Generalized stochastic approach for constitutive equation in linear elasticity: a random matrix model

Johann Guilleminot · Christian Soize

44 citations0/0 files storedInternational Journal for Numerical Methods in Engineering

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Probabilistic and Robust Engineering Design Elasticity and Material Modeling Composite Material Mechanics

Abstract

SUMMARY This work is concerned with the construction of stochastic models for random elasticity matrices, allowing either for the generation of elasticity tensors exhibiting some material symmetry properties almost surely (integrating the statistical dependence between the random stiffness components) or for the modeling of random media that requires the mean of a stochastic anisotropy measure to be controlled apart from the level of statistical fluctuations. To this aim, we first introduced a decomposition of the stochastic elasticity tensor on a deterministic tensor basis and considered the probabilistic modeling of the random components, having recourse to the MaxEnt principle. Strategies for random generation and estimation were further reviewed, and the approach was exemplified in the case of a material that was transversely isotropic almost surely. In a second stage, we made use of such derivations to propose a generalized model for random elasticity matrices that took into account, almost separately, constraints on both the level of stochastic anisotropy and the level of statistical fluctuations. An example was finally provided and showed the efficiency of the approach. Copyright © 2011 John Wiley & Sons, Ltd.

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References

1991Stochastic Finite Elements: A Spectral Approach 2000A nonparametric model of random uncertainties for reduced matrix models in structural dynamics 2007Microstructural Randomness and Scaling in Mechanics of Materials 2001Maximum entropy approach for modeling random uncertainties in transient elastodynamics 2004Random matrix theory for modeling uncertainties in computational mechanics 2005Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators 2008Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes, random fields and random matrices 2010A multi‐scale spectral stochastic method for homogenization of multi‐phase periodic composites with random material properties

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