On yield criteria in plasticity coupled with damage

The coupling of elasto-plasticity and damage is still the subject of many papers, namely in the construction of evolution laws for internal parameters. In this paper we propose to partly overcome some difficulties by using the only basic fact that a plastic-damaged body is made up of two physical constituents, namely the matrix material and the micro-defects. The elasto-plastic matrix material is the resisting skeleton connecting the elements of the body and the micro-defects bring their own contributions to reversible and irreversible strains. Naturally strong couplings exist between the stress states of the body and the matrix material. These considerations will lead to generalisations and new formulations of the so-called equivalence principles and a new equivalence principle will be proposed. Finally, concerning the irreversible strains due to both plasticity of the matrix and growing of micro-defects, we will prove that yield conditions must be used simultaneously on the body as well as on the matrix, leading to some non-smooth resultant yield-damage surface. The modified Gurson model for porous material is then analysed in order to illustrate this last point. In this paper, large strains are considered, but time-dependant plasticity and thermal effects are excluded.