Stochastic multi-scale modeling of carbon fiber reinforced composites with polynomial chaos

Abstract A stochastic multi-scale modeling framework for uncertainty quantification of carbon fiber reinforced composites with a non-intrusive method called Polynomial Chaos Decomposition with Differentiation (PCDD) is presented. The performance behavior and reliability of the composites are dependent on its constituents properties (fiber and matrix properties) in addition to ply-orientation, ply-thickness, and loading conditions; hence, the uncertainties are considered using two stages: i) micro-scale modeling, and ii) macro-scale modeling. In the first stage, stochastic micro-scale modeling with PCDD is carried out to obtain the effective material properties of a lamina that are influenced by the uncertainties in its constituents. Then, these stochastic effective material properties are considered along with the uncertainties in geometrical properties of the laminate such as ply thicknesses and ply orientation to determine the stochastic performance of the laminate. The framework was applied for multi-scale buckling analysis and reliability estimation. Another approach for polynomial chaos called Stochastic Point Collocation (COLL) was also studied, and the results obtained with PCDD and COLL were compared with a large number of Latin Hypercube Sampling simulations. The results demonstrated the computational superiority of the proposed framework to achieve high accuracy stochastic response models as well as invaluable information about composites using a stochastic approach.