Microplane-damage-based Effective Stress and Invariants

Abstract

This paper addresses some issues of the application of the effective stress tensor to coupled damage-plasticity from the point of view of a microplane. In this paper, damage and effective stress are defined on microplanes. The effective stress tensor of Murakami (1988) can be recovered as the second-order fabric tensor of the effective stress vector. The effective second invariant J ₂ is defined as the integration of the square of the effective shear stress over the unit sphere. It is revealed that the J ₂ possesses the form of the Hill (1950) anisotropic yield function based on the definition. Therefore, one can also use the Hill (1950) model to describe coupled anisotropic-damage-plasticity except for the conventional approach of effective stress.

Keywords

microplane effective stress anisotropic yield function

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References

Carol, I. and Bazant, Z.P. (1997). Damage and Plasticity in Microplane Theory , Int. J. Solids & Struct., 34: 3807-3835 .

Drucker, D.C. and Prager, W. (1952). Soil Mechanics and Plastic Analysis for Limit Design , Q. Appl. Math., 10: 157-165 .

Kachanov, L.M. (1958). Time of the Rupture Process Under Creep Conditions , Izv. Akad. Nauk., USSR. Otd. Tekhn. Nauk., 8: 26-31 .

Krajcinovic, D. (1996). Damage Mechanics, North-Holland, Amsterdam .

Hill, R. (1950). The Mathematical Theory of Plasticity, Clarendon Press, Oxford .

Liu, C. , Huang, Y. and Stout, M.G. (1997). On the Asymmetric Yield Surface of Plastically Orthotropic Materials: A Phenomenological Study , Acta Mater., 45: 2397-2406 .

Lemaitre, J. (1992). A Course on Damage Mechanics, Springer-Verlag, Berlin, Heidelberg, New York .

Lemaitre, J. , Desmorat, R. and Sauzay, M. (2000). Anisotropic Damage Law of Evolution , European Journal of Mechanics A-Solids, 19: 187-208 .

Leukart, M. and Ramm, E. (2003). A Comparison of Damage Models Formulated on Different Material Scales , Computational Materials Science, 28: 749-762 .

10.

Lubarda, V.A. and Krajcinovic, D. (1993). Damage Tensors and the Crack Density Distribution , Int. J. Solids & Struct., 30: 2859-2877 .

11.

Murakami, S. (1988). Mechanical Modelling of Material Damage , ASME Journal of Engineering Materials and Technology, 55: 280-286 .

12.

Rabotnov, I.N. (1963). On the Equations of State for Creep , Progress in Applied Mechanics - The Prager Anniversary, 8: 307-315 .

13.

Yang, Q. , Li, Z.K. and Tham, L.G. (2001). An Explicit Expression of Second Order Fabric-tensor Dependent Elastic Compliance Tensor , Mechanics Research Communications, 28: 255-260 .

14.

Zheng, Q.S. and Betten, J. (1996). On Damage Effective Stress and Equivalence Hypothesis , Int. J. Damage Mech., 6: 319-340 .