Vine copulas for accelerated prediction of composite strength variability

Abstract

Composite materials are essential for many advanced engineering applications, but numerical quantification of strength variability can be computationally expensive. This paper proposes a novel methodology that drastically reduces the number of finite element simulations required to characterise composite material strength variability using the concept of vine copulas. This concept provides a flexible tool for the representation of high-dimensional dependencies. The methodology considers spatial scatter of three material variabilities: fibre volume fraction, fibre misalignment and fibre strength. First, the cross-correlation between stress, fibre volume fraction and fibre misalignment is fitted by a vine copula using results from a limited number of finite element simulations. Next, the vine copula is used to predict new conditional stress realisations when given realisations for the fibre volume fraction and fibre misalignment. This effectively replaces the finite element simulations with a vine copula that is much faster to evaluate. The methodology is verified by predicting the tensile failure load of a unidirectional composite coupon. Predictions are very similar to an exclusively finite element-based approach, while reducing the number of finite element simulations by a factor of 200.