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A continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from statictests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level. A multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
A continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from statictests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level. A multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Lifetime aspects including fatigue failure of concrete structures were traditionally only of minor importance. Because of the growing interest in maxing out the capacities of concrete, its fatigue failure under compression has become an issue. A variety of interacting phenomena such as e.g. loss of prestress, degradation due to chemical reactions or creep and shrinkage influence the fatigue resistance. Failure due to cyclic loads is generally not instantaneous, but characterized by a steady damage accumulation. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required, which accurately captures order effects and full three-dimensional stress states.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales.
However, a key limitation of those models is that they generally do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles. This is due to the computational effort necessary to explicitly resolve every cycle which exceeds the currently available computational resources. The limitation can only be overcome by the application of multiscale methods in time.
The objective of the paper is the development of numerical methods for the simulation of concrete under fatigue loading using temporal multiscale methods.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses [1]. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from static tests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level.
Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach [2]. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Finally, the developed methods will be validated and compared to experimental data.
[1] Vitaliy Kindrachuk, Marc Thiele, Jörg F. Unger. Constitutive modeling of creep-fatigue interaction for normal strength concrete under compression, International Journal of Fatigue, 78:81-94, 2015
[2] Vitaliy Kindrachuk, Jörg F. Unger. A Fourier transformation-based temporal integration scheme for viscoplastic solids subjected to fatigue deterioration, International Journal of Fatigue, 100:215-228, 2017
Lifetime aspects including fatigue failure of concrete structures were traditionally only of minor importance. Because of the growing interest in maxing out the capacities of concrete, its fatigue failure under compression has become an issue. A variety of interacting phenomena such as e.g. loss of prestress, degradation due to chemical reactions or creep and shrinkage influence the fatigue resistance. Failure due to cyclic loads is generally not instantaneous, but characterized by a steady damage accumulation. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required, which accurately captures order effects and full three-dimensional stress states.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales.
However, a key limitation of those models is that they generally do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles. This is due to the computational effort necessary to explicitly resolve every cycle which exceeds the currently available computational resources. The limitation can only be overcome by the application of multiscale methods in time.
The objective of the paper is the development of numerical methods for the simulation of concrete under fatigue loading using temporal multiscale methods.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from static tests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level.
Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Finally, the developed methods will be validated and compared to experimental data.
A key limitation of the most constitutive models that reproduce a Degradation of quasi-brittle materials is that they generally do not address issues related to fatigue. One reason is the huge computational costs to resolve each load cycle on the structural level. The goal of this paper is the development of a temporal Integration scheme, which significantly increases the computational efficiency of the finite element method in comparison to conventional temporal integrations.
The essential constituent of the fatigue model is an implicit gradient-enhanced formulation of the damage rate. The evolution of the field variables is computed as amultiscale Fourier series in time.On a microchronological scale attributed to single cycles, the initial boundary value problem is approximated by linear BVPs with respect to the Fourier coefficients. Using the adaptive cycle jump concept, the obtained damage rates are transferred to a coarsermacrochronological scale associated with the duration of material deterioration. The performance of the developedmethod is hence improved due to an efficient numerical treatment of the microchronological problem in combination with the cycle jump technique on the macrochronological scale. Validation examples demonstrate the convergence of the obtained solutions to the reference simulations while significantly reducing the computational costs.
Additive manufacturing of alkali-activated materials currently attracts a lot of attention, because of the possibility to produce customized high-performance elements for a range of applications, potentially being more resource-efficient than conventionally produced parts. Here, we describe a new additive manufacturing process for alkali-activated materials that is based on selective laser-heating of lithium aluminate/microsilica slurries. The new process-material combination allows to manufacture elements with complex geometries at high building rates and high accuracy. The process is versatile and transferrable to structures of sizes differing by orders of magnitude. The mechanical strength of the obtained materials was in the range of values reported for conventional metakaolin-based geopolymers, and superior to what has been hitherto reported for alkali-activated materials produced by additive manufacturing. This mechanical performance was obtained despite the fact that the degree of reaction of the lithium aluminate and the microsilica was low, suggesting that significant reactions took place only at the surface of the microsilica particles.
