The major objective of this paper is to give a rational approach to identify the dam-age parameters in tensorial form, based on the microstructure of the defects (voids,cavities, microcracks) and the overall physical properties of a solid materiah First,the general representations for the effective linear and nonlinear reversible physicalproperties (e.g. elastic and piezoelectric moduli) of a material representative volumeelement (RVE) containing a single defect of any shape are investigated. Second, itis emphasized that the orientation distribution functions (ODFs) of shapes, separa-tions, etc., of defects constitute the dominant and physically measurable signaturesof the changing microstructure of a damaged material, by assuming that the matrixbehaves reversibly during damage nucleation and growth. Third, it is shown thatthe ODFs can be expanded as absolutely convergent Fourier series with irreducibletensorial coefficients, and that these infinitely many irreducible tensorial coefficient sconstitute the full list of generic damage variables. Furthermore, to specify any givenphysical property, only certain leading tensorial coefficients in these series are need-ed and, therefore, these leading coefficients act as the real damage tensors for sucha physical property. These physically based damage tensors vary significantly fromone physical property to another. For example, it is shown that only the second andfourth tensorial coefficients effect the linear elastic moduli, while only the first andthird tensorial coefficients are needed in linear piezoelectricity theory. Finally, it isobserved from a simple example that the evolution equations for these physicallybased damage tensors normally involve tensorial terms of higher order than thoseneeded to define the considered physically based damage tensors. Consequently, theevolution equations are not self-closed.