227
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Modeling and simulation of viscoelastic solids under large numbers of loading cycles

, &
Pages 1542-1558 | Received 06 Sep 2021, Accepted 30 Jan 2022, Published online: 21 Feb 2022

References

  • P. Parandoush, and D. Lin, A review on additive manufacturing of polymer-fiber composites, Compos. Struct., vol. 182, pp. 36–53, 2017. DOI: 10.1016/j.compstruct.2017.08.088.
  • L. Adam, O. Lietaer, S. Mathieu, and I. Doghri, Numerical simulation of additive manufacturing of polymers and polymer-based composites. In: K. Friedrich and R. Walter (eds.), Structure and Properties of Additive Manufactured Polymer Components, pp. ISBN: 978–0–12–819535–2., Elsevier Science, Amsterdam, Netherlands, 2020.
  • M. R. Gudimetla, and I. Doghri, A finite strain thermodynamically-based constitutive framework coupling viscoelasticity and viscoplasticity with application to glassy polymers, Int. J. Plast., vol. 98, pp. 197–216, 2017. DOI: 10.1016/j.ijplas.2017.08.001.
  • J. S. Kim, and A. H. Muliana, A time-integration method for the viscoelastic–viscoplastic analyses of polymers and finite element implementation, Int. J. Numer. Meth. Eng., vol. 79, no. 5, pp. 550–575, 2009. DOI: 10.1002/nme.2569.
  • S. Haouala, and I. Doghri, Modeling and algorithms for two-scale time homogenization of viscoelastic-viscoplastic solids under large numbers of cycles, Int. J. Plast., vol. 70, pp. 98–125, 2015. DOI: 10.1016/j.ijplas.2015.03.005.
  • A. Krairi, I. Doghri, and G. Robert, Multiscale high cycle fatigue models for neat and short fiber reinforced thermoplastic polymers, Int. J. Fatigue, vol. 92, pp. 179–192, 2016. DOI: 10.1016/j.ijfatigue.2016.06.029.
  • J. C. Simo, and T. J. Hughes, Computational Inelasticity, Vol. 7. Springer Science & Business Media, Berlin, Germany, 2006.
  • M. Hammoud, M. Beringhier, and J. C. Grandidier, A reduced simulation applied to the viscoelastic fatigue of polymers, Comptes Rendus Mécanique., vol. 342, no. 12, pp. 671–691, 2014. DOI: 10.1016/j.crme.2014.07.008.
  • P. Zerbe, B. Schneider, and M. Kaliske, Viscoelastic-viscoplastic-damage modeling of thermoplastics under long-term cyclic loading, Proc. Appl. Math. Mech., vol. 16, no. 1, pp. 413–414, 2016. DOI: 10.1002/pamm.201610195.
  • Carson J. R, On a general expansion theorem for the transient oscillations of a connected system, Phys. Rev., vol. 10, no. 3, pp. 217, 1917.
  • J. R. Carson, Electric circuit theory and the operational calculus, Bell Syst. Techn. J., vol. 5, no. 2, pp. 336–384, 1926. DOI: 10.1002/j.1538-7305.1926.tb04305.x.
  • C. Friebel, I. Doghri, and V. Legat, General mean-field homogenization schemes for viscoelastic composites containing multiple phases of coated inclusions, Int. J. Solids Struct., vol. 43, no. 9, pp. 2513–2541, 2006. DOI: 10.1016/j.ijsolstr.2005.06.035.
  • M. Lévesque, M. D. Gilchrist, N. Bouleau, K. Derrien, and D. Baptiste, Numerical inversion of the Laplace-Carson transform applied to homogenization of randomly reinforced linear viscoelastic media, Comput. Mech., vol. 40, no. 4, pp. 771–789, 2007. DOI: 10.1007/s00466-006-0138-6.
  • A. Rekik, and R. Brenner, Optimization of the collocation inversion method for the linear viscoelastic homogenization, Mech. Res. Commun., vol. 38, no. 4, pp. 305–308, 2011. DOI: 10.1016/j.mechrescom.2011.04.003.
  • J. Mandel, Cours de Mécanique Des Milieux Continus, Vol. I–II., Gauthier, Villars, 1966.
  • J. Abate, and W. Whitt, A unified framework for numerically inverting Laplace transforms, INFORMS J Comput., vol. 18, no. 4, pp. 408–421, 2006. DOI: 10.1287/ijoc.1050.0137.
  • H. Dubner, and J. Abate, Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform, J. Acm., vol. 15, no. 1, pp. 115–123, 1968. DOI: 10.1145/321439.321446.
  • J. Abate, and W. Whitt, The Fourier-series method for inverting transforms of probability distributions, Queueing Syst., vol. 10, no. 1–2, pp. 5–87, 1992. DOI: 10.1007/BF01158520.
  • D. P. Gaver, Jr, Observing stochastic processes, and approximate transform inversion, Oper. Res., vol. 14, no. 3, pp. 444–459, 1966. DOI: 10.1287/opre.14.3.444.
  • H. Stehfest, Algorithm 368: Numerical inversion of Laplace transforms [d5], Commun. ACM., vol. 13, no. 1, pp. 47–49, 1970. DOI: 10.1145/361953.361969.
  • C. Wellekens, Generalisation of Vlach's method for the numerical inversion of the Laplace transform, Electron. Lett., vol. 6, no. 23, pp. 742–744, 1970. DOI: 10.1049/el:19700514.
  • R. Schapery, A method of viscoelastic stress analysis using elastic solutions, J. Franklin Inst., vol. 279, no. 4, pp. 268–289, 1965. DOI: 10.1016/0016-0032(65)90339-X.
  • T. L. Cost, and E. B. Becker, A multidata method of approximate Laplace transform inversion, Int. J. Numer. Meth. Eng., vol. 2, no. 2, pp. 207–219, 1970. DOI: 10.1002/nme.1620020206.
  • M. Lévesque, Modélisation du comportement mécanique de matériaux composites viscoélastiques non linéaires par une approche d’homogénéisation, PhD thesis, ENSAM, Paris, 2004.
  • I. Viktorova, B. Dandurand, S. Alekseeva, and M. Fronya, Modeling the creep of polymer-based nanocomposites by using an alternative nonlinear optimization approach, Mech. Compos. Mater., vol. 48, no. 6, pp. 693–704, 2013. DOI: 10.1007/s11029-013-9313-y.
  • W. N. Findley, J. S. Lai, and K. Onaran, Creep and Relaxation of Nonlinear Viscoelastic materials - With an Introduction to Linear Viscoelasticity, Dover Publications, New York, NY, 1989.
  • E. Baquet, Modélisation thermomécanique visco-hyperélastique du comportement d’un polymère semi-cristallin: application au cas d’une matrice polyamide 6.6, PhD thesis, École Nationale Supérieure des Mines de Paris, Paris, 2011.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.