# Research Projects

**Basics of constitutive formulations, crystal kinematics, homogenization, multiple scales, and multiphysics approaches in crystal plasticity finite element modeling: theory, experiments, applications**

F. Roters^{a,*}, P. Eisenlohr^{a}, L. Hantcherli^{a}, D. D. Tjahjanto^{a}, T. R. Bieler^{b} , D. Raabe^{a}

^{a}Max-Planck-Institut für Eisenforschung, Düsseldorf, Germany

^{b}Chemical Engineering and Materials Science, Michigan State University, East Lansing MI, USA**Abstract**

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.

[more]**Influence of dislocation climb on the creep rates in γ'-strengthened Ni base superalloy single crystals: A discrete dislocation dynamics study**

**Orientation dependence of shear banding in fcc single crystals**

#### Mechanism Oriented Steel Development

#### Dual-Phase Steels: Advances in Microstructure-Oriented Processing and Micromechanically Guided Design

**The mechanical size effect as a mean-ﬁeld breakdown phenomenon: Example of microscale single crystal beam bending**

**Computationally efficient and quantitatively accurate multiscale simulation of solid-solution strengthening by ab initio calculation**

**Ab initio study of compositional trends in solid solution strengthening in metals with low Peierls stresses**

**Theory-guided bottom-up design of b-titanium alloys as biomaterials based on first principles calculations: Theory and experiments**

**beta-Ti alloys**for

**biomedical applications**using a quantum mechanical approach in conjunction with experiments. Parameter-free

**density functional theory**calculations are used to provide theoretical guidance in selecting and optimizing Ti-based alloys...