TY - JOUR A1 - Unger, Jörg F. A1 - Kindrachuk, Vitaliy T1 - A Fourier transformation-based temporal integration scheme for viscoplastic solids subjected to fatigue deterioration JF - International Journal of Fatigue N2 - Using continuum damage mechanics (CDM) for lifetime prediction requires numerical integration of evolving damage until the onset of failure. The primary challenge for the simulation of structural fatigue failure is caused by the enormous computational costs due to cycle-by-cycle temporal integration throughout the whole loading history, which is in the order of 103–107 cycles. As a consequence, most approaches circumvent this problem and use empirical methods such as Wöhler curves. They are well suited for approximating the lifetime, but they are not capable to capture a realistic degradation of the material including redistribution of stresses. The main objective of the paper is to provide a technique for finite element (FE) simulations of structures under fatigue loading while reducing computational costs. A Fourier transformation-based temporal integration (FTTI) scheme is proposed, which adapts the conventional FE method for modeling the viscoplastic deterioration in a structure subjected to cyclic loading. The response fields are represented by a Fourier series which assumes a temporal scale separation: a microchronological (short time) scale arises from the oscillatory loading and a macrochronological (long time) scale is due to the slow material relaxation resulting from yielding and damage evolution. The original dynamic boundary value problem (BVP) is approximated by the stationary BVP on the microchronological scale. Alternation of the displacement field on the macrochronological scale is correlated with evolution of the history variables by means of a high order adaptive cycle jump method. Performance and significant acceleration of the FE simulations is demonstrated at different loading scenarios for a constitutive damage model where the progressive damage accumulation is driven by viscoplastic yielding. KW - Fatigue KW - Accelerated time integration KW - Continuum damage mechanics KW - Fourier series PY - 2017 DO - https://doi.org/10.1016/j.ijfatigue.2017.03.015 SN - 0142-1123 SN - 1879-3452 VL - 100 IS - 1 SP - 215 EP - 228 PB - Elsevier Ltd. AN - OPUS4-39616 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Kindrachuk, Vitaliy A1 - Titscher, Thomas A1 - Unger, Jörg F. T1 - A Fourier transformation-based method for gradient-enhanced modeling of fatigue JF - International journal for numerical methods in engineering 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 DO - 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 -