Effective Elastic Moduli of Two-Dimensional Brittle Solids With Interacting Microcracks, Part II: Evolutionary Damage Models

In Part I of this series, basic formulations of stationary micromechanical theory and overall responses are presented for two-dimensional brittle solids with randomly dispersed microcracks. The basic formulations hinge on an ensemble average approach which includes pairwise microcrack interactions. In this paper, statistical micromechanical evolutionary models are proposed to account for “cleavage 1” growth of randomly oriented and located microcracks under microcrack interaction effects. Biaxial tension/compression loadings are also considered to take into account mixed microcrack opening and closure effects. Efficient numerical integration algorithms for the proposed ensemble averaged constitutive equations are subsequently given. Further, uniaxial and biaxial tests are presented to illustrate the proposed models and procedures. Finally, a higher-order microcrack interaction model within the proposed micromechanical framework is discussed.