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.
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 manifold; Elasticity; Energy; Lattice model; Nonlinear system; Steel 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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