Probabilistic analysis and optimization of energy absorbing components made of nanofiber enhanced composite materials

An enhanced thermoset polymer matrix with randomly distributed carbon nanofibers (CNFs) is combined with conventional long fibers to form a hybrid composite material for application to impact energy absorbing components. The multi-inclusion method in combination with functionally graded interphase is used for stiffness characterization and shear-lag theory combined with quasi-isotropic lamination approximation is used for strength prediction. Axial crush simulations are performed using MD Nastran with a micromechanics-based progressive failure analysis constitutive model. The stochastic uncertainties in the geometric and material properties of CNF as well as the three-dimensional, non-homogeneous CNF–matrix interphase are represented using probability theory. Through Monte Carlo simulations, these uncertainties are propagated to the homogenized macroscopic properties of the nano-enhanced matrix and subsequently to the stiffness and strength properties of the composite laminate as well as the energy absorbing characteristics of the crush tube. A probabilistic design optimization problem is formulated for minimizing the failure probability associated with the specific energy absorption of the composite tube. A dual surrogate modeling approach is used for approximating the failure probability and solving the optimization problem using sequential quadratic programming. The modeling approach, uncertainty analysis, and probabilistic optimization results are presented and discussed.