Uncertainty quantification and global sensitivity analysis for progressive failure of fiber-reinforced composites

In this paper, a framework for the stochastic progressive failure analysis (PFA) of fiber-reinforced composites is presented. The nonlinear responses of composite structures are hugely influenced by the randomness in material properties of plies, thereby yielding significantly different responses compared with that with deterministic simulations. Moreover, performing PFA using finite element analysis (FEA) is a computationally intensive process that becomes unaffordable while performing uncertainty analysis that requires numerous FEA runs. So, to alleviate this computational cost while maintaining an acceptable accuracy, an efficient technique called polynomial chaos expansion (PCE) was implemented. Another advantage of PCE is that it allows performing global sensitivity analysis (GSA) to estimate the influence of the random inputs on the stochastic responses as a post-processing step without any additional cost. The effects of randomness in material properties on the first ply failure load and ultimate failure responses of a composite laminate were compared with the framework using PCE as well as 5000 LHS simulations and the results underlined the cost-effectiveness as well as the high accuracy of PCE. Moreover, the GSA successfully identified the influential random material properties that correlated well with the failure modes. Thus, the presented approach and the results of this study will be instrumental in understanding the failure as well as improving the design of composite structures.