Elastic Solid Material Research Articles

Propagation of Stoneley Waves at an Interface Between Two Microstretch Elastic Half-spaces

Frequency equations for Stoneley waves at unbonded and bonded interfaces between two dissimilar microstretch elastic half-spaces have been derived. Eringen’s theory of microstretch elastic solid material is employed for mathematical analysis. It is found that Stoneley waves in a microstretch elastic solid medium are dispersive. Numerical computations are performed for a particular model to study the variation of phase velocity with respect to wavenumber, and reveal that for small values of non-dimensional wave number, the effect of microstretch property of the medium has a significant effect on dispersion curves, while no effect is observed for higher values of the non-dimensional wavenumber. The results of Tajuddin, Murty and Stoneley have been derived as particular cases of the present problem, and some other interesting particular cases have also been discussed.

Quasi-isostatic molding of refractory saggers

The advantages of quasi-isostatic molding in production of refractory saggers are considered. The proposed method, in which an elastic solid material acts as the molding medium, is a simplified version of isostatic molding.

Comparison between the Material Symmetry Approaches of Gurtin and Noll

The material symmetry condition of Noll is compared with that of Gurtin for elastic solids. (In this paper elastic solids refer to simply elastic solid materials.) We demonstrate that the difference between the two approaches is due to the fact that Gurtin's involves an additional rotation of the configuration. We show that the two ideas of material symmetry are equivalent for elastic solids in the context of finite elasticity theory. However, the procedures for applying these two approaches to classical linear elasticity theory are different. Also, we observe that both methods can be directly applied to the invariant infinitesimal theory of Casey and Naghdi without starting with the case of finite deformations.

A Finite Volume Scheme for Elastodynamic Equations. 1st Report. Algorithm for Elastodynamics.

In the present investigation. a computational procedure is developed for behaviors of stress waves induced in elastic solid material. Finite volume method is applied to the elastodynamic equations and flux vectors for computations are evaluated according to Godunov method. In order to obtain second order accuracy, the two-stage Runge-Kutta method is used for time integration and the MUSCL approach is employed for flux evaluation. Simulations are conducted for stress waves in a rectangle solid and in a wedge at the appex angle of 165 degrees. The computational results are quite reasonable.

Phase transitions of elastic solid materials

Phase transitions of elastic solid materials

Earthquake Waves and the Elasticity of the Earth

DR. C. G. KNOTT delivered a lecture on “Earthquake Waves and the Elasticity, of the Earth” before the Geological Society on June 9. He pointed out that seismograph records of the earthmovements due to distant earthquakes proves that an earthquake is the source of two types of wave motion which pass through the body of the earth, and a third type which passes round the surface of the earth. Before earthquake records were obtained, mathematicians had shown that these three types of wavemotion existed in and over a sphere consisting of elastic solid material. Many volcanic phenomena, however, suggest the quite different conception of a molten interior underlying the solid crust. At first statement these views seem to be antagonistic, but there is no difficulty in reconciling them. Whatever be the nature of the material lying immediately below the accessible crust, it must become at a certain depth a highly heated fairly homogeneous substance behaving like an elastic solid, with two kinds of elasticity giving rise to what are called the compressional and distortional waves. The velocities of these waves are markedly different, being at every depth nearly in the ratio of 1.8 to 1. Both increase steadily within the first thousand miles of descent towards the earth's centre, the compressional wavevelocity ranging from 4.5 miles per second at the surface to 8 miles per second at depths of 1000 miles and more; the corresponding velocities of the distortional wave are 2.5 and 4.3 at the surface and at the 1000-mile depth respectively. At greater depths these high velocities seem to fall off slightly; but the records fail to give us clear information as to velocities at depths greater than about 2500 miles. Down to this depth the earth behaves towards these waves as a highly elastic solid. The elastic constants, which at first increase with depth more rapidly than the density, become proportional to the density, for the velocity of propagation becomes practically steady. About halfway down, however, the material seems to lose its rigidity (in the elastic sense of the term), and viscosity possibly takes its place, so that the distortional wave disappears. In other words, there is a nucleus of about 1600 miles radius which cannot transmit distortional waves. This nucleus is enclosed by a shell of highly elastic material transmitting both compressional and distortional waves exactly like an elastic solid.

The Deformation of Rocks under Tidal Load

I HAVE read with interest Prof. Milne's letter under the above title in NATURE of July 13, and congratulate him on the promising character of the results. As he himself remarks, the subject theoretically is not a new one. Its geophysical interest lies largely in the possibility of deriving information from the observed phenomena as to the elastic character of the earth's crust. Several difficulties, however, stand in the way of this information. The earliest mathematical treatment of the problem, so far as I am aware, is that by Sir G. H. Darwin, to which Prof. Milne refers. The problem which he actually solved relates to the effect of load on the surface of an elastic solid material which is homogeneous, isotropic, and incompressible. In ignorance of this solution, I obtained another1 in 1896—a simple deduction from the important solution by Prof. Boussinesq for material bounded by an infinite plane—;which is somewhat more general, in so far as it does not assume incompressibility in the material, but otherwise is subject to the same limitations. In practice, the most important of these limitations are probably the assumptions of homogeneity and isotropy. Very possibly, an expert mathematician familiar with recent developments of the mathematical theory of elasticity might have no serious difficulty in removing these restrictions in part or in whole. For instance, if a solution were obtained for the case where there is a relatively thin superficial layer differing in elastic quality from the remainder, it would immediately throw light on what is to be expected from differences in the surface strata.