The methods of computational damage mechanics are well-established for the description of degradation of materials under monotone loading. An extension to structural damage induced by cyclic loading is however significantly limited. This is due to enormous computational costs required to resolve each load cycle by conventional temporal incremental integration schemes while a typical fatigue loading history comprises between thousands and millions of cycles. Despite the permanent increase of computational resources and algorithmic performance, a successful approach is rather based on the development of novel multiscale in time integration schemes.
A Fourier transformation-based temporal integration (FTTI) is represented, which takes advantage of temporal scale separation incorporated into the cycle jump method. The response fields are approximated by a Fourier series whose coefficients undergo the evolution on a long-time scale. This is correlated with the evolution of the history variables, including damage, by means of the adaptive cycle jump method of various orders. The necessary extrapolation rates are obtained from the underlying solution of a short-time scale problem, which results from the oscillatory boundary condition and fulfills the global equilibrium of the Fourier coefficients. In this way, a remarkable speedup is achieved because the number of cycles to be fully integrated dramatically decreases.
The key idea behind the FTTI method is that the global in space equilibrium problem is linear since it is decoupled from the evolution equations. The latter are solved in the quadrature points under response fields prescribed throughout the whole load cycle. Consequently, integration of a single load cycle is much more efficient than the conventional single scale integration where the global equilibrium iteration and the local iteration of the evolution equations are coupled. This results in an additional speedup of the FTTI method.
The performance of the FTTI technique is demonstrated for two different constitutive behaviors: a viscoplastic model with a damage variable governed by the local equivalent viscoplastic strain; a quasi-brittle response where the damage variable is driven by a non-local equivalent strain. The latter is implicitly introduced as proposed by Peerlings. Both, the explicit and implicit extrapolation schemes are validated. The FTTI solutions agree very well with the reference cycle-by -cycle solutions, while significantly reducing the computational costs. The adaptive determination of the jump length can properly recognize the particular responses throughout the fatigue loading history (stationary fatigue, acceleration of fatigue damage when approaching failure) as well as stress redistribution phenomena.
The amount of data generated worldwide is constantly increasing. These data come from a wide variety of sources and systems, are processed differently, have a multitude of formats, and are stored in an untraceable and unstructured manner, predominantly in natural language in data silos. This problem can be equally applied to the heterogeneous research data from materials science and engineering. In this domain, ways and solutions are increasingly being generated to smartly link material data together with their contextual information in a uniform and well-structured manner on platforms, thus making them discoverable, retrievable, and reusable for research and industry. Ontologies play a key role in this context. They enable the sustainable representation of expert knowledge and the semantically structured filling of databases with computer-processable data triples.
In this perspective article, we present the project initiative Materials-open-Laboratory (Mat-o-Lab) that aims to provide a collaborative environment for domain experts to digitize their research results and processes and make them fit for data-driven materials research and development. The overarching challenge is to generate connection points to further link data from other domains to harness the promised potential of big materials data and harvest new knowledge.
A phenomenological criterion for an optical assessment of PE-HD fracture surfaces obtained from FNCT
(2021)
The full-notch creep test (FNCT) is a common test method to evaluate the environmental stress cracking (ESC) behavior of high-density polyethylene (PE-HD), e.g. for container materials. The test procedure as specified in ISO 16770 provides a comparative measure of the resistance against ESC using the time to failure of PE-HD specimens under constant mechanical load in a well-defined liquid test environment. Since the craze-crack damage mechanism underlying the ESC phenomenon is associated with brittle failure, the occurrence of a predominantly brittle fracture surface is a prerequisite to consider an FNCT measurement as representative for ESC, i.e. a time to failure dominated by craze-crack propagation.
The craze-crack propagation continuously reduces the effective residual cross-sectional area of the specimen during the test, which results in a corresponding increase of the effective mechanical stress. Thus, a transition to ductile shear deformation is inevitable at later stages of the test, leading usually to a pronounced central ligament.
