Introduction to computational methods of damage mechanics under stochastic actions

This paper reviews and discusses some basic ingredients necessary for the study of damaged continua with diffused defects like microcracks, pores, dislocations, etc., under stochastic loading histories and, in particular, under sequences of impulses described by Poisson arrival processes. The mechanical model of a continuum with microstructure is adopted: in other words, the state of the continuum is described by the usual displacement field and by an additional field of a second-order non-symmetric tensor which describes the microstructural rearrangement of the material due to the presence of defects. It is shown that the time evolution of this tensor, usually assumed empirically on the basis of experimental results, is governed by a balance equation. The discretization of the problem and integral measures of damage, useful for the numerical solutions, are also discussed.