F. Rotersa,*, P. Eisenlohra, L. Hantcherlia, D. D. Tjahjantoa, T. R. Bielerb , D. Raabea
aMax-Planck-Institut für Eisenforschung, Düsseldorf, Germany
bChemical Engineering and Materials Science, Michigan State University, East Lansing MI, USA
This article reviews continuum-based variational formulations for describing the elastic–plastic deformation of anisotropic heterogeneous crystalline matter. These approaches, commonly referred to as crystal plasticity finite element models, are important both for basic microstructure-based mechanical predictions as well as for engineering design and performance simulations involving anisotropic media. Besides the discussion of the constitutive laws, kinematics, homogenization schemes, and multiscale approaches behind these methods we also present some examples including in particular comparisons of the predictions with experiments. The applications stem from such diverse fields as orientation stability, microbeam bending, single-and bicrystal deformation, nanoindentation, recrystallization, multiphase steel (TRIP) deformation, and damage prediction for the microscopic and mesoscopic scales and multiscale predictions of rolling textures, cup drawing, Lankfort (r) values, and stamping simulations for the macroscopic scale.