Abstract
This paper considers tensorial representations of several microerack distribution functions due to tensile and compressive principal stresses in brittle materials in the framework of continuum mechanics. The common framework for deriving the damage tensors of different order from any density function is suggested. Second and fourth order damage tensors are derived for Dirac-. truncated Gauss-, and trigonometrical (cos 2 -) microcrack distributions using harmonic Fourier-like series. Each distribution is investigated under different combinations of tensile and compressive principal stresses for three-dimensional load cases. It is emphasized that only the trigonometrical distribution yields a spherical crack density surface for the fourth order tensor approximation under three equal principal stresses.
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