Therefore, an optical evaluation of FNCT fracture surfaces concerning their brittleness is essential. An enhanced imaging analysis of FNCT fracture surfaces enables a detailed assessment of craze-crack Propagation during ESC. In this study, laser scanning microscopy (LSM) was employed to evaluate whether FNCT fracture surfaces are representative with respect to craze-crack propagation and ESC. Based on LSM height data, a phenomenological criterion is proposed to assess the validity of distinct FNCT measurements. This criterion is
supposed to facilitate a quick evaluation of FNCT results in practical routine testing. Its applicability is verified on a sample basis for seven different commercial PE-HD container materials.
Nachdem im Verbundprojekt COORAL das Hauptaugenmerk auf überkritisches CO2 gelegt wurde, d. h. Transport über kurze Strecken bei erhöhter Temperatur, wurde in CLUSTER ein größeres lokales Transport-Netzwerk betrachtet, bei dem CO2 bei geringeren Temperaturen, also vorwiegend im flüssigen Zustand transportiert wird. Wurden in COORAL die CO2-Ströme von Kohlekraftwerken untersucht, ging es in CLUSTER zusätzlich um die Emissionen von relevanten Industrien, deren CO2-Emissionen nicht ohne Weiteres vermieden werden können.
Aufgrund der Erfahrungen in COORAL konnte eine Auswahl von kommerziellen Werkstoffen getroffen werden, die für einen konkreten Einsatz für CCS zur Verfügung stünden. Die gemischten und fluktuierenden CO2-Zusammensetzungen sind bei geeigneten Begrenzungen der Begleit¬stoffe im CO2 bezüglich Korrosionsvorgänge beherrschbar. Die Machbarkeit eines lokalen CCS-Clusters erscheint daher gegeben, soweit dies die Anlagen für Kompression, Transport und Injektion betrifft.
For the additive manufacturing of large components typically powder-based methods are used. A powder is deposited layer by layer by means of a recoater, then, the component structure is printed into each individual layer. We introduce here the new method of local laser drying, which is a suspension-based method specially developed for the manufacturing of large voluminous ceramic parts. The structure information is directly written into the freshly deposited layer of suspension by laser drying. Initially, the technology was developed for ceramic suspensions, however, first experiments with geopolymers reveal a high potential for this class of materials. Metakaolin, fly ash and lithium aluminate-based one-part geopolymers were used in first experiments. The local annealing of the geopolymer slurry results in a drying and crosslinking reaction and, thus, in a local consolidation of the material. First parts made are introduced and their properties are discussed.
During their lifetime, polymer components subjected to mechanical loads and environmental influences show a loss of their mechanical properties required for their specific applications. In this respect, the craze-crack damage mechanism slow crack growth (SCG) is relevant for PE-HD components used in high-performance applications such as pipes and containers for the storage and transport of dangerous goods. SCG is considered to be the major failure mechanism in polyolefins and it typically occurs suddenly and unexpectedly. Due to the fields of application, SCG is a safety relevant issue. To test for the resistance of PE-HD pipe and container materials against SCG, the full-notch creep test (FNCT) is widely applied in Europe. In this study, SCG phenomena in PE-HD are investigated in detail based on an improved FNCT, especially including the consideration of the influence of environmental liquids effecting the damage mechanism. Using an enhanced fracture surface and a crack propagation analysis with imaging techniques such as light microscopy (LM), laser scanning microscopy (LSM), X-ray computed tomography (CT-scan) and scanning electron microscopy (SEM), detailed data concerning SCG are obtained.
The combined application of FNCT and such imaging techniques is explicitly advantageous and recommended to gain important information on damage occurring to PE-HD induced by mechanical stress and the influence of environmental liquids, which is essential within the Fourth Industry Revolution.
The full-notch creep test (FNCT) is a common method to evaluate the environmental stress cracking (ESC) behavior of high-density polyethylene (PE-HD) container materials . The test procedure as specified in ISO 16770 provides a comparative measure of the resistance against ESC using the time to failure of specimens mechanically loaded in a well-defined liquid environment. Since the craze-crack damage mechanism underlying the ESC process is associated with brittle failure, the occurrence of globally brittle fracture surfaces is a prerequisite to consider an FNCT measurement as representative for ESC . Therefore, an optical evaluation of FNCT fracture surfaces concerning their brittleness is essential. Due to the experimental setup, an inevitable increase of the true mechanical stress and the associated appearance of small ductile parts on fracture surfaces is induced in any case. Hence, an FNCT experiment is considered as 'valid', if the corresponding fracture surface is predominantly brittle . Based on laser scanning microscopy (LSM) height data of FNCT fracture surfaces , a universal and easy-to-use phenomenological criterion was developed to assess the validity of distinct FNCT experiments. This criterion is supposed to facilitate a quick evaluation of FNCT results in practical routine testing.
