In this Note, we present a unified approach to the information-theoretic modeling and simulation of a class of elasticity random fields, for all physical symmetry classes. The new stochastic representation builds upon a Walpole tensor decomposition, which allows the maximum entropy constraints to be decoupled in accordance with the tensor (sub)algebras associated with the class under consideration. In contrast to previous works where the construction was carried out on the scalar-valued Walpole coordinates, the proposed strategy involves both matrix-valued and scalar-valued random fields. This enables, in particular, the construction of a generation algorithm based on a memoryless transformation, hence improving the computational efficiency of the framework. Two applications involving weak symmetries and sampling over spherical and cylindrical geometries are subsequently provided. These numerical experiments are relevant to the modeling of elastic interphases in nanocomposites, as well as to the simulation of spatially dependent wood properties for instance.
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Brian Staber 1; Johann Guilleminot 1
@article{CRMECA_2017__345_6_399_0,
author = {Brian Staber and Johann Guilleminot},
title = {Stochastic modeling and generation of random fields of elasticity tensors: {A} unified information-theoretic approach},
journal = {Comptes Rendus. M\'ecanique},
pages = {399--416},
publisher = {Elsevier},
volume = {345},
number = {6},
year = {2017},
doi = {10.1016/j.crme.2017.05.001},
language = {en},
}
TY - JOUR AU - Brian Staber AU - Johann Guilleminot TI - Stochastic modeling and generation of random fields of elasticity tensors: A unified information-theoretic approach JO - Comptes Rendus. Mécanique PY - 2017 SP - 399 EP - 416 VL - 345 IS - 6 PB - Elsevier DO - 10.1016/j.crme.2017.05.001 LA - en ID - CRMECA_2017__345_6_399_0 ER -
%0 Journal Article %A Brian Staber %A Johann Guilleminot %T Stochastic modeling and generation of random fields of elasticity tensors: A unified information-theoretic approach %J Comptes Rendus. Mécanique %D 2017 %P 399-416 %V 345 %N 6 %I Elsevier %R 10.1016/j.crme.2017.05.001 %G en %F CRMECA_2017__345_6_399_0
Brian Staber; Johann Guilleminot. Stochastic modeling and generation of random fields of elasticity tensors: A unified information-theoretic approach. Comptes Rendus. Mécanique, Volume 345 (2017) no. 6, pp. 399-416. doi : 10.1016/j.crme.2017.05.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2017.05.001/
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