Journal ArticleDOI
Variational principles for dynamic problems for inhomogeneous elastic media
TLDR
In this paper, the Hashin-Shtrikman principle in the static limit is used to derive variational principles for elastodynamic problems, which reduce to the hashin-shtein principle.About:
This article is published in Wave Motion.The article was published on 1981-01-01. It has received 221 citations till now. The article focuses on the topics: Variational principle.read more
Citations
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Journal ArticleDOI
On cloaking for elasticity and physical equations with a transformation invariant form
TL;DR: In this paper, the form of the conventional elastodynamic equations changes under curvilinear transformations, and they are mapped to a more general form in which the density is anisotropic and additional terms appear which couple the stress not only with the strain but also with the velocity.
Book ChapterDOI
Variational and Related Methods for the Overall Properties of Composites
TL;DR: In this paper, the authors focus on variational and related methods for the overall properties of composites, such as fiber-reinforced composites or polycrystals, whose properties vary in a complicated fashion from point to point over a small, microscopic length scale, while they appear on average to be uniform.
Journal ArticleDOI
On modifications of Newton's second law and linear continuum elastodynamics
Graeme W. Milton,John R. Willis +1 more
TL;DR: In this paper, the second law of motion is replaced by a more general law which is a better approximation for describing the motion of seemingly rigid macroscopic bodies, where the relation between the force and the acceleration is non-local (but causal) in time.
Journal ArticleDOI
Metamaterials beyond electromagnetism
TL;DR: This review includes homogeneous metamaterials as well as intentionally inhomogeneous meetamaterial architectures designed by coordinate-transformation-based approaches analogous to transformation optics, and gives an overview on the current state of the art regarding theory and experiment from the viewpoint of an experimentalist.
Journal ArticleDOI
Variational Principles for Inhomogeneous Non-linear Media
D. R. S. Talbot,John R. Willis +1 more
References
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Journal ArticleDOI
A variational approach to the theory of the elastic behaviour of multiphase materials
Zvi Hashin,S. Shtrikman +1 more
TL;DR: In this paper, the authors derived upper and lower bounds for the effective elastic moduli of quasi-isotropic and quasi-homogeneous multiphase materials of arbitrary phase geometry.
Journal ArticleDOI
On some variational principles in anisotropic and nonhomogeneous elasticity
Zvi Hashin,S. Shtrikman +1 more
TL;DR: In this article, the authors extended these variational principles to anisotropic and nonhomogeneous elasticity for polycrystals, and applied them to the theory of the elastic behavior of polycrystal polymers.
Book ChapterDOI
The Linear Theory of Elasticity
TL;DR: Linear elasticity is one of the more successful theories of mathematical physics and its pragmatic success in describing the small deformations of many materials is uncontested The origins of the three-dimensional theory go back to the beginning of the 19th century and the derivation of the basic equations by Cauchy, Navier, and Poisson The theoretical development of the subject continued at a brisk pace until the early 20th century with the work of Beltrami, Betti, Boussinesq, Kelvin, Kirchhoff, Lame, Saint-Venant, Somigl
Journal ArticleDOI
A variational approach to the theory of the elastic behaviour of polycrystals
Zvi Hashin,S. Shtrikman +1 more
TL;DR: In this article, the authors derived lower and upper bounds for the elastic moduli of polycrystals in terms of the modulus of the constituting crystals, and showed that the present bounds are a considerable improvement of the well-known Voigt and Reuss bounds.
Book ChapterDOI
Variational and Related Methods for the Overall Properties of Composites
TL;DR: In this paper, the authors focus on variational and related methods for the overall properties of composites, such as fiber-reinforced composites or polycrystals, whose properties vary in a complicated fashion from point to point over a small, microscopic length scale, while they appear on average to be uniform.
Related Papers (5)
On modifications of Newton's second law and linear continuum elastodynamics
Graeme W. Milton,John R. Willis +1 more