On the stochastic deformation process in a randomly structured polycrystalline solid

The concepts of the stochastic micromechanial approach to the response behaviour of engineering materials are, first, illustrated. A stochastic micromechanical model is, then, formulated for the deformation of a class of randomly structured material, namely a polycrystalline solid. Due to the discrete nature of the microstructure, the relevant field quantities are considered as random variables or functions of such variables, and the accompanying deformation process is treated as a stochastic process of the Markov-type which leads to Chapman–Kolmogrov functional character. An eventual time-dependent, non-homogeneous stochastic damage process is then examined in terms of the intensities of transformation in the microstructure.