A displacement equivalence-based damage model for brittle materials-Part I: Theory

In this paper, a displacement equivalence-based damage model for brittle materials is proposed. A new damage deactivation criterion, which depends on both the stress and strain states of the materials, is adopted. Based on the concept of effective stress, the virtual undamaged configuration is introduced, and the assumption of displacement equivalence is proposed to correlate the damaged and the virtual undamaged configurations. Then, an additional crack-opening-induced normal deformation is introduced, and the three-dimensional (3D) effect of these opened cracks is also considered. The evolution rule of damage is deduced using the Onsager relations, which also ensure that the second law of thermodynamics is satisfied.