In modern multi-scale modeling of heterogeneous and composite materials, the Representative Volume Element (RVE) is designed to capture the relevant statistical properties of the material, providing computational efficiency when multiple small-volume ensemble realizations can approximate the accuracy of a “large” RVE. However, the inherent aleatory uncertainty of the microstructure remains and must be quantified. We aim to develop suitable techniques to quantify this uncertainty.

Volume element with associated uncertainty indicator.

Some significant material classes, such as long-fiber reinforced thermoplastics, cannot be characterized by traditional Representative Volume Elements (RVEs) with periodic boundary conditions. However, non-periodic microstructures or non-periodic displacement boundary conditions introduce a non-trivial boundary layer error in the numerical results. As a remedy we analyze the use of innovative techniques which allow for highly accurate results from digital volume images, i.e., originating from µ-CT images.

FFT-based computational homogenization methods allow to efficiently compute the effective material response of complex materials discretized on a regular grid. However, due to the grid-like structure, interfaces that are not parallel to the grid are resolved in a jagged manner, which leads to an error in the approximation of the local fields in the vicinity of material interfaces. We aim to improve the accuracy of FFT-based computational homogenization methods while preserving their efficiency. In this context, it is crucial to ensure the mesh-independent robustness of the microscale solvers, which requires advanced preconditioning and stabilization techniques.

Discrete (red-blue) vs. continuous (yellow) description of a material interface.