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Probabilistic entropy in homogenization of the periodic fiber‐reinforced composites with random elastic parameters
Author(s) -
Kamiński Marcin
Publication year - 2012
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.3350
Subject(s) - homogenization (climate) , probabilistic logic , finite element method , mathematics , entropy (arrow of time) , statistical physics , mathematical analysis , computer science , structural engineering , physics , engineering , statistics , quantum mechanics , biology , biodiversity , ecology
SUMMARY The purpose of this elaboration is to develop an efficient method for a determination of the probabilistic entropy loss in the homogenization process of the periodic composites with random material characteristics. A definition of this entropy convenient for the Gaussian continuous distribution is adopted and implemented into the computer algebra system MAPLE. Homogenization of the fiber‐reinforced composite with randomly defined Young's moduli of the constituents is carried out in the FEM and homogenization‐oriented code based on the four‐noded plane strain elements. Probabilistic procedure has triple character and is alternatively based on the Monte Carlo simulation, on the generalized stochastic perturbation‐based analysis, and on the recently developed semi‐analytical determination of homogenized tensor using the response function method. Because of this triple usage of the probabilistic methods, it is possible to make a detailed comparison of all those techniques, especially in view of the entropy variation during the homogenization. This procedure may be linked with other homogenization techniques, also for various constitutive models and/or for the upper and lower bounds on the effective tensor components. Copyright © 2012 John Wiley & Sons, Ltd.