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.

Résumé

On présente un développement d'une théorie sur l'endommagement élastique anisotrope en déduisant un tenseur modifié décrivant l'effet de l'endommagement pour un système d'équations de contraintes effectives susceptible d'inclure l'effet d'un endommagement dans un matériau anisotrope. Le tenseur modifié supprime la restriction de la connaissance a priori des directions des contraintes principales imposées par un tenseur d'effet d'endommagement développé précédemment; il peut à présent entrer dans les applications pratiques en construction de l'analyse des ruptures.

On montre qu'il est possible de réduire le tenseur proposé à une valeur scalaire dans le cas d'un dommage isotrope, dès lors qu'il est exprimé non seulement suivant les directions principales, mais dans un système de coordonnées arbitraires, ce qui est une condition nécessaire pour en vérifier la validité.

On choisit une traction multiaxiale et une torsion pure pour illustrer l'application de la théorie ainsi que des variables d'endommagement associées, susceptibles d'être déterminées expérimentalement à l'aide d'éprouvettes de laboratoire.

Les variables d'endommagement mesurées confirment la présence d'un dommage anisotrope dans le cas d'une éprouvette d'un matériau initialement isotrope; son amplitude est plus prononcée à des contraintes ou des déformations plus importantes.

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Chow, C.L., Wang, J. An anisotropic theory of elasticity for continuum damage mechanics. Int J Fract 33, 3–16 (1987). https://doi.org/10.1007/BF00034895

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Keywords

  • Stress Equation
  • Damage Variable
  • Material Specimen
  • Continuum Damage Mechanic
  • Damage Theory