A mathematical model for plasticity and damage: A discrete calculus formulation

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:312

Article; Proceedings Paper

Dassios, Ioannis^1,2,3  Jivkov, Andrey P.¹  Abu-Muharib, Andrew¹  James, Peter⁴ 

[1] Univ Manchester, Sch Mech Aerosp & Civil Engn, Mech Phys Solids Res Team, Manchester, Lancs, England

[2] Univ Limerick, MACSI, Dept Math & Stat, Limerick, Ireland

[3] Univ Coll Dublin, ERC, Dublin, Ireland

[4] AMEC Foster Wheeler, Warrington, Cheshire, England

关键词: Discrete calculus;    Lattice model;    Steel microstructure;    Plasticity;    Damage;    Non-linear system;   

DOI  :  10.1016/j.cam.2015.08.017

来源: Elsevier

【 摘 要 】

In this article we propose a discrete lattice model to simulate the elastic, plastic and failure behaviour of isotropic materials. Focus is given on the mathematical derivation of the lattice elements, nodes and edges, in the presence of plastic deformations and damage, i.e. stiffness degradation. By using discrete calculus and introducing non-local potential for plasticity, a force-based approach, we provide a matrix formulation necessary for software implementation. The output is a non-linear system with allowance for elasticity, plasticity and damage in lattices. This is the key tool for explicit analysis of micro-crack generation and population growth in plastically deforming metals, leading to macroscopic degradation of their mechanical properties and fitness for service. An illustrative example, analysing a local region of a node, is given to demonstrate the system performance. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free