THE FOUNDATIONS OF CONTINUUM DAMAGE MECHANICS

Abstract

Damage Mechanics has become a useful theory in describing the nonlinear behavior of solids driven by the nucleation and growth of cracks and microcracks. This approach, based on the first principles of mechanics and thermodynamics, has also been combined with classical theories of plasticity to address a wide range of loading applications. In spite of the many different damage mechanics models and representations that are proposed, the foundation of damage mechanics is not well understood or at least not thoroughly published giving rise to the many inaccurate definitions and formulations. The intent of this paper is to provide the background of the continuum damage mechanics outlining the fundamentals on which this field theory is set up. The internal variable theory of continuum thermodynamics is reviewed and is shown that with Legendre transformation technique, various potential functions can be developed for damage mechanics formulation in either stress or strain space. The concept of constrained or neighboring equilibrium state is also introduced and is explained. The paper will conclude with the derivation of the general damage potential and a suggestion is given for the isotropic damage formulation with the resulting uniaxial stress-strain relation.