Stochastic modeling of damage evolution in composites under environmental ageing

A mathematical model is proposed for predicting damage evolution and stiffness degradation in composite materials under environmental ageing. Environmental parameters such as moisture, temperature, and ultraviolet (UV) radiation cause hygrothermal loads on the structure, which leads to damage evolution. The present work establishes a constitutive model for treating the damage density as a random variable. A forward stochastic differential equation (FSDE) is proposed to predict the damage density evolution. Damage nucleation and annihilation rates are taken into consideration in terms of Brownian motions. A second-order damage tensor is developed using the solution of the FSDE. The damage tensor is incorporated into the constitutive model for predicting the elastic moduli. Finally, the proposed model is verified against experimental observations under certain hygrothermal conditions.