Solvable fracture model with local load transfer

A stochastic fracture model of N ordered elements with one-sided local transfer of load is proposed and solved. The probability of total collapse is calculated as a function of the applied load and we find that, assuming Weibull-type distributions to describe the elemental strengths, in the limit of large N, the global strength of the set is proportional to (logN${)}^{\mathrm{-}1}$. To solve the model, use is made of the fact that when the length of a crack surpasses a critical value, the associated avalanche necessarily destroys the whole set. The antecedents of this model in materials science and seismology are indicated.