THE RELATIONSHIP BETWEEN DAMAGE VARIABLES AND THEIR EVOLUTION LAWS AND MICROSTRUCTURAL AND PHYSICAL-PROPERTIES

The major objective of this paper is to give a rational approach to id entify the dam age parameters in tensorial form, based on the microstr ucture of the defects (voids, cavities, microcracks) and the overall p hysical properties of a solid material. First, the general representat ions for the effective linear and nonlinear reversible physical proper ties (e.g. elastic and piezoelectric moduli) of a material representat ive volume element (RVE) containing a single defect of any shape are i nvestigated. Second, it is emphasized that the orientation distributio n functions (ODFs) of shapes, separations, etc., of defects constitute the dominant and physically measurable signatures of the changing mic rostructure of a damaged material, by assuming that the matrix behaves reversibly during damage nucleation and growth. Third, it is shown th at the ODFs can be expanded as absolutely convergent Fourier series wi th irreducible tensorial coefficients, and that these infinitely many irreducible tensorial coefficients constitute the full list of generic damage variables. Furthermore, to specify any given physical property , only certain leading tensorial coefficients in these series are need ed and, therefore: these leading coefficients act as the real damage t ensors for such a physical property. These physically based damage ten sors vary significantly from one physical property to another. For exa mple, it is shown that only the second and fourth tensorial coefficien ts effect the linear elastic moduli, while only the first and third te nsorial coefficients are needed in linear piezoelectricity theory. Fin ally, it is observed from a simple example that the evolution equation s for these physically based damage tensors normally involve tensorial terms of higher order than those needed to define the considered phys ically based damage tensors. Consequently, the evolution equations are not self-closed.