Polyether and -ester urethanes (PU) were exposed to artificial weathering at 40 °C and artificial UV radiation in a weathering chamber. In 3 parallel exposures, humidity was varied between dry, humid, and wet conditions. Material alteration was investigated by various analytical techniques like size exclusion chromatography
(SEC), liquid chromatography-infrared spectroscopy (LC-FTIR), thermal-desorption gas chromatography-mass spectrometry (TD-GC-MS), fluorescence mapping and dynamic mechanical analysis (DMA). Our results show that depending on the weathering conditions, different degradation effects can be observed. By means of SEC an initial strong decrease of the molar masses and a broadening of the mass distributions was found. After a material dependent time span this was followed by a plateau where molar mass changes were less significant. A minor moisture-dependent degradation effect was only found for polyester PU. Fluorescence measurements on two materials revealed an increase in the luminescence intensity upon weathering process reaching a saturation level after about 500 h. The changes in the optical properties observed after different exposure conditions and times were very similar. The TD-GC-MS data showed the fate of the stabilizers and antioxidant in the course of weathering. LC-FTIR measurements revealed a change in peak intensities and the ratio of urethane and carbonyl bands.
Assessing the structural integrity of carbon-fibre sandwich panels in fire: Bench-scale approach
(2019)
The fire resistance of lightweight sandwich panels (SW) with carbon fibre/epoxy skins and a poly(methacryl imide) (PMI) foam core is investigated in compression under direct application of a severe flame (heat flux=200 kW m−2). A bench-scale test procedure was used, with the sample held vertically. The epoxy decomposition temperature was quickly exceeded, with rapid flash-over and progressive core softening and decomposition.
There is a change in failure mode depending on whether the load is greater or less than 50% of the unexposed failure load, or in other words if one or two skins carry the load. At high loads, failure involved both skins with a single clear linear separation across each face. There is an inflection in the failure time relationship in the ∼50% load region, corresponding to the time taken for heat to be transmitted to the rear face, along with a change in the rear skin failure mode from separation to the formation of a plastic hinge. The integrity of the carbon front face, even with the resin burnt out, and the low thermal diffusivity of the core, both play key roles in prolonging rear face integrity, something to be borne in mind for future panel design. Intumescent coatings prolong the period before failure occurs. The ratio of times to failure with and without protection is proposed as a measure of their effectiveness. Apart from insulation properties, their adhesion and stability under severe fire impact play a key role.
Das langsame Risswachstum (slow crack growth, SCG) sowie der umgebungsbedingte Spannungsriss (environmental stress cracking, ESC) sind relevante Schädigungsmechanismen für teilkristalline Werkstoffe auf Basis von Polyethylen hoher Dichte (PE-HD).
Der Vortrag gibt einerseits einen Überblick über die grundlegenden Struktur-Eigenschafts-Beziehungen in diesem Kontext, andererseits werden auch verschiedene praxisorientierte Prüfverfahren vorgestellt. Letztere wurden in gemeinsamen Forschungsprojekten von BAM und LBF mit dem Schwerpunkt Gefahrgutbehälter bzw. Pflanzenschutzmittel vergleichend untersucht und durch weitergehende Analytik ergänzt.
Carbon Capture Utilization and Storage (CCUS) is a promising technology to reach the target for reduction of CO2 emissions. Crucial points for a sustainable and future-proof CCUS system are reliability and cost efficiency of the whole process chain, including separation of CO2 from the source, compression of CO2, its subsequent transportation to the injection site and injection into geological formations, e.g. aquifers. Recent studies have shown that even at a very low concentration of impurities, condensation of sulfuric and nitric acids in dense phase CO2 are possible and observable. Thus, impact of impure CO2 stream toward corrosion susceptibility of materials to be used in CCUS system need to be considered. In this talk, basing on results achieved from two German long-term projects (COORAL and CLUSTER), the dominating impurities of the CO2 stream and corrosion mechanisms are addressed. Investigations cover the whole CCUS process chain and provide a material recommendation for certain parts.
