Uncertainty quantification for viscoelastic composite materials using time-separated stochastic mechanics

Abstract

With the growing use of composite materials, the need for high-fidelity simulation techniques of the related behavior increases. One important aspect to take into account is the uncertainty of the response due to fluctuations of the material parameters of the constituent materials of the homogenized composite. This inherent randomness leads to stochastic stresses on the microscale and uncertain macroscale response. Until now, the viscoelastic response of the matrix material seriously hindered the application of efficient methods to predict the composite material behavior. In this work, a novel method based on the time-separated stochastic mechanics (TSM) is developed to address this problem. We present how the uncertainty of the microscale stresses of a representative volume element and the homogenized macroscale stresses can be approximated with a low number of deterministic finite element simulations. Quantities of interest are the expectation, standard deviation, and the probability distribution function of the stresses on micro- and macroscale. The results showcase that the TSM is able to approximate the reference results very well at a minimal fraction of the computational cost needed for Monte Carlo simulations.