Constitutive inequalities for the damage of elastic-brittle materials

Starting from the requirement that the principle of determinism be satisfied, two constitutive inequalities are derived for one-dimensional strain- and stress-based continuum damage models. The one-dimensional constitutive inequality corresponding to the strain-based formulation turns out to be much less restrictive than the one associated to the stress-based formulation and is extended to the three-dimensional case. This extension gives a general constitutive inequality for the damage of elasticbrittle materials.