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Applications of Tensor Functions in Continuum Damage Mechanics

Department of Mathematical Models in Materials Science Technical University Aachen D-5100 Aachen, Templergraben 55 Germany

The mechanical behaviour of anisotropic solids requires a suitable mathe matical modelling. The properties of tensor functions with several argument tensors con stitute a rational basis for a consistent mathematical modelling of complex material be haviour.

This paper presents certain principles, methods, and recent successful applications of tensor functions in continuum mechanics. The rules for specifying irreducible sets of ten sor invariants and tensor generators for material tensors of rank two and four are also dealt with.

Furthermore, it is very important to determine the scalar coefficients in constitutive and evolutional equations. This problem is explained in more detail.

Key Words: anisotropy • canonical form • constitutive equations • continuum damage mechanics • creep • creep rupture • creep rupture time • damage tensor • evolutional equa tions • irreducible invariants • Monkman-Grant relationship • material behaviour • material tensor • net-stress concept • tensor function • tensor generator • tensorial interpolation • ter tiary creep • time to rupture.

International Journal of Damage Mechanics, Vol. 1, No. 1, 47-59 (1992)
DOI: 10.1177/105678959200100103


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