Reconstruction of a constitutive law for rubber from in silico experiments using Ogden's laws

Maya de Buhan 1 Antoine Gloria 2, 3 Patrick Le Tallec 4 Marina Vidrascu 5
3 MEPHYSTO - Quantitative methods for stochastic models in physics
LPP - Laboratoire Paul Painlevé - UMR 8524, ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe
5 REO - Numerical simulation of biological flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6
Abstract : This article deals with the following data assimilation problem: construct an analytical approximation of a numerical constitutive law in three-dimensional nonlinear elasticity. More precisely we are concerned with a micro-macro model for rubber. Macroscopic quantities of interest such as the Piola-Kirchhoff stress tensor can be approximated for any value of the strain gradient by numerically solving a nonlinear PDE. This procedure is however computationally demanding. Hence, although conceptually satisfactory, this physically-based model is of no direct practical use. The aim of this article is to circumvent this difficulty by proposing a numerical strategy to reconstruct from in silico experiments an accurate analytical proxy for the micro-macro constitutive law.
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Maya de Buhan, Antoine Gloria, Patrick Le Tallec, Marina Vidrascu. Reconstruction of a constitutive law for rubber from in silico experiments using Ogden's laws. International Journal of Solids and Structures, Elsevier, 2015, pp.16. ⟨10.1016/j.ijsolstr.2015.02.026⟩. ⟨hal-00933240⟩

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