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

Antoine Gloria 1, 2 Patrick Le Tallec 3 Marina Vidrascu 4, 5
1 SIMPAF - SImulations and Modeling for PArticles and Fluids
LPP - Laboratoire Paul Painlevé - UMR 8524, Inria Lille - Nord Europe
2 MEPHYSTO - Quantitative methods for stochastic models in physics
Inria Lille - Nord Europe, ULB - Université Libre de Bruxelles [Bruxelles], LPP - Laboratoire Paul Painlevé - UMR 8524
4 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
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 have 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.
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Antoine Gloria, Patrick Le Tallec, Marina Vidrascu. Foundation, analysis, and numerical investigation of a variational network-based model for rubber. Continuum Mechanics and Thermodynamics, Springer Verlag, 2014, 26 (1), pp.1--31. ⟨10.1007/s00161-012-0281-6⟩. ⟨hal-00673406v2⟩

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