A data-driven stochastic approach to model and analyze test data on fatigue response

A stochastic approach to model and analyze test data on the fatigue response of materials and laminated composites is developed. The developed approach is ‘data-driven’ in nature. It has been customary to describe the fatigue response of metallic and laminated composite materials using a suitable parameter that can serve as the indicator and descriptor of damage accumulation. In the present methodology, the fatigue response of the material is quantified by interpreting the corresponding material parameter to be an embedded Markov process. The true probability distributions of the fatigue response parameter are extracted from sample test data based on an analytical approach, and they are used in the formulation. To this end, the Maximum Entropy Method is incorporated into the formulation. A recursive stochastic matrix equation is developed based on the test data using the theory of reliability and Fokker–Plank–Kolmogorov equation. Application of the methodology to a composite laminate is demonstrated.