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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access





Published: Sat, 06 Jan 2018 00:00:00 GMT

Last Build Date: Sat, 06 Jan 2018 02:49:46 GMT

 



Scattering of In-plane Elastic Waves by an Anisotropic Circle

Sat, 06 Jan 2018 00:00:00 GMT

Summary
The 2D scattering of in-plane elastic waves by a circle is considered when the surrounding medium is isotropic and the medium inside the circle is anisotropic (orthotropic). The equations inside the circle are transformed to polar coordinates and then depend explicitly on the azimuthal angle through trigonometric functions. Making expansions in trigonometric series in the azimuthal coordinate give a coupled system of ordinary differential equations in the radial coordinate that is solved by power series expansions. With the solution inside the circle complete the scattering problem is solved essentially as in the classical case. The elements of the transition (T) matrix of the circle are given explicitly for low frequencies (long wavelengths). For low frequencies some numerical examples are given showing the strong influence of anisotropy.



Periodic auxetics: Structure and design

Mon, 11 Dec 2017 00:00:00 GMT

Summary
Materials science has adopted the term of auxetic behavior for structural deformations where stretching in some direction entails lateral widening, rather than lateral shrinking. Most studies, in the last three decades, have explored repetitive or cellular structures and used the notion of negative Poisson’s ratio as the hallmark of auxetic behavior. However, no general auxetic principle has been established from this perspective. In the present article, we show that a purely geometric approach to periodic auxetics is apt to identify essential characteristics of frameworks with auxetic deformations and can generate a systematic and endless series of periodic auxetic designs. The critical features refer to convexity properties expressed through families of homothetic ellipsoids.