Disorder is an inherent property of practically all materials, both natural and man-made. Heterogeneity occurring on different length scales plays a crucial role in the mechanical response and fracture behavior of materials. On the one hand, the presence of flaws, voids, and grain boundaries reduces the fracture strength, on the other hand, however, they improve the damage tolerance of materials which has a high practical importance for construction components.

Beyond artificially made (tailored) materials, structural heterogeneity of local stiffness is an important feature of biological materials as well. One of the most known examples of such biological composite materials is nacre which exhibits extraordinary mechanical properties compared to its constituent materials. These features can be partly attributed to the interplay of the local variation of stiffness and strength. In order to obtain a comprehensive understanding of fracture processes of heterogeneous materials it is necessary to take into account disorder both in local stiffness and strength of material elements when constructing discrete stochastic models.

We investigate the fracture of heterogeneous materials in the framework of fiber bundle models taking into account two sources of quenched disorder: the random fracture strength and the local variation of the stiffness of material elements are represented by uncorrelated random variables. Focusing on the limit of equal load sharing we give an analytic description of the macroscopic response of the system, while the microscopic process of fracture is explored by computer simulations under stress controlled loading. If the stiffness of fibers is the only source of disorder the mechanical response of the system is determined by the tail of the stiffness distribution showing a transition from perfectly brittle to quasi-brittle behavior. Our study revealed that the presence of strength disorder has an astonishing stabilizing effect, i.e. any finite amount of strength disorder leads to quasi-brittle response irrespective of the stiffness distribution. On the micro-level fracture proceeds in bursts which are characterized by power law distributions. The exponent of the power law proved to be sensitive to the relative amount of the two disorders.