An inverse-problem based stochastic approach to model the cumulative damage evolution of composites

Fibre-reinforced composites are often selected for high-responsibility structural applications due to their high specific stiffness and strength, and corrosion resistance. These materials have a rather good rating as regards to life time in fatigue, but the same does not occur with the number of cycles to initial damage or with the evolution of damage. Due to material heterogeneity, random nature of fatigue loading and random environment conditions, the damage phenomenon is a cumulative evolutionary stochastic process in essence, characterized by changes in laminate compliance with time. As a consequence, it is more appropriately examined within a probabilistic framework. An approach that considers stochastic damage accumulation by means of discrete time Markov chains is proposed in this work to analyze damage evolution of composite laminates. Additionally a unitary time transformation by means of monotonic cubic Hermite splines has been introduced to take into account the nonstationary effects with a reduced set of model parameters. An inverse procedure is proposed to find the optimal stochastic model parameters together with the time transformation parameters. A numerical comparative study of the above-proposed technique is presented. Selection.