  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.
