A mathematical model for elasticity using calculus on discrete manifolds

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Title: A mathematical model for elasticity using calculus on discrete manifolds
Authors: Dassios, Ioannis K.
O'Keeffe, Gary
Jivkov, Andrey P.
Permanent link: http://hdl.handle.net/10197/10636
Date: 27-Apr-2018
Online since: 2019-05-23T09:58:36Z
Abstract: We propose a mathematical model to represent solid materials with discrete lattices and to analyse their behaviour by calculus on discrete manifolds. Focus is given on the mathematical derivation of the lattice elements by taking into account the stored energy associated with them. We provide a matrix formulation of the nonlinear system describing elasticity with exact kinematics, known as finite strain elasticity in continuum mechanics. This formulation is ready for software implementation and may also be used in atomic scale models as an alternative to existing empirical approach with pair and cohesive potentials. An illustrative example, analysing a local region of a node, is given to demonstrate the model performance.
Funding Details: Irish Research Council
Science Foundation Ireland
Type of material: Journal Article
Publisher: Wiley Online Library
Journal: Mathematical Methods in the Applied Sciences
Volume: 41
Issue: 18
Start page: 9057
End page: 9070
Copyright (published version): 2018 John Wiley & Sons, Ltd.
Keywords: Discrete manifoldElasticityEnergyLattice modelNonlinear systemSteel microstructure
DOI: 10.1002/mma.4892
Language: en
Status of Item: Peer reviewed
Appears in Collections:Electrical and Electronic Engineering Research Collection

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