We would like to highlight that one of the contributions of our papers 1 2 is to propose the assumption of displacement equivalence and the other contribution is to apply this assumption to derive a constitutive model for brittle materials. For simplification, the material is assumed to be ideal brittle, and hence only elastic damage is considered. We have indicated that it is a simplified model, which is invalid for the case of the material under triaxial compression and for the case of the principal directions of damage not coinciding with those of stress and strain.
The displacement equivalence-based damage model for brittle materials has been generalized for quasibrittle materials such as concrete by dealing with the above two cases, as presented in Chap. 5 of Ref. 3. The first modification is to consider the case in which the principal directions of damage do not coincide with those of...
