Continuum Damage Models based on Energy Equivalence: Part I — Isotropic Material Response

An energy equivalence method for modeling damage effects in material response is proposed. In the present article, the main issues of the method are discussed for the less complicated case of isotropic constitutive functions. Otherwise, the material response addressed is supposed to be (rate-independent) elasto-plastic exhibiting isotropic and kinematic hardening. In order to make clear the difference to other continuum damage models, it suffices to deal here with isotropic damage expressed in terms of a scalar state variable. Our approach is based on the concept of effective stress and effective strain combined with a principle of energy equivalence as explained in the article. As a result, both the yield function and the evolution equations governing the hardening response of the damaged material are obtained from a given undamaged model material. Characteristic properties of the damage theory proposed are illustrated by comparing predicted responses with those according to damage models based on the principle of strain equivalence.