A general formulation for transition probabilities of Markov model and theapplication to fracture of composite materials

A generalized method for formulating unit-jump Markov chain model is presen ted. This method uses geometric series to determine the transition probabil ities instead of using a moment generation function. Recursive equation for the transition probabilities has been derived in terms of the mean values. Present method is also compared by other method for robustness. Applicatio n of the unit-jump Markov chain model for characterizing fracture process o f composites is described. By introducing a proper scaling factor, the enti re probability history of the crack propagation at any loading states can b e evaluated by the present model. (C) 2000 Elsevier Science Ltd. All rights reserved.