Towards stochastic continuum damage mechanics. (February 2020) - Malyarenko, Anatoliy; Ostoja-Starzewski, Martin
Highlights: stochastic generalisation of continuum damage mechanics. explicit representation of damage tensors as mean-square continuous, wide-sense homogeneous and isotropic random fields. explicit spectral expansion of damage tensor random fields. two special examples of damage tensor random fields. Abstract: In classical continuum damage mechanics, the distribution of cracks over differently oriented planes is an even deterministic function defined on the unit sphere. The coefficients of its Fourier expansion are completely symmetric and completely traceless tensors of even rank, the so-called fabric or damage tensors. We propose a stochastic generalisation of the above described mathematical model, where damage tensors are mean-square continuous wide-sense homogeneous and isotropic random fields.