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 de®nitions of the damage parameter and thermodynamic principles, which give relationships between macroscopic and e€ective de®nitions of stress and strain. These relationships are used to obtain yield condition and plastic ¯ow 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 de®nition of e€ective stress is used. Contradictory damage parameters based on di€erent damage measuring techniques and equivalence hypotheses in CDM are clari®ed.