An inter-scale stiffness propagation method with nonintrusive modeling of stochastic porosity in unidirectional composites

Porosity is a primary source of stiffness uncertainty in fiber-reinforced composites. However, explicitly modeling pores with prescribed geometry at the composite-scale leads to prohibitive computational cost for uncertainty quantification. This study proposes an inter-scale stiffness propagation method linking matrix-scale stochastic porosity to stiffness uncertainty of unidirectional fiber-reinforced (UD) composites. In such nonintrusive modeling of porosity, the local volume effect strongly influences the quantification accuracy. Pores in the matrix are modeled as spheres distributed by a Poisson point process. Their radius follows a truncated Gaussian law, leading to a porosity field whose covariance follows a Matérn-type form independent of local volume. The decay of porosity variance with increasing volume size, attributed to local volume averaging, is confirmed, indicating a similar behavior in finite element (FE) homogenization at the matrix-scale. The variance of matrix stiffness is found to decrease with growing local volume size, and its consistent negative correlation with porosity is thereby established. The stiffness-porosity joint distribution is then constructed by the conditional Gaussian mapping method. Finally, the stiffness calculation model at the composite-scale is developed, and the uncertainty induced by pores at the matrix-scale is quantified by Monte Carlo simulation. The results show that the nonintrusive modeling of stochastic porosity enables reliable stiffness propagation and efficient pore-induced uncertainty quantification.