TY - JOUR A1 - Kindrachuk, Vitaliy A1 - Titscher, Thomas A1 - Unger, Jörg F. T1 - A Fourier transformation-based method for gradient-enhanced modeling of fatigue N2 - 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. KW - Accelerated temporal integration KW - Fourier series KW - Gradient-enhanced fatigue model PY - 2018 U6 - https://doi.org/10.1002/nme.5740 SN - 1097-0207 SN - 0029-5981 VL - 114 IS - 2 SP - 196 EP - 214 PB - Wiley AN - OPUS4-44008 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Titscher, Thomas A1 - Unger, Jörg F. A1 - Oliver, J. T1 - High-order cycle jump integration of a fatigue damage model N2 - Accurate models for the long term behavior of concrete structures are important to ensure a durable and reliable design. A variety of interacting phenomena, such as the loss of prestress, the degradation due to chemical reactions or creep and shrinkage, influence the fatigue resistance. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required. The presented fatigue model is an extension of a static damage model to allow easy coupling in a multiphysics context. The evolution equation of the damage driving variable is enhanced to allow damage growth below the static limit. The model is defined in the time domain and does not include the number of cycles as a parameter. Thus, it can capture both static and cyclic failure. Additionally, this allows calibrating the majority of the model parameters static experiments. The model is integrated by resolving each loading cycle, requiring about ten time steps per cycle. The high computational costs are handled via a time scale separation. The short time scale describes one cycle with marginal changes in the internal variables. These changes are integrated along the large time scale of material deterioration. Various high-order time integration schemes are compared. Wöhler curves relate loading amplitudes to the number of cycles that the material endures. They are used to validate the model against experimental data. T2 - 6th European Conference on Computational Mechanics (ECCM 6) CY - Glasgow, UK DA - 11.06.2018 KW - Fatigue damage KW - Time scale separation KW - Cycle jump PY - 2018 AN - OPUS4-45706 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -