Lattice and Particle Modeling of Damage Phenomena

Research output: Chapter in Book/Report/Conference proceedingChapter


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.

Original languageEnglish (US)
Title of host publicationHandbook of Damage Mechanics
Subtitle of host publicationNano to Macro Scale for Materials and Structures: Second Edition: Volume 1
Number of pages37
ISBN (Electronic)9783030602420
ISBN (Print)9783030602413
StatePublished - Jan 1 2022


  • Brittle transition
  • Diffusive fracture
  • Markov jump process
  • Stiffness tensor
  • Triangular lattice

ASJC Scopus subject areas

  • General Engineering
  • General Materials Science


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