The mechanical behavior of many applied materials arises from their microstructure. Thus, to aid the design, development and industrialization of new materials, robust computational homogenization methods are indispensable. The present thesis is devoted to investigating and developing FFT-based micromechanics solvers for efficiently computing the (thermo)mechanical response of nonlinear composite materials with complex microstructures.

An overview of different methods for the derivation of extended continuum models is given. A gradient plasticity theory is established in the context of small deformations and single slip by considering the invariance of an extended energy balance with respect to Euclidean transformations, where the plastic slip is considered as an additional degree of freedom. Thermodynamically consistent flow rules at the grain boundary are derived. The theory is applied to a two- and a three-phase laminate.

A physically-based dislocation theory of plasticity is derived within an extended continuum mechanical context. Thermodynamically consistent flow rules at the grain boundaries are derived. With an analytical solution of a three-phase periodic laminate, dislocation pile-up at grain boundaries and dislocation transmission through the grain boundaries are investigated. For the finite element implementations, numerically efficient approaches are introduced based on accumulated field variables.

Wir präsentieren einen Algorithmus zur schnellen Erzeugung von SMC Mikrostrukturen hoher Güte, durch Verwendung einer exakten Schließung und eines quasi-zufälligen Samplings. Darüber hinaus stellen wir ein modulares Framework zur Modellierung anisotroper Schädigung vor. Unser Konzept der Extraktionstensoren und Schädigungsfunktionen ermöglicht die Beschreibung komplexer Vorgänge. Darüber hinaus schlagen wir einen ganzheitlichen Multiskalenansatz zur Bestimmung anisotroper Versagenskriterien vor. - We introduce an algorithm that allows for a fast generation of SMC composite microstructures. An exact closure approximation and a quasi-random orientation sampling ensure high fidelity. Furthermore, we present a modular framework for anisotropic damage evolution. Our concept of extraction tensors and damage-hardening functions enables the description of complex damage-degradation. In addition, we propose a holistic multiscale approach for constructing anisotropic failure criteria.

artensite forms under rapid cooling of austenitic grains accompanied by a change of the crystal lattice. Large deformations are induced which lead to plastic dislocations. In this work a transformation model based on the sharp interface theory, set in a finite strain context is developed. Crystal plasticity effects, the kinetic of the singular surface as well as a simple model of the inheritance from austenite dislocations into martensite are accounted for.

Computational homogenization permits to capture the influence of the microstructure on the cyclic mechanical behavior of polycrystalline metals. In this work we investigate methods to compute Laguerre tessellations as computational cells of polycrystalline microstructures, propose a new method to assign crystallographic orientations to the Laguerre cells and use Bayesian optimization to find suitable parameters for the underlying micromechanical model from macroscopic experiments.

The aim of this work is to model and experimentally characterize the anisotropic material behavior of SMC composites on the macroscale with consideration of the microstructure. Temperature-dependent thermoelastic behavior and failure behavior are modeled and the corresponding material properties are determined experimentally. Additionally, experimental biaxial damage investigations are performed. A parameter identification merges modeling and experiments and validates the models.

Materials of industrial interest often show a complex microstructure which directly influences their macroscopic material behavior. For simulations on the component scale, multi-scale methods may exploit this microstructural information. This work is devoted to a multi-scale approach for brittle materials. Based on a homogenization result for free discontinuity problems, we present FFT-based methods to compute the effective crack energy of heterogeneous materials with complex microstructures.

Effective mechanical properties of fiber-reinforced composites strongly depend on the microstructure, including the fibers' orientation. Studying this dependency, we identify the variety of fiber orientation tensors up to fourth-order using irreducible tensors and material symmetry. The case of planar fiber orientation tensors, relevant for sheet molding compound, is presented completely. Consequences for the reconstruction of fiber distributions and mean field homogenization are presented.