An anisotropic theory of elasticity for continuum damage mechanics

Abstract

This paper presents the development of an anisotropic elastic damage theory. This is achieved by deriving a modified damage effect tensor M(D) for the effective stress equations capable of including the effect of anisotropic material damage. The modified tensor removes the restriction of a priori knowledge of the directions of principal stresses imposed by a damage effect tensor developed earlier and can now be made for general practical engineering applications of failure analysis. Reduction of the proposed tensor to a scalar for isotropic damage is shown to be possible when it is expressed not only in the principal directions but also in any arbitrary coordinate system, a necessary condition to verify the validity of the proposed tensor. Uniaxial tension and pure torsion are chosen to illustrate the application of the theory as well as associated damage variables that may be experimentally determined using laboratory size specimens. The measured damage variables confirm the presence of anisotropic damage from an initially isotropic material specimen and the magnitude is more pronounced at higher stresses and strains.

Foundational aspects of a multi-scale modeling framework for composite materials

“…D can be a zeroth-, second-, or fourth-order tensor, depending on the model employed. The hypothesis of equivalent elastic energy is used to evaluate M ijkl and establish a relation between the damaged and undamaged stiffnesses [50,51]. The hypothesis, detailed in [52,53], specifically assumes that the elastic complimentary energy W C in a damaged material with the actual stress is equal to that in a hypothetical undamaged material with the fictitious effective stress, i.e.,…”

Discrete 3D model as complimentary numerical testing for anisotropic damage

“…This key differentiability feature ensures the stresses-strains continuity under complex non proportional loading. Anisotropic damage is generally represented by a tensorial thermodynamics variable D (Chaboche, 1978;Leckie and Onat, 1981;Cordebois and Sidoroff, 1982;Ladevèze, 1983;Chow and Wang, 1987;Murakami, 1988;Ju, 1989;Halm and Dragon, 1998;Lemaitre and Desmorat, 2005) taken next as a second order tensor. An anisotropic damage model for concrete has been proposed based on these assumptions (Desmorat, 2004;Desmorat et al, 2007), based also on a splitting of the Gibbs free enthalpy (Papa and Taliercio, 1996;Lemaitre et al, 2000) − into a deviatoric part fully affected by the damage tensor D through the effective tensor H = (1−D) −1/2 , − and on a hydrostatic part affected by a sensitivity to hydrostatic stresses scalar function h(D) for positive hydrostatic stresses and not affected by damage for negative hydrostatic stresses.…”

Experimental and Analytical Characterization of .BETA.-Tricalcium Phosphate Particle Reinforced Poly-L-Lactide Composites

“…The effective rigidity of the debonded particles is calculated based on the analysis developed by Chow and Wong (17) , and expressed as following equation,…”