Ernesti Felix. A computational multi-scale approach for brittle materials

Karlsruher Institut für Technologie (KIT), 2023. — (Schriftenreihe Kontinuumsmechanik im Maschinenbau 26). – ISBN 978-3-7315-1285-1.Вычислительный многомасштабный подход для хрупких материалов
rials used in an industrial context often exhibit a complex mi crostructure which directly influences the macroscopic material be havior. For simulations on the component scale, multi-scale meth ods may exploit the microstructural information. In particular ho mogenization methods are often used due to their well formulated mathematical background.
In a first step we focus on the characterization of complex microstruc tures. We investigate the applicability of Minkowski tensors, which originate from stochastic geometry, to characterize microstructures. We identify in particular a normalized tensor, the quadratic normal tensor, as a suitable characterizerIntroduction
Fundamental concepts
Characterizing digital microstructures by the Minkowski-based QNT
Computing the effective crack energy on a combinatorially consistent grid
The effective crack energy of heterogeneous and locally anisotropic microstructures
On the influence of the boundary conditions when computing the effective crack energy
Summary and conclusions
Minkowski tensors for specific shapes
Performance of additional penalty factor choices for ADMM