Irreversibility, Stability and Maximum Dissipation in Elastoplastic Damage

Abstract

The relation between the maximum dissipation principle, the irreversibility condition of Ilyushin and Drucker's stability postulate is studied in the present paper. For simple elastoplastic material models, it is well known that these three postulates require orthogonality between the plastic strain rate and the yield surface. The objective of this work is to investigate this relation for more general material models containing internal variables coupled with the elastic strains. It can be shown that the irreversibility and stability conditions pose the same restriction on the directions of dissipative fluxes, but do not determine uniquely this direction. The postulate of maximum dissipation is a stronger restriction to the evolution equations than Ilyushin's condition. The results are applied to damage mechanics models. For models describing elasticity and damage, a normality law in damage force space is obtained. In the case of plasticity with damage, the postulates imply orthogonality neither in the stress space nor in the damage force space. Usual non-associated flow rules for elastoplasticity with damage violate Drucker's stability postulate. The only convenient way to formulate a model, which fulfills the postulates of Ilyushin and Drucker a priori, is the use of an associated flow rule.