Theoretical foundations and numerical applications of multiscale modeling in solid mechanics, from atomistics all the way up to the macroscopic continuum scale with a focus on scale-bridging methods (including the theory of homogenization, computational homogenization techniques, modeling by methods of atomistics, coarse-grained atomistics, mesoscale models, multiscale constitutive modeling).
Learning objective
To acquire the theoretical background and practical experience required to develop and use theoretical-computational tools that bridge across scales in the multiscale modeling of solids.
Content
Microstructure and unit cells, theory of homogenization, computational homogenization by the finite element method and Fourier-based techniques, discrete-to-continuum coupling methods, atomistics and molecular dynamics, coarse-grained atomistics for crystalline solids, quasicontinuum techniques, analytical upscaling methods and models, multiscale constitutive modeling, selected topics of multiscale modeling.
Lecture notes
Lecture notes and relevant reading materials will be provided.
Literature
No textbook is required. Reference reading materials are suggested.
Prerequisites / Notice
Continuum Mechanics I or II and Computational Mechanics I or II (or equivalent).
