Macroscopic Theories of Cumulative Damage I: Strain Formulation.

Abstract : This article is devoted to the formulation of a mechanical constitutive theory accounting for deformation-induced material degradation, such as that resulting from the growth of small flaws. As in a previous investigation by the authors, the degrading material is modeled here as an effectively materially-uniform, simple body in the sense of Noll, 'damage' being interpreted as a permanent alteration in the stress-functional of this effective continuum. The authors' previous theory, which did not account for continued damage at constant strain, is shown here to provide a measure of damage incurred during a given strain history relative to the equilibrium configuration defined by the current value of strain. It is then shown that this 'relative damage functional' can be used to generate an absolute measure of damage if it is accepted that no damage can accrue in the absence of stress. In view of the physical assumptions introduced here, the present formulation appears to encompass fatigue and spallation phenomena as well as the slow deformation of most composite materials.