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Keywords
(8)
Heterogeneous Material
Maximum Entropy Principle
Microstructures
Positive Definite Matrix
Probabilistic Model
Random Field
Random Matrix
Stochastic Model
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A probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures
A probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures,10.1016/j.cma.2011.01.016,Comput
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A probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures
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Citations: 2
)
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J. Guilleminot
,
A. Noshadravan
,
C. Soize
,
R. G. Ghanem
In this paper, we address the construction of a prior
stochastic model
for nonGaussian deterministicallybounded positivedefinite matrixvalued random fields in the context of mesoscale modeling of heterogeneous elastic microstructures. We first introduce the micromechanical framework and recall, in particular, Huet’s Partition Theorem. Based on the latter, we discuss the nature of hierarchical bounds and define, under some given assumptions, deterministic bounds for the apparent elasticity tensor. Having recourse to the
Maximum Entropy Principle
under the constraints defined by the available information, we then introduce two
random matrix
models. It is shown that an alternative formulation of the boundedness constraints further allows constructing a
probabilistic model
for deterministicallybounded positivedefinite matrixvalued random fields. Such a construction is presented and relies on a class of random fields previously defined. We finally exemplify the overall methodology considering an experimental database obtained from EBSD measurements and provide a simple numerical application.
Journal:
Computer Methods in Applied Mechanics and Engineering  COMPUT METHOD APPL MECH ENG
, vol. 200, no. 17, pp. 16371648, 2011
DOI:
10.1016/j.cma.2011.01.016
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Citations
(2)
Environmental worry: a Concept to Explain Differences in Environmentally Conscious Behaviour?
(
Citations: 1
)
Brigitte Steinheider
,
Volker Hodapp
Journal:
Mechanics of Materials  MECH MATER
, vol. 202, no. 2, pp. 273289, 1999
Simultaneous separation and preconcentration of Cr(III), Cu(II), Cd(II) and Pb(II) from environmental samples prior to inductively coupled plasma optical emission spectrometric determination
Li Zhang
,
Zhenhua Li
,
Xianghui Du
,
Ruijun Li
,
Xijun Chang
Journal:
Spectrochimica Acta Part Amolecular and Biomolecular Spectroscopy  SPECTROCHIM ACTA PT AMOL BIO