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Theory of fracture formation in a heterogeneous fibrillar membrane

We present a statistical model of fracture in hierarchical structured heterogeneous materials. We describe the material as a network of fibre bundles. The time to fracture is analytically derived as a function of the bundle size and the local stress. This provides a straightforward criterium for material selection. The original framework here proposed proves versatile: it can be adapted to various practical specific cases upon tuning of its parameters which corresponds to experimentally measurable quantities.