Applications of Tensor Functions in Damage Mechanics of Anisotropic Materials

Conference paper
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 9)


This article will provide a short survey of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The tertiary creep phase is accompanied by the formation of microscopic cracks on the grain boundaries, so that damage accumulation occurs.

The damage state in a uni-axial tension specimen is discussed and the time to rupture has been calculated.

Then, the paper is concerned with the creep behaviour of materials in a state of multiaxial stress. Because of its microscopic nature, damage generally has an anisotropic character even if the material was originally isotropic. The fissure orientation and length cause anisotropic macroscopic behaviour. Therefore, damage in an isotropic or anisotropic material which is in a state of multi-axial stress can only be described in a tensorial form. Thus, tensorial constitutive and damage evolutional equations have been developed. Some examples for practical use and simplified representations are proposed. Furthermore, important damage effective stress concepts are discussed in detail.

Finally, some own experiments should be mentioned, which have been carried out in order to examine the validity of the mathematical modelling.


Anisotropy constitutive equations creep rupture damage effective stress tensor functions time to rupture experimental results 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  1. 1.Mathematical Models in Materials ScienceTechnical University AachenAachenGermany

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