Extended Hashin-Shtrikman variational principles

Petr Procházka; Jiří Šejnoha

Applications of Mathematics (2004)

  • Volume: 49, Issue: 4, page 357-372
  • ISSN: 0862-7940

Abstract

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Internal parameters, eigenstrains, or eigenstresses, arise in functionally graded materials, which are typically present in particulate, layered, or rock bodies. These parameters may be realized in different ways, e.g., by prestressing, temperature changes, effects of wetting, swelling, they may also represent inelastic strains, etc. In order to clarify the use of eigenparameters (eigenstrains or eigenstresses) in physical description, the classical formulation of elasticity is presented, and the two most important Lagrange’s and Castigliano’s variational principles are formulated in the sequel. Then the classical Hashin-Shtrikman principles are recalled and the involvement of eigenparameters is studied in more detail.

How to cite

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Procházka, Petr, and Šejnoha, Jiří. "Extended Hashin-Shtrikman variational principles." Applications of Mathematics 49.4 (2004): 357-372. <http://eudml.org/doc/33189>.

@article{Procházka2004,
abstract = {Internal parameters, eigenstrains, or eigenstresses, arise in functionally graded materials, which are typically present in particulate, layered, or rock bodies. These parameters may be realized in different ways, e.g., by prestressing, temperature changes, effects of wetting, swelling, they may also represent inelastic strains, etc. In order to clarify the use of eigenparameters (eigenstrains or eigenstresses) in physical description, the classical formulation of elasticity is presented, and the two most important Lagrange’s and Castigliano’s variational principles are formulated in the sequel. Then the classical Hashin-Shtrikman principles are recalled and the involvement of eigenparameters is studied in more detail.},
author = {Procházka, Petr, Šejnoha, Jiří},
journal = {Applications of Mathematics},
keywords = {extended Hashin-Shtrikman variational principle; eigenparameter; transformation field analysis; eigenstrains; eigenstresses; effective moduli},
language = {eng},
number = {4},
pages = {357-372},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Extended Hashin-Shtrikman variational principles},
url = {http://eudml.org/doc/33189},
volume = {49},
year = {2004},
}

TY - JOUR
AU - Procházka, Petr
AU - Šejnoha, Jiří
TI - Extended Hashin-Shtrikman variational principles
JO - Applications of Mathematics
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 49
IS - 4
SP - 357
EP - 372
AB - Internal parameters, eigenstrains, or eigenstresses, arise in functionally graded materials, which are typically present in particulate, layered, or rock bodies. These parameters may be realized in different ways, e.g., by prestressing, temperature changes, effects of wetting, swelling, they may also represent inelastic strains, etc. In order to clarify the use of eigenparameters (eigenstrains or eigenstresses) in physical description, the classical formulation of elasticity is presented, and the two most important Lagrange’s and Castigliano’s variational principles are formulated in the sequel. Then the classical Hashin-Shtrikman principles are recalled and the involvement of eigenparameters is studied in more detail.
LA - eng
KW - extended Hashin-Shtrikman variational principle; eigenparameter; transformation field analysis; eigenstrains; eigenstresses; effective moduli
UR - http://eudml.org/doc/33189
ER -

References

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