A variational framework for the modeling of glassy polymers under finite strains

  • Jan-Michel C. Farias
  • Laurent Stainier
  • Eduardo Alberto FancelloEmail author
Original Article


In this paper, a viscoelastic model able to capture important mechanical features of a wide class of glassy polymers is presented. Among them, the ability of reproducing the highly nonlinear rate-dependent stress response and the post-yield strain softening phenomenon. The simplicity of the proposition allows to recover the same mathematical structure of classical constitutive approaches, well suited for the use of implicit finite element codes. To this aim, the flow resistance concept, elsewhere known as shear strength, is reframed as a state variable of an accumulated strain measure. Three alternative expressions for this function are presented. The model is cast within a variational framework in which consistent constitutive updates are obtained by a minimization procedure. Convenient choices for the conservative and dissipative potentials reduce the local constitutive problem to the solution of a single nonlinear scalar equation, emulating the simplest case of viscoelastic models. Numerical tests on the constitutive model show excellent agreement with experimental data. Finally, a 3D simulation of a standard specimen with heterogeneous material properties illustrates the ability of the present proposition to be implemented in implicit finite element codes.


Glassy polymers Variational principles Viscoelasticity Finite strain 



Eduardo A. Fancello and Jan-Michel C. Farias thank the financial support provided by CNPq-Brazil (Grant 313146/2017-9).

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringFederal University of Santa CatarinaFlorianópolisBrazil
  2. 2.Research Institute in Civil and Mechanical Engineering (GeM - UMR6183 CNRS/ECN/UN)Ecole Centrale de NantesNantesFrance

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