We are pleased to announce that we will have Prof. Dr. Matti Schneider from the UDE as our guest. Prof. Schneider is famous for pushing the application Fourier-based numerical methods on micromechanical problems to new limits.
Micromechanics seeks to provide constitutive models of heterogeneous materials based on the knowledge of the material behavior of the individual materials constituting the microstructure and the geometric arrangement of these materials within the microstructure. Modern computational micromechanics methods are used to compute the nonlinear response of materials with quite complex microstructure and permit to reduce the experimental effort necessary to characterize the relevant material behavior, in particular for long-term loading. Due to the complex microstructures characteristic for materials used in industry, computational methods based on regular, i.e., Cartesian, grids are frequently used. Computational strategies based on the fast Fourier transform (FFT) turn out to be particularly performing due to the excellent implementation of available FFT packages and the automatic preconditioning provided by the formulation. The talk is intended to give a gentle introduction to such FFT-based methods for micromechanics with a focus on ''modern'' developments, i.e., the use of finite element and finite difference discretizations. Moreover, we plan to discuss how to overcome the limitation to periodic boundary conditions traditionally associated with FFT-based methods for micromechanics.