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International Journal for Uncertainty Quantification

Impact factor: 1.000

ISSN Print: 2152-5080
ISSN Online: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2012003901
pages 73-100

VALIDATION OF A PROBABILISTIC MODEL FOR MESOSCALE ELASTICITY TENSOR OF RANDOM POLYCRYSTALS

Arash Noshadravan
University of Southern California, Department of Civil and Environmental Engineering, USA
Roger Ghanem
Department of Aerospace and Mechanical Engineering, University of Southern California, 210 KAP Hall, Los Angeles, California 90089, USA
Johann Guilleminot
Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME, Marne la Vallée, France
Ikshwaku Atodaria
Arizona State University, School for Engineering of Matter, Transport and Energy, Tempe, Arizona 85287-6106, USA
Pedro Peralta
Arizona State University, School for Engineering of Matter, Transport and Energy, Tempe, Arizona 85287-6106, USA

ABSTRACT

In this paper, we present validation of a probabilistic model for mesoscale elastic behavior of materials with microstructure. The linear elastic constitutive matrix of this model is described mathematically as a bounded random matrix. The bounds reflect theoretical constraints consistent with the theory of elasticity. We first introduce a statistical characterization of an experimental database on morphology and crystallography of polycrystalline microstructures. The resulting statistical model is used as a surrogate to further experimental data, required for calibration and validation. We then recall the construction of a probabilistic model for the random matrix characterizing the apparent elasticity tensor of a heterogeneous random medium. The calibration of this coarse scale probabilistic model using an experimental database of microstructural measurements and utilizing the developed microstructural simulation tool is briefly discussed. Before using the model as a predictive tool in a system level simulation for the purpose of detection and prognosis, the credibility of the model must be established through evaluating the degree of agreement between the predictions of the model and the observations. As such, a procedure is presented to validate the probabilistic model from simulated data resulting from subscale simulations. Suitable quantities of interest are introduced and predictive accuracy of the model is studied by comparing probability density functions of response quantities of interest. The validation task is exercised under both static and dynamic loading condition. The results indicate that the probabilistic model of mesoscale elasticity tensor is adequate to predict the response quantity of interest in the elastostatic regime. The scatter in the model predictions is found to be consistent with the fine scale response. In the case of elastodynamic, the model predicts the mean behavior for lower frequency for which we have a quasistatic regime.