Projects per year
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 elastic ity 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.
Original language  English 

Pages (fromto)  90579070 
Number of pages  14 
Journal  Mathematical Methods in the Applied Sciences 
Volume  41 
Issue number  18 
Early online date  27 Apr 2018 
DOIs  
Publication status  Published  1 Dec 2018 
Keywords
 discrete manifold, lattice model, steel microstructure, elasticity, energy, nonlinear system
Research Beacons, Institutes and Platforms
 Manchester Energy
 Advanced materials
Fingerprint
Dive into the research topics of 'A mathematical model for elasticity using calculus on discrete manifolds'. Together they form a unique fingerprint.Projects
 1 Finished

Geometric Mechanics of Solids: new analysis of modern engineering materials  GEMS
1/11/16 → 31/10/21
Project: Research

A discrete model for forcebased elasticity and plasticity
Dassios, I., Tzounas, G., Milano, F. & Jivkov, A., 1 Jul 2024, In: Journal of Computational and Applied Mathematics. 444, 14 p., 115796.Research output: Contribution to journal › Article › peerreview
Open AccessFile22 Downloads (Pure) 
A guide to the finite and virtual element methods for elasticity
Berbatov, K., Lazarov, B. & Jivkov, A., Nov 2021, In: Applied Numerical Mathematics. 169, p. 351395 45 p.Research output: Contribution to journal › Article › peerreview
Open AccessFile195 Downloads (Pure) 
Boundary value problem on a weighted graph relevant to the static analysis of truss structures
Kodsi, C. & Jivkov, A., 17 Jun 2021, In: SIAM Journal of Applied Mathematics. 81, 3, p. 11901201 12 p.Research output: Contribution to journal › Article › peerreview