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Isotropy
About: Isotropy is a research topic. Over the lifetime, 30050 publications have been published within this topic receiving 663626 citations.
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2,600 citations
TL;DR: In this article, the correlation of theory and experiment for incompressible isotropic elastic solids under finite strain was extended to incorporate the effects of compressibility (under isothermal conditions) with the result that experimental data on the compressibility of rubberlike materials are adequately accounted for.
Abstract: A method of approach to the correlation of theory and experiment for incompressible isotropic elastic solids under finite strain was developed in a previous paper (Ogden 1972) Here, the results of that work are extended to incorporate the effects of compressibility (under isothermal conditions) The strain-energy function constructed for incompressible materials is augmented by a function of the density ratio with the result that experimental data on the compressibility of rubberlike materials are adequately accounted for At the same time the good fit of the strain-energy function arising in the incompressibility theory to the data in simple tension, pure shear and equibiaxial tension is maintained in the compressible theory without any change in the values of the material constants A full discussion of inequalities which may reasonably be imposed upon the material parameters occurring in the compressible theory is included
2,519 citations
TL;DR: In this article, it was shown that the Reuss and Voigt approximations can be used to estimate, accurately, the mean sound velocity of a crystal, which is proportioned to the Debye temperature.
2,488 citations
TL;DR: In this paper, the effective shear modulus of two types of composite material models are compared. And the results are found to differ from those of the well-known Kerner and Hermans formulae for the same models.
Abstract: S olutions are presented for the effective shear modulus of two types of composite material models. The first type is that of a macroscopically isotropic composite medium containing spherical inclusions. The corresponding model employed is that involving three phases: the spherical inclusion, a spherical annulus of matrix material and an outer region of equivalent homogeneous material of unlimited extent. The corresponding two-dimensional, polar model is used to represent a transversely isotropic, fiber reinforced medium. In the latter case only the transverse effective shear modulus is obtained. The relative volumes of the inclusion phase to the matrix annulus phase in the three phase models are taken to be the given volume fractions of the inclusion phases in the composite materials at large. The results are found to differ from those of the well-known Kerner and Hermans formulae for the same models. The latter works are now understood to violate a continuity condition at the matrix to equivalent homogeneous medium interface. The present results are compared extensively with results from other related models. Conditions of linear elasticity are assumed.
1,994 citations
TL;DR: In this paper, the elasticity and consolidation theory of isotropic materials is extended to the general case of anisotropy and the method of derivation is also different and more direct.
Abstract: The author's previous theory of elasticity and consolidation for isotropic materials [J. Appl. Phys. 12, 155–164 (1941)] is extended to the general case of anisotropy. The method of derivation is also different and more direct. The particular cases of transverse isotropy and complete isotropy are discussed.
1,864 citations