Mechanics of Time-Dependent Materials

, Volume 21, Issue 4, pp 549–575 | Cite as

Generalization of the ordinary state-based peridynamic model for isotropic linear viscoelasticity

  • Rolland DelormeEmail author
  • Ilyass Tabiai
  • Louis Laberge Lebel
  • Martin Lévesque


This paper presents a generalization of the original ordinary state-based peridynamic model for isotropic linear viscoelasticity. The viscoelastic material response is represented using the thermodynamically acceptable Prony series approach. It can feature as many Prony terms as required and accounts for viscoelastic spherical and deviatoric components. The model was derived from an equivalence between peridynamic viscoelastic parameters and those appearing in classical continuum mechanics, by equating the free energy densities expressed in both frameworks. The model was simplified to a uni-dimensional expression and implemented to simulate a creep-recovery test. This implementation was finally validated by comparing peridynamic predictions to those predicted from classical continuum mechanics. An exact correspondence between peridynamics and the classical continuum approach was shown when the peridynamic horizon becomes small, meaning peridynamics tends toward classical continuum mechanics. This work provides a clear and direct means to researchers dealing with viscoelastic phenomena to tackle their problem within the peridynamic framework.


Linear viscoelasticity Relaxation Creep Peridynamics Classical continuum mechanics Thermodynamics 



Fruitful discussions with Marc Alexander Schweitzer, Serge Prud’homme and Patrick Diehl are gratefully acknowledged. The help with the mathematics given by Valentine Roos, Mathieu and Francisque Delorme is also gratefully acknowledged.


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Laboratory for Multiscale Mechanics, Mechanical Engineering Dept.Polytechnique MontrealMontrealCanada
  2. 2.Advanced Composite and Fiber Structures Laboratory, Mechanical Engineering Dept.Polytechnique MontrealMontrealCanada

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