Damage evolution and localization in heterogeneous materials under dynamical loading: stochastic modelling

A mathematical model of damage evolution in heterogeneous materials, which takes into account the random nature of local failure, is developed on the basis of the theory of stochastic equations. A damage evolution law, which allows for the energy dissipation due to the new surface formation as well as the influence of local (thermic) fluctuations is obtained. The kinetic differential equation for time-dependent probability distribution of a damage parameter is derived theoretically. Damage evolution and damage localization under dynamical loading are investigated numerically on the basis of the model developed.