A multifield description of continua endowed by diffused microcracks, recently proposed by the authors [Mariano and Augusti, Math. Mech. Sol. 3 (l998) l83--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 second order approximation of the microcrack density function m(P n, t) that represents the distribution of the number of microcracks in each direction n in a neighborhood (mesodomain) of the point P: m(P n, t) is considered as a submartingale process in each point P leading to a stochastic field over the continuum body. Generalized measures of internal actions represent the interactions voids--voids and void--matrix. They perform work in the variation of relevant conjugated fields. Invariance requirements on the overall power allows to deduce both the usual balance of forces and the balance of generalized internal actions, obtaining a model different from the classical internal variable models not only conceptually but also formally. The introduction of a damage entropy flux, whose divergence is the production of configurational entropy, allows to include damage criteria within the context of Clausius--Duhem inequality. The basic features of an appropriate finite-element discretization are formalized in the case of linear elastic brittle materials: the stochastic distribution of microcracks is considered through the stochastic nature of the elements of the stiffness matrix. Among other assets, the multifield
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机译：作者最近提出了由弥散微裂纹赋予的连续体的多场描述[Mariano and Augusti，Math。机甲索尔[3（l998）l83--200]在确定性上下文中扩展为涵盖微裂纹分布和演化的某些随机方面。连续体的微裂纹状态由张量场描述，该张量场定义为微裂纹密度函数m（P n，t）的二阶近似值，该函数表示在n个方向上的每个方向n的微裂纹数量分布。 P点：m（P n，t）被认为是每个点P中的次市场过程，导致连续体上的随机场。内部行为的广义度量表示了交互作用-空洞和空洞-矩阵。他们在相关共轭场的变化中执行工作。对总功率的不变性要求可以推论出通常的力平衡和广义内部作用的平衡，不仅在概念上而且在形式上都获得了不同于经典内部变量模型的模型。引入损伤熵通量（其散度是构型熵的产生）允许在Clausius-Duhem不等式的上下文中包括损伤标准。在线性弹性脆性材料的情况下，适当的有限元离散化的基本特征被形式化：微裂纹的随机分布是通过刚度矩阵元素的随机性质来考虑的。在其他资产中，多领域
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