HAL: hal-00686132, version 1

DOI: 10.1016/j.probengmech.2011.07.004

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Probabilistic Engineering Mechanics 28, SI (2012) Pages: 118-124

Probabilistic modeling of apparent tensors in elastostatics: A MaxEnt approach under material symmetry and stochastic boundedness constraints

J. Guilleminot (  Corresponding author ) 1, C. Soize 1

(2012)

In this work, we address the stochastic modeling of apparent elasticity tensors, for which both material symmetry and stochastic boundedness constraints have to be taken into account, in addition to the classical constraint of invertibility. We first introduce a stochastic measure of anisotropy, which is defined using metrics in the set of elasticity tensors and used for quantitatively characterizing the fulfillment of material symmetry constraints. After having defined a numerical approximation for the stochastic boundedness constraint, we then propose a methodology allowing one to unify maximum entropy based models that have been previously derived by considering some of these constraints and which consists in constructing a probabilistic model for an auxiliary random variable. The latter can be interpreted as a stochastic compliance tensor, for which the available information to be used in the maximum entropy formulation can be readily deduced from the one considered for the elasticity tensor. A numerical illustration of the approach to an elastic microstructure is finally provided.

1:	Laboratoire de Modélisation et Simulation Multi Echelle (MSME)
	Université Paris-Est Marne-la-Vallée (UPEMLV) – Université Paris-Est Créteil Val-de-Marne (UPEC) – CNRS : UMR8208

Research team: Mechanics

Subject

:

Mathematics/Probability Engineering Sciences/Mechanics/Mechanics of the solides Physics/Mechanics/Mechanics of the solides Engineering Sciences/Mechanics/Mechanics of materials Physics/Mechanics/Mechanics of materials

Keyword(s): uncertainty quantification – random matrix – anisotropy – bounded tensors – elasticity tensor – material symmetry – maximum entropy principle – stochastic model – anisotropic elastic materials – random uncertainties – heterogeneous material – information theory – chaos

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From: Christian Soize <>

Submitted on: Saturday, 7 April 2012 17:07:11

Updated on: Tuesday, 19 March 2013 09:53:16