Antiferromagnetism in a doped spin-Peierls model: Classical and quantum behaviors

We investigate the sequential cracking of thin brittle coatings attached adhesively to substrates. The focus of our study are uniaxial tensile loading conditions, where we monitor the behavior in a continuous picture and the coating strength follows a two-parameter Weibull distribution. For fracture well under way we derive an approximate analytical expression for the distribution of fragment lengths. We recover that the distribution scales with the average fragment length and that is a power function of the applied strain , i.e. , where depends on the distribution of the strength of the coating and on the adhesive's nonlinearity. Furthermore we compare our approximate analytical expression with numerical solutions and with simulations' findings. Received 16 February 2000