The University of Massachusetts Amherst
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Variability response functions for effective material properties

TitleVariability response functions for effective material properties
Publication TypeJournal Article
Year of Publication2010
AuthorsArwade SR, Deodatis G
JournalProbabilistic Engineering Mechanics Probabilistic Engineering Mechanics
Start Page174
Date Published04/2011
KeywordsHomogenization, Material properties, Random fields, Uncertainty quantification

The variability response function (VRF) is a well-established concept for efficient evaluation of the variance and sensitivity of the response of stochastic systems where properties are modeled by random fields that circumvents the need for computationally expensive Monte Carlo (MC) simulations. Homogenization of material properties is an important procedure in the analysis of structural mechanics problems in which the material properties fluctuate randomly, yet no method other than MC simulation exists for evaluating the variability of the effective material properties. The concept of a VRF for effective material properties is introduced in this paper based on the equivalence of elastic strain energy in the heterogeneous and equivalent homogeneous bodies. It is shown that such a VRF exists for the effective material properties of statically determinate structures. The VRF for effective material properties can be calculated exactly or by Fast MC simulation and depends on extending the classical displacementVRF to consider the covariance of the response displacement at two points in a statically determinate beam with randomly fluctuating material properties modeled using random fields. Two numerical examples are presented that demonstrate the character of theVRF for effective material properties, the method of calculation, and results that can be obtained from it.