Depending on the CO2 generating and the capture process as well as on consecutive purification steps applied, CO2 streams from different emitters may differ in their composition. When CO2 streams with different compositions are fed into a larger pipeline network, there are several aspects that must be considered: i) chemical reactions, such as acid formation, may occur within the joint CO2 stream; ii) there may be a variation of mass flow rate and CO2 stream composition within the pipeline network if the feed-in behavior of different CO2 sources changes with time. Potential impacts of changing CO2 stream compositions and mass flow rates in CCS cluster systems were investigated in the collaborative project "CLUSTER" (see also www.bgr.bund.de/CLUSTER). In this presentation, we focus on the experimental investigations of formation and condensation of strong acids and their impacts on the corrosion of pipeline steels. When SO2, NO2, O2 and H2O are present simultaneously in CO2 streams chemical cross-reactions may occur leading to the formation of strong acids such as sulfuric and nitric acid. To prevent this acid formation the concentration of at least one of these four impurities must be kept very low (e.g., Rütters et al., 2016). At temperatures below the acid dew point temperature, acids will condense, e.g., on pipeline steel surfaces. In turn, these acid condensates may trigger steel corrosion. To better understand the process of acid formation and condensation and its implications for steel corrosion, exposure tests were performed on pipeline steel X70 in dense CO2 with varying SO2, NO2 and O2 concentration under high pressure and at 278 K in an observable autoclave, in which water was added as droplets or as vapor. Further, electrochemical tests were carried out with X70 specimens immersed in 500 mL CO2-saturated synthetic condensate solution or in droplets of the same solution on the specimen’s surface. Depending on impurity concentrations in the CO2 streams, condensates consisting of different relative amounts of nitric and sulfuric acid were formed. In condensates containing both nitric and sulfuric acid, corrosion rates were higher than the sum of those of the individual acids. In addition, corrosion products and forms depended on the condensate composition. Investigations of water droplets on steel surfaces in impurity-containing dense-phase CO2 revealed the diffusion of SO2 and NO2, followed by cross-reactions forming corresponding acids. An increase in droplet size (from 1 to 5 µl) lead to higher corrosion rates. However, in comparison to measurements in bulk solution, corrosion reactions in droplets resulted in thick, high-resistance corrosion products and observed droplet corrosion rates were significantly lower. In addition, the possibility of acid droplet formation and growth in impure liquid CO2 is influenced by the wetting behavior of the acid droplet on the steel surface. Thus, the contact angle between a water droplet and the surface steel specimens in a CO2 atmosphere was investigated in a high pressure view cell following the sessile drop method. The contact angle wasand found to be larger at higher CO2 pressures (studied from 5 to 20 MPa) and at higher temperatures (e.g. 278 K to 333 K). Further, measured contact angles were larger on rough than on smooth metal surfaces. In addition, acid formation reduced the contact angle, i.e. lead to better wetting, thereby stimulating condensation that was followed by a corrosion process. These detailed insights on the complex interplay of acid formation, condensation, wetting behavior and corrosion allow a better assessment of material suitability for pipeline transportation of impure CO2 streams
CO2 quality specifications are not only a matter of CO2 purity (i.e. CO2 content).
The “rest” also matters, in particular contents of reactive impurities affecting material corrosion (and rock alteration).
Also chemical reactions in CO2 stream needs to be considered, in particular when combining CO2 streams of different compositions.
The durability of concrete structures and its performance over the lifetime is strongly influenced by many interacting phenomena such as e.g. mechanical degradation due to fatigue loading, loss of prestress, degradation due to chemical reactions or creep and shrinkage. Failure due to cyclic loading is generally not instantaneous, but characterized by a steady damage accumulation.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales. A key limitation is that the models often do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles.
The objective of this paper is the presentation of numerical methods for the simulation of concrete under fatigue loading using a temporal multiscale method.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different time integration schemes.