Complex fiber bundle model for optimization of heterogeneous materials

We propose a complex fiber bundle model for the optimization of heterogeneous materials, which consists of many simple bundles. We also present an exact and compact recursion relation for the failure probability of a simple fiber bundle model with local load sharing, which is more efficient than the ones reported previously. Using a ''renormalization method'' and the recursion relation developed for the simple bundle, we calculate the failure probabilities of the complex fiber bundle. When the total number of fibers is given, we find that there exists an optimum way to organize the complex bundle, in which one gets a stronger bundle than in other ways.

Failure of fiber bundles with local load sharing

We develop a recursion-relation approach for calculating the failure probabilities of a fiber bundle with local load sharing. This recursion relation is exact, so it provides a way to test the validity of the various approximate methods. Applying the exact calculation to uniform and Weibull threshold distributions, we find that the most probable failure load coincides with the average strength as the size of the system N --> infinity.