A mathematical model for elasticity using calculus on discrete manifolds. (27th April 2018)

• Record Type: Journal Article
• Authors: Dassios, Ioannis; O'Keeffe, Gary; Jivkov, Andrey P.
• Other Names: Anguelov Roumen guestEditor.; Banasiak Jacek guestEditor.; Debbouche Amar guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 18(2018)
• Page Start: 9057
• Page End: 9070
• Publication Date: 2018-04-27
• Subjects: discrete manifold -- elasticity -- energy -- lattice model -- nonlinear system -- steel microstructure; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4892
• Languages: English
• ISSNs: 0170-4214

Abstract

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.