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A mathematical model for plasticity and damage: A discrete calculus formulation
Date Issued
2017-03-01
Date Available
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.
Sponsorship
Science Foundation Ireland
Other Sponsorship
Engineering and Physical Sciences Research Council (EPSRC) via the Nuclear EngD Doctoral Training Centre at The University of Manchester’s Dalton Nuclear Institute
AMEC-Clean Energy Europe
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
Language
English
Status of Item
Peer reviewed
ISSN
0377-0427
This item is made available under a Creative Commons License
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AS6158408231444511523839302929_content_1.pdf
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609.28 KB
Format
Owning collection
Scopus© citations
21
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