1. A mathematical model for elasticity using calculus on discrete manifolds
- Author
-
G.J. O’Keeffe, Andrey P. Jivkov, and Ioannis Dassios
- Subjects
Pure mathematics ,ResearchInstitutes_Networks_Beacons/02/06 ,General Mathematics ,discrete manifold, lattice model, steel microstructure, elasticity, energy, non-linear system ,01 natural sciences ,Lattice model ,0103 physical sciences ,Discrete manifold ,medicine ,0101 mathematics ,Elasticity (economics) ,010306 general physics ,Manchester Energy ,Calculus (medicine) ,Mathematics ,Energy ,General Engineering ,ResearchInstitutes_Networks_Beacons/03/02 ,medicine.disease ,Elasticity ,010101 applied mathematics ,Nonlinear system ,Steel microstructure ,Advanced materials ,Lattice model (physics) - 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. Irish Research Council Science Foundation Ireland Engineering and Physical Sciences Research Council (EPSRC)
- Published
- 2018