Stochastic evolution of microcracks in continua

A multifield description of continua endowed by diffused microcracks, recen tly proposed by the authors [Mariano and Augusti, Math. Mech. Sol. 3 (1998) 183-200] within a deterministic context, is extended to cover some of the stochastic aspects of microcrack distribution and evolution. The microcrack state of the continuum is described by a tensor field defined as the secon d order approximation of the microcrack density function m(P, n, t) that re presents the distribution of the number of microcracks in each direction n in a neighborhood (mesodomain) of the point P: m(P, rt, t) is considered as a submartingale process in each point P, leading to a stochastic field ove r the continuum body. Generalized measures of internal actions represent the interactions voids-v oids and void-matrix. They perform work in the variation of relevant conjug ated fields. Invariance requirements on the overall power allows to deduce both the usual balance of forces and the balance of generalized internal ac tions, obtaining a model different from the classical internal variable mod els not only conceptually but also formally. The introduction of a damage e ntropy flux, whose divergence is the production of configurational entropy, allows to include damage criteria within the context of Clausius-Duhem ine quality. The basic features of an appropriate finite-element discretization are form alized in the case of linear elastic brittle materials: the stochastic dist ribution of microcracks is considered through the stochastic nature of the elements of the stiffness matrix. Among other assets, the multifield approa ch overcomes the mesh dependence of the numerical results obtained on the b asis of the more used internal variable schemes. (C) 1999 Elsevier Science S.A. All rights reserved.