Computational Mechanics

, Volume 63, Issue 4, pp 725–745 | Cite as

Computational modeling of the large deformation and flow of viscoelastic polymers

  • Tong Shen
  • Rong Long
  • Franck VernereyEmail author
Original Paper


Deformation of soft polymeric materials often involves complex nonlinear or transient mechanical behaviors. This is due to the dynamic behaviors of polymer chains at the molecular level within the polymer network. In this paper, we present a computational formulation to describe the transient behavior (e.g., viscoelasticity) of soft polymer networks with dynamic bonds undergoing large to extreme deformation. This formulation is based on an Eulerian description of kinematics and a theoretical framework that directly connects the molecular-level kinetics of dynamic bonds to the macroscopic mechanical behavior of the material. An extended finite element method is used to discretize the field variables and the governing equations in an axisymmetric domain. In addition to validating the framework, this model is used to study how the chain dynamics affect the macroscopic response of material as they undergo a combination of flow and elasticity. The problems of cavitation rheology and polymer indentation under extreme deformation are investigated in this context.



The author acknowledges the support of the National Science Foundation under the NSF CAREER award 1350090. Research reported in this publication was also partially supported by the National Institute of Arthritis and Musculoskeletal and Skin Diseases of the National Institutes of Health under Award Number 1R01AR065441. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mechanical EngineeringUniversity of Colorado BoulderBoulderUSA

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