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Continuum Mechanics and Thermodynamics

, Volume 26, Issue 1, pp 1–31 | Cite as

Foundation, analysis, and numerical investigation of a variational network-based model for rubber

  • Antoine GloriaEmail author
  • Patrick Le Tallec
  • Marina Vidrascu
Original Article

Abstract

Since the pioneering work by Treloar, many models based on polymer chain statistics have been proposed to describe rubber elasticity. Recently, Alicandro, Cicalese, and the first author rigorously derived a continuum theory of rubber elasticity from a discrete model by variational convergence. The aim of this paper is twofold. First, we further physically motivate this model and complete the analysis by numerical simulations. Second, in order to compare this model to the literature, we present in a common language two other representative types of models, specify their underlying assumptions, check their mathematical properties, and compare them to Treloar’s experiments.

Keywords

Rubber elasticity Polymer physics Variational convergence Numerical methods 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Antoine Gloria
    • 1
    • 2
    Email author
  • Patrick Le Tallec
    • 3
  • Marina Vidrascu
    • 4
  1. 1.Université Libre de Bruxelles (ULB)BrusselsBelgium
  2. 2.Project-team SIMPAFVilleneuve d’AscqFrance
  3. 3.LMSÉcole polytechniquePalaiseauFrance
  4. 4.Project-team REOInria Paris-RocquencourtLe ChesnayFrance

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