FFT-based computational micromechanics and homogenizing fiber-reinforced composites

This talk is concerned with modern methods for computing the effective material properties of heterogenenous materials.

In the first part, we shall discuss computational methods that became increasingly popular in the last decade and are specifically designed for complex microstructures, the so-called FFT-based computational homogenization methods, where FFT stands for the fast Fourier transform. We also discuss recent developments on numerical solution methods that are both memory-efficient and fast.

In the second part of the talk, we focus on fiber-reinforced composites which are frequently used in lightweight design. The corresponding microstructures feature (non-overlapping) cylindrical inclusions dispersed at a specific volume fraction and orientation state within a volume element, serving as a cut-out of a specific realization of a stochastic fiber-reinforced microstructure. We discuss how to generate such microstructures, and also shed light on the ensuing ramifications for the effective elastic moduli for such structures (using the computational methods discussed earlier).