In this paper the four classical hashin-shtrikman variational principles, applied to the homogenization problem for periodic composites with a nonlinear hyperelastic constitutive behavior, are analyzed. It is proved that two of them are indeed minimum principles while the other two are saddle point principles. As a consequence, every approximation of the former ones provide bounds on the effective properties of composite bodies, while approximations of the latter ones may supply inconsistent bounds, as it is shown by two numerical examples. Nevertheless, the approximations of the saddle point principles are expected to provide better estimates than the approximations of the minimum principles.

Bisegna, P., Luciano, R. (1999). Consistent hashin-shtrikman bounds on the effective properties of periodic composite materials. JOURNAL OF APPLIED MECHANICS, 66(4), 858-866 [10.1115/1.2791789].

Consistent hashin-shtrikman bounds on the effective properties of periodic composite materials

BISEGNA, PAOLO;
1999-01-01

Abstract

In this paper the four classical hashin-shtrikman variational principles, applied to the homogenization problem for periodic composites with a nonlinear hyperelastic constitutive behavior, are analyzed. It is proved that two of them are indeed minimum principles while the other two are saddle point principles. As a consequence, every approximation of the former ones provide bounds on the effective properties of composite bodies, while approximations of the latter ones may supply inconsistent bounds, as it is shown by two numerical examples. Nevertheless, the approximations of the saddle point principles are expected to provide better estimates than the approximations of the minimum principles.
1999
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore ICAR/08 - SCIENZA DELLE COSTRUZIONI
English
Con Impact Factor ISI
Composite materials; microstructure; effective moduli
Bisegna, P., Luciano, R. (1999). Consistent hashin-shtrikman bounds on the effective properties of periodic composite materials. JOURNAL OF APPLIED MECHANICS, 66(4), 858-866 [10.1115/1.2791789].
Bisegna, P; Luciano, R
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/23558
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