Energy correlations between a damaged macroscopic continuum and its sub-scale

An energy correlation hypothesis between a damaged macroscopic continuum an d its sub-scale virgin, or matrix, material is established in the present p aper. Two energy equivalence principles are proposed based on the geometric al definitions of the damage parameter and thermodynamic principles, which give relationships between macroscopic and effective definitions of stress and strain. These relationships are used to obtain yield condition and plas tic flow rule for the damaged material when the mechanical properties of un damaged virgin, or matrix, material are given. It is shown that a link betw een the void growth model (VGM) and the continuum damage mechanics (CDM) ex ists when a more general definition of effective stress is used. Contradict ory damage parameters based on different damage measuring techniques and eq uivalence hypotheses in CDM are clarified. (C) 2000 Elsevier Science Ltd. A ll rights reserved.