Stochastic modeling of the Ogden class of stored energy functions for hyperelastic materials: the compressible case

TitleStochastic modeling of the Ogden class of stored energy functions for hyperelastic materials: the compressible case
Publication TypeJournal Article
Year of Publication2017
AuthorsB Staber, and J Guilleminot
JournalZamm Zeitschrift Für Angewandte Mathematik Und Mechanik
Volume97
Start Page273
Issue3
Pagination273 - 295
Date Published03/2017
Abstract

This paper is devoted to the modeling of compressible hyperelastic materials whose response functions exhibit uncertainties at some scale of interest. The construction of parametric probabilistic representations for the Ogden class of stored energy functions is specifically considered and formulated within the framework of Information Theory. The overall methodology relies on the principle of maximum entropy, which is invoked under constraints arising from existence theorems and consistency with linearized elasticity. As for the incompressible case discussed elsewhere, the derivation essentially involves the conditioning of some variables on the stochastic bulk and shear moduli, which are shown to be statistically dependent random variables in the present case. The explicit construction of the probability measures is first addressed in the most general setting. Subsequently, particular results for classical Neo-Hookean and Mooney-Rivlin materials are provided. Salient features of the probabilistic representations are finally highlighted through forward Monte-Carlo simulations. In particular, it is seen that the models allow for the reproduction of typical experimental trends, such as a variance increase at large stretches. A stochastic multiscale analysis, where uncertainties on the constitutive law of the matrix phase are taken into account through the proposed approach, is also presented.

URLhttp://doi.wiley.com/10.1002/zamm.201500255http://api.wiley.com/onlinelibrary/tdm/v1/articles/10.1002%2Fzamm.201500255
DOI10.1002/zamm.201500255
Short TitleZamm Zeitschrift Für Angewandte Mathematik Und Mechanik