A Fourier transformation‐based method for gradient‐enhanced modeling of fatigue

A Fourier transformation‐based method for gradient‐enhanced modeling of fatigue 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 a multiscale 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 coarser macrochronological scale associated with the duration of material deterioration. The performance of the developed method 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal for Numerical Methods in Engineering Wiley

A Fourier transformation‐based method for gradient‐enhanced modeling of fatigue

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Publisher
Wiley
Copyright
Copyright © 2018 John Wiley & Sons, Ltd.
ISSN
0029-5981
eISSN
1097-0207
D.O.I.
10.1002/nme.5740
Publisher site
See Article on Publisher Site

Abstract

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 a multiscale 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 coarser macrochronological scale associated with the duration of material deterioration. The performance of the developed method 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.

Journal

International Journal for Numerical Methods in EngineeringWiley

Published: Jan 13, 2018

Keywords: ; ;

References

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