Derivation of higher-order terms in FFT-based numerical homogenization
For researchers in computational homogenization, this provides a method to compute higher-order corrections, but it is incremental as it extends an existing scheme.
The paper derives higher-order terms in FFT-based numerical homogenization for quasi-static linear elasticity, extending the Basic Scheme to solve a hierarchy of linear problems from an asymptotic expansion, with numerical results for the first two orders.
In this paper, we first introduce the reader to the Basic Scheme of Moulinec and Suquet in the setting of quasi-static linear elasticity, which takes advantage of the fast Fourier transform on homogenized microstructures to accelerate otherwise time-consuming computations. By means of an asymptotic expansion, a hierarchy of linear problems is derived, whose solutions are looked at in detail. It is highlighted how these generalized homogenization problems depend on each other. We extend the Basic Scheme to fit this new problem class and give some numerical results for the first two problem orders.