Quasi-Static Brittle Damage Evolution in Elastic Materials with Multiple Damaged States

We present energetic and strain-threshold models for the quasi-static evolution of brutal brittle damage for geometrically-linear elastic materials. By allowing for anisotropic elastic moduli and multiple damaged states we present the issues for the first time in a truly elastic setting, and show that the threshold methods developed in (Garroni, A., Larsen, C. J., Threshold-based quasi-static brittle damage evolution, Archive for Rational Mechanics and Analysis 194 (2), 585–609, 2009) extend naturally to elastic materials with non-interacting damage. We show the existence of solutions and that energetic evolutions are also threshold evolutions.