Constitutive relations in plasticity, damage and fracture mechanics based on a work property

Abstract This paper is devoted to restrictions imposed by a work property of Drucker-Iliushin's type on the general class of mechanical systems with an elastic range which contains plastic, damaged and cracked media. The analysis is purely mechanical and quasi-static. Starting from very weak assumptions relative to this constitutive class, we obtain a fundamental inequality which generalizes Hill's maximal work principle. So we can justify, for instance: the convexity of the elastic domain and the normality rule of the plastic strain rate in stress space for the infinitesimal and some finite plasticity theories, Griffith's criterion in brittle fracture mechanics, and we obtain some original results for elastic and elastic plastic damaged materials. It must be noted that the procedure is purely deductive, the assumptions are explicit and the results are implications .