Damage mechanics: Basic variables in continuum theories

It is shown that any type of material damage that causes stiffness degradation can be described in the most general case by means of an eighth-order damage tensor but that the principle of strain equivalence permits a reduction to a tensor of rank four. The actual number of independent damage parameters in such a tensor is related to the material and damage symmetry, and is found to be two for the isotropic case. The evolution of damage defines a path within the damage domain defined by these two parameters and is linked to the constitutive properties of the material. One thermodynamically consistent set of such equations is developed for a specific material.; Comparisons with existing theories are made. Physically meaningful damage parameters are also identified to aid in experimental evaluation.