### Abstract

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 language | English (US) |
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Title of host publication | Handbook of Damage Mechanics |

Subtitle of host publication | Nano to Macro Scale for Materials and Structures |

Publisher | Springer New York |

Pages | 203-238 |

Number of pages | 36 |

ISBN (Electronic) | 9781461455899 |

ISBN (Print) | 9781461455882 |

DOIs | |

State | Published - Jan 1 2015 |

### ASJC Scopus subject areas

- Engineering(all)
- Materials Science(all)

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## Cite this

*Handbook of Damage Mechanics: Nano to Macro Scale for Materials and Structures*(pp. 203-238). Springer New York. https://doi.org/10.1007/978-1-4614-5589-9