Research Area Simulation - Associated Project

Computational homogenization of non-linear and inelastic material laws in tensor-train format

Advisors: Schneider, Böhlke (ITM)

Materials with complex microstructure, e.g., fiber composites, are indispensable for modern technological applications. Usually these materials exhibit anisotropic elastic, viscous and plastic behavior, which is difficult to characterize experimentally.
From a computational point of view the challenge is to perform numerical simulations on digital volume images containing several billions of points in combination with material laws which incorporate the time dimension. The amount of data to be stored and processed just on the micro-scale is overwhelming and prohibits fully coupled macro-micro-simulations (e.g., FE2, FE-FFT).
Thus, the idea of this project is to develop and apply modern numerical techniques for computational mechanics to achieve numerical upscaling. The goal is to identify effective anisotropic material laws on the macro-scale which do not require full-field simulations on the micro-level. The task is to compute effective non-quadratic potentials for arbitrarily complex material laws using efficient and robust computational methods. For instance, model order reduction and deep learning techniques can be applied to achieve this computation of effective potentials.

Figure: Local solution fields for macroscopic temperature gradient in x-direction, left: heat flux magnitude normalized to macroscopic heat flux, right: temperature gradient normalized to macroscopic temperature gradient