10. Two-Dimensional Discrete Damage Models: Lattice and Rational Models

Many materials exhibit a discontinuous and inhomogeneous nature on various spatial scales that can lead to complex mechanical behaviors difficult to reproduce with continuum-based models. “Among these complex phenomena is damage evolution with nucleation, propagation, interaction, and coalescence of cracks that can result in a plethora of macroscale deformation forms.” Discontinua-based models are computational methods that represent material as an assemblage of distinct elements interacting with one another. The mesoscale methods of computational mechanics of discontinua presented in this our two essays can be, arguably, divided into three broad and intervening categories: spring network (lattice) models, discrete/distinct-element methods (DEM), and particle models. The distinct-element computational methods such as molecular dynamics and smoothed-particle hydrodynamics are outside the scope of the present overview. The objective of this chapter is to briefly survey the spring network models and their main applications. The discrete-based models have been extensively applied in the last decade to three-dimensional configurations. However, since the scope of this article is limited to two-dimensional (2D) models for practical purposes, these important advances are ignored. Likewise, one-dimensional (1D) fiber bundle models are also excluded from this account.