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

An energy correlation hypothesis between a damaged macroscopic continuum and its sub-scale virgin, or matrix, material is established in the present paper. Two energy equivalence principles are proposed based on the geometrical 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 plastic flow rule for the damaged material when the mechanical properties of undamaged virgin, or matrix, material are given. It is shown that a link between the void growth model (VGM) and the continuum damage mechanics (CDM) exists when a more general definition of effective stress is used. Contradictory damage parameters based on different damage measuring techniques and equivalence hypotheses in CDM are clarified.