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Uncertainty quantification in computational stochastic multiscale analysis of nonlinear elastic materials

Alexandre Clément 1 Christian Soize 2, * Julien Yvonnet 1
* Corresponding author
2 Mechanics
MSME - Laboratoire de Modélisation et Simulation Multi Echelle
Abstract : This paper is devoted to a computational stochastic multiscale analysis of nonlinear structures made up of heterogeneous hyperelastic materials. At the microscale level, the nonlinear constitutive equation of the material is characterized by a stochastic potential for which a polynomial chaos representation is used. The geometry of the microstructure is random and characterized by a high number of random parameters. The method is based on a deterministic non-concurrent multiscale approach devoted to micro-macro nonlinear mechanics which leads us to characterize the nonlinear constitutive equation with an explicit continuous form of the strain energy density function with respect to the large scale Cauchy Green strain states. The problem is transformed into another one consisting in identifying the potential on a polynomial chaos expansion. Several strategies, based on novel algorithms dedicated to high stochastic dimension, are used and adapted for the class of multi-modal random variables which may characterize the potential. with classical methods.
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Alexandre Clément, Christian Soize, Julien Yvonnet. Uncertainty quantification in computational stochastic multiscale analysis of nonlinear elastic materials. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2013, 254 (-), pp.61-82. ⟨10.1016/j.cma.2012.10.016⟩. ⟨hal-00749582⟩

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