage, i.e. stiffness degradation. By using discrete calculus and introducing non-local potential for plasticity, a force-based approach, we provide a matrix formulation necessary for software implementation. The output is a non-linear system with allowance for elasticity, plasticity and damage in lattices. This is the key tool for explicit analysis of micro-crack generation and population growth in plastically deforming metals, leading to macroscopic degradation of their mechanical properties and fitness for service. An illustrative example, analysing a local region of a node, is given to demonstrate the system performance.
Funding Details: Science Foundation Ireland
Type of material: Journal Article
Publisher: Elsevier BV
Journal: Journal of Computational and Applied Mathematics
Volume: 312
Start page: 27
End page: 38
Copyright (published version): 2015 Elsevier
Keywords: Discrete calculusLattice modelSteel microstructurePlasticityDamageNon-linear system
DOI: 10.1016/j.cam.2015.08.017
Language: en
Status of Item: Peer reviewed
Appears in Collections:Electrical and Electronic Engineering Research Collection

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