Lattice and particle modeling of damage phenomena

Lattice (spring network) models offer a powerful way of simulating mechanics of materials as a coarse scale cousin to molecular dynamics and, hence, an alternative to finite element models. In general, lattice nodes are endowed with masses, thus resulting in a quasiparticle model. These models, having their origins in spatial trusses and frameworks, work best when the material may naturally be represented by a system of discrete units interacting via springs or, more generally, rheological elements. This chapter begins with basic concepts and applications of spring networks, in particular the anti-plane elasticity, planar classical elasticity, and planar nonclassical elasticity. One can easily map a specific morphology of a composite material onto a particle lattice and conduct a range of parametric studies; these result in the so-called damage maps. Considered next is a generalization from statics to dynamics, with nodes truly acting as quasiparticles, application being the comminution of minerals. The chapter closes with a discussion of scaling and stochastic evolution in damage phenomena as stepping-stone to stochastic continuum damage mechanics.