Fatigue fracture in ductile materials, e. g. metals, is caused by cyclic plasticity. Especially regarding the high numbers of load cycles, plastic material models resolving the full loading path are computationally very demanding. Herein, a model with particularly small computational effort is presented. It provides a macroscopic, phenomenological description of fatigue fracture by combining the phase-field method for brittle fracture with a classic durability concept. A local lifetime variable is obtained, which degrades the fracture resistance progressively. By deriving the stress-strain path from cyclic material characteristics, only one increment per load cycle is needed at maximum. The model allows to describe fatigue crack initiation, propagation and residual fracture and can reproduce Paris behaviour. arXiv:1903.06465v3 [cond-mat.mtrl-sci] 23 Oct 2019 Recently, several propositions to extend the phase-field method to fatigue [16,17,18,19,20] have been published. Representatively for the range of different approaches, two models which are able to reproduce Paris behaviour shall be highlighted here: Carrara et al. [19] introduce a phase-field model for fatigue fracture in brittle materials. The basic idea of their approach is that due to repetitive loading the crack resistance decreases, allowing cracks to evolve even far below the static crack resistance. The fracture toughness is modified depending on a measure of locally accumulated elastic strain energy density. Mesgarnejad et al. [20] follow a similar approach, but link the lowering of the fracture toughness also to the phase-field, localising the degradation to the vicinity of the crack tip.Although the authors use different approaches, they are not yet overcoming one key challenge inherent to fatigue crack initiation and propagation: The immense computational effort related to the high number of load cycles. This issue is addressed in the present paper. In particular, we introduce an efficient phase-field model of fatigue fracture in ductile materials, such as metals. Analogously to [19], it is based on the reduction of the critical fracture energy, but uses a different local fatigue measure. In contrast to brittle materials, fatigue crack propagation in ductile materials is caused by cyclic plastic deformations. The straightforward way to treat the problem with an elasto-plastic material model is numerically expensive. Therefore, a different approach is chosen. With the help of the LSA, a local lifetime variable is introduced, accounting for cumulative elasto-plastic deformations. Since the stress-strain path within a load cycle is derived from material curves from cyclic experiments, the explicit simulation of each load cycle would be redundant and can therefore be avoided, saving computational costs. In other words, instead of introducing a ductile phasefield model, an elastic, brittle phase-field formulation which considers the elasto-plastic origins of fatigue is presented. As cracks are described on a macroscopic scale, microscopic effects are...

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Fiber-reinforced plastics (FRPs) with adaptive properties make lightweight structures feasible that not only possess a high mechanical force absorption but are also able to adapt their mechanical characteristics, such as geometry and rigidity, to external influences. Within the framework of the basic research presented here, new adaptive FRPs are developed on a basis of textile reinforcement semi-finished products integrated with actuators made from shape-memory alloys (SMAs). The realization of adaptive FRPs requires not only knowledge of the material-specific actuatory properties of the functional materials. It also necessitates the development of textile-technical solutions fully exploiting the actuatory potential of the SMAs within the composite. Promising approaches are hybrid yarn structures based on friction spinning technology. In order to reduce the great experimental effort, modeling and simulation of the SMA's material behavior and of the adaptive FRPs' complex composite behavior are carried out by means of finite element methods. It is shown that the developed actuators generate sufficiently high tensions of about 700-800 N/mm 2 , to bend the FRP specimen up to 45 .In comparison to conventional isotropic materials such as metals, lightweight constructions from fiber-reinforced plastics (FRPs) have many advantages with regards to the design of material properties. A purposeful alignment and array of the reinforcement thread layers permits the local and global suitable adjustment of strength and rigidity in the FRPs. The applicationoriented material characteristics of FRP composites enable the material and energy-efficient realization of components used in vehicle and aerospace engineering, in the field of regenerative energies, for example, as highly resilient rotor blades in wind power plants.Apart from the possibility to purposefully realize mechanical gradient properties in the reinforcement textile and the composite component by integrating functional threads, the principle of laminated layer construction of FRPs promises great potential in the functionalization of lightweight structures and components. 1-3 By integrating functional elements in the form of sensors and actuators in or between the individual reinforcement layers and the thereby realizable active functional constructions, the high performance already achieved by FRPs can be considerably increased. The integration of actuatorily operating materials allows for the execution of FRPs whose properties can be set selectively, for instance in order to