On three-dimensional microcrack density distribution

This paper considers tensorial representations of several microcrack distri bution fractions due to tensile and compressive principal stresses in britt le materials in the framework of continuum mechanics. The common framework for deriving the damage tensors of different order from any density functio n is suggested. Second and fourth order damage tensors are derived for Dira c-, truncated Gauss-, and trigonometrical (cos(2)-) microcrack distribution s using harmonic Fourier-like series. Each distribution is investigated und er different combinations of tensile and compressive principal stresses for three-dimensional load cases. It is emphasized that only the trigonometric al distribution yields a spherical crack density surface for the fourth ord er tensor approximation under three equal principal stresses.