Reflection of plane waves from the flat boundary of a micropolar elastic halfspace

Microstructure effect on wave propagation, and plane wave reflection from stress free flat surface in micropolar elastic half-spac

A mixture theory for geophysical fluids

International audienceA continuum theory is developed for a geophysical fluid consisting of two species. Balance laws are given for the individual components of the mixture, modeled as micropolar viscous fluids. The continua allow independent rotational degrees of freedom, so that the fluids can exhibit couple stresses and a non-symmetric stress tensor. The second law of thermodynamics is used to develop constitutive equations. Linear constitutive equations are constituted for a heat conducting mixture, each species possessing separate viscosities. Field equations are obtained and boundary and initial conditions are stated. This theory is relevant to an atmospheric mixture consisting of any two species from rain, snow and/or sand. Also, this is a continuum theory for oceanic mixtures, such as water and silt, or water and oil spills, etc

Bifurcation analysis of rotating axially compressed imperfect nano-rod

Static stability problem for axially compressed rotating nano-rod clamped at one and free at the other end is analyzed by the use of bifurcation theory. It is obtained that the pitchfork bifurcation may be either super- or sub-critical. Considering the imperfections in rod's shape and loading, it is proved that they constitute the two-parameter universal unfolding of the problem. Numerical analysis also revealed that for non-locality parameters having higher value than the critical one interaction curves have two branches, so that for a single critical value of angular velocity there exist two critical values of horizontal force

Solitary and compact-like shear waves in the bulk of solids

We show that a model proposed by Rubin, Rosenau, and Gottlieb [J. Appl. Phys. 77 (1995) 4054], for dispersion caused by an inherent material characteristic length, belongs to the class of simple materials. Therefore, it is possible to generalize the idea of Rubin, Rosenau, and Gottlieb to include a wide range of material models, from nonlinear elasticity to turbulence. Using this insight, we are able to fine-tune nonlinear and dispersive effects in the theory of nonlinear elasticity in order to generate pulse solitary waves and also bulk travelling waves with compact support

Torsional Monopoles and Torqued Geometries in Gravity and Condensed Matter

Torsional degrees of freedom play an important role in modern gravity theories as well as in condensed matter systems where they can be modeled by defects in solids. Here we isolate a class of torsion models that support torsion configurations with a localized, conserved charge that adopts integer values. The charge is topological in nature and the torsional configurations can be thought of as torsional `monopole' solutions. We explore some of the properties of these configurations in gravity models with non-vanishing curvature, and discuss the possible existence of such monopoles in condensed matter systems. To conclude, we show how the monopoles can be thought of as a natural generalization of the Cartan spiral staircase.Comment: 4+epsilon, 1 figur

Hyperelastic cloaking theory: Transformation elasticity with pre-stressed solids

Transformation elasticity, by analogy with transformation acoustics and optics, converts material domains without altering wave properties, thereby enabling cloaking and related effects. By noting the similarity between transformation elasticity and the theory of incremental motion superimposed on finite pre-strain it is shown that the constitutive parameters of transformation elasticity correspond to the density and moduli of small-on-large theory. The formal equivalence indicates that transformation elasticity can be achieved by selecting a particular finite (hyperelastic) strain energy function, which for isotropic elasticity is semilinear strain energy. The associated elastic transformation is restricted by the requirement of statically equilibrated pre-stress. This constraint can be cast as \tr {\mathbf F} = constant, where $\mathbf{F}$ is the deformation gradient, subject to symmetry constraints, and its consequences are explored both analytically and through numerical examples of cloaking of anti-plane and in-plane wave motion.Comment: 20 pages, 5 figure

The influence of void size on the micropolar constitutive properties of model heterogeneous materials

In this paper the mechanical behaviour of model heterogeneous materials consisting of regular periodic arrays of circular voids within a polymeric matrix is investigated. Circular ring samples of the materials were fabricated by machining the voids into commercially available polymer sheet. Ring samples of differing sizes but similar geometries were loaded using mechanical testing equipment. Sample stiffness was found to depend on sample size with stiffness increasing as size reduced. The periodic nature of the void arrays also facilitated detailed finite element analysis of each sample. The results obtained by analysis substantiate the observed dependence of stiffness on size. Classical elasticity theory does not acknowledge this size effect but more generalized elasticity theories do predict it. Micropolar elasticity theory has therefore been used to interpret the sample stiffness data and identify constitutive properties. Modulus values for the model materials have been quantified. Values of two additional constitutive properties, the characteristic length and the coupling number, which are present within micropolar elasticity but absent from its classic counterpart have also been determined. The dependence of these additional properties on void size has been investigated and characteristic length values compared to the length scales inherent within the structure of the model materials

On the origin dependence of multipole moments in electromagnetism

The standard description of material media in electromagnetism is based on multipoles. It is well known that these moments depend on the point of reference chosen, except for the lowest order. It is shown that this "origin dependence" is not unphysical as has been claimed in the literature but forms only part of the effect of moving the point of reference. When also the complementary part is taken into account then different points of reference lead to different but equivalent descriptions of the same physical reality. This is shown at the microscopic as well as at the macroscopic level. A similar interpretation is valid regarding the "origin dependence" of the reflection coefficients for reflection on a semi infinite medium. We show that the "transformation theory" which has been proposed to remedy this situation (and which is thus not needed) is unphysical since the transformation considered does not leave the boundary conditions invariant.Comment: 14 pages, 0 figure

Non-minimal Wu-Yang wormhole

We discuss exact solutions of three-parameter non-minimal Einstein-Yang-Mills model, which describe the wormholes of a new type. These wormholes are considered to be supported by SU(2)-symmetric Yang-Mills field, non-minimally coupled to gravity, the Wu-Yang ansatz for the gauge field being used. We distinguish between regular solutions, describing traversable non-minimal Wu-Yang wormholes, and black wormholes possessing one or two event horizons. The relation between the asymptotic mass of the regular traversable Wu-Yang wormhole and its throat radius is analysed.Comment: 9 pages, 2 figures, typos corrected, 2 references adde

The Cauchy Problem for a One Dimensional Nonlinear Peridynamic Model

This paper studies the Cauchy problem for a one-dimensional nonlinear peridynamic model describing the dynamic response of an infinitely long elastic bar. The issues of local well-posedness and smoothness of the solutions are discussed. The existence of a global solution is proved first in the sublinear case and then for nonlinearities of degree at most three. The conditions for finite-time blow-up of solutions are established.Comment: To appear in Journal of Differential Equations (added references, corrected typos, minor revision in Section 2, 18 pages