Asymptotic Approximations Used in Probabilistic Failure Modeling of Woven Fiber Networks

Approximate numerical results for the strength distributions of large woven fiber networks are given. The system under consideration consists of fibers arranged in a mutually orthogonal, simple weave pattern. The goal is to estimate the cumulative distribution function for failure of the network as a function of the fiber properties and the failure mechanism. Based on a two-dimensional load sharing model developed earlier and appropriate asymptotic theory, we have constructed conservative upper bound approximations for arbitrarily large networks. Additionally, we have introduced a translation ratio that may be used to relate the lower tail behavior of diverse networks experiencing different biaxial loading conditions.