Rational split of the strain tensor in elastoplastic damage mechanics

The basic step in constructing a sound non-linear constitutive model is in accounting for the inelastic deformations. Different investigators partition the state tensors in various ways. This paper discusses the specific implications and limitations of such partitioning of the infinitesimal strain tensor in view of the irreversible changes taking place at a material point. Emphasis is placed on those models which take into consideration the process of damage. It is demonstrated that the damage process affects both the elastic and the plastic behaviours and the most proper partitioning of the strain tensors assumes elastic-damage and plastic-damage constituents. The constraints posed by the use of a single damage variable are elaborated using the concepts of thermodynamics. It is shown that two damage variables are required to depict completely the loading-unloading-reloading of a general non-linear elastoplastic-damaged material. This is further illustrated by deriving a new elastoplastic damage constitutive equation.