scholarly journals The Elastic Anisotropy of Keratinous Solids I. The Dilatational Elastic Constants

1954 ◽  
Vol 7 (3) ◽  
pp. 336 ◽  
Author(s):  
K RacheI Makinson
Keyword(s):  
Elastic Waves ◽  
Radial Direction ◽  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
Total Reflection ◽  
Histological Structure ◽  
Reflection Method ◽  
Fibre Direction ◽  
Principal Axes ◽  
Velocity Of Propagation

The elastic anisotropy of four forms of a-keratin, ram's horn, rhinoceros horn, baleen (whalebone), and the cortex of African porcupine quill, has been studied by measurement of the velocity of propagation of dilatational elastic waves of 5 Mc/s frequency along the principal axes, by the total reflection method. It has been found that ram's horn is transversely isotropic about the radial direction and that rhinoceros horn is approximately transversