DAMAGE EVOLUTION AND LOCALIZATION IN HETEROGENEOUS MATERIALS UNDER DYNAMICAL LOADING - STOCHASTIC MODELING

A mathematical model of damage evolution in heterogeneous materials, w hich takes into account the random nature of local failure, is develop ed on the basis of the theory of stochastic equations. A damage evolut ion law, which allows for the energy dissipation due to the new surfac e formation as well as the influence of local (thermic) fluctuations i s obtained. The kinetic differential equation for time-dependent proba bility distribution of a damage parameter is derived theoretically. Da mage evolution and damage localization under dynamical loading are inv estigated numerically on the basis of the model developed.