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Fatigue fracture is one of the main causes of failure in engineering structures. However, its simulation still remains a challenge. To this end, an efficient phase-field model for fatigue fracture is introduced. The phase-field method regularizes the crack description and allows for a straight-forward simulation of crack initiation and arbitrary crack patterns. The effects of fatigue are included in the model via the Local Strain Approach. This concept introduces assumptions on the cyclic stress-strain behavior and the fatigue resistance of the material, making use of experimental cyclic material data. In this way, the phase-field model can remain elastic, while the introduced fatigue damage still includes cyclic plasticity in a simplified way. Therefore, the model reduces computational time significantly compared to other phase-field fatigue models, also, because it can cover several load cycles in just one computation increment. The model is parametrized and validated for aluminum sheet material and proves to be able to reproduce the typical fatigue crack growth behavior of this material. Details on the implementation are provided. The model is presented in a general framework for phase-field models for fatigue fracture, which is also used for a comprehensive overview and classification of existing models in the literature. The model is extended to deal with residual stresses in the material, which exert great influence on the fatigue crack growth behavior, as experiments and simulations show consistently. Also, anisotropic material properties are included through yet another model extension. Particularly, the direction-dependent fracture toughness of rolled aluminum sheets is considered. Simulations reproduce characteristic crack paths caused by this anisotropy. Finally, the model's assumptions regarding cyclic plastic material behavior are put to a test. To this end, a phase-field fatigue ansatz with elastic-plastic material model of Armstrong-Frederick type is implemented. It serves as a reference to define the range of application of the efficient, yet simplified fatigue model presented in this thesis.

The phase-field formulation for fracture based on the framework of representative crack elements is extended to transient thermo-mechanics. The finite element formulation is derived starting from the variational principle of total virtual power. The intention of this manuscript is to demonstrate the potential of the framework for multi-physical fracture models and complex processes inside the crack. The present model at hand allows to predict realistic deformation kinematics and heat fluxes at cracks. At the application of fully coupled, transient thermo-elasticity to a pre-cracked plate, the opened crack yields thermal isolation between both parts of the plate. Inhomogeneous thermal strains result in a curved crack surface, inhomogeneous recontact and finally heat flow through the crack regions in contact. The novel phase-field framework further allows to study processes inside the crack, which is demonstrated by heat radiation between opened crack surfaces. Finally, numerically calculated crack paths at a disc subjected to thermal shock load are compared to experimental results from literature and a curved crack in a three-dimensional application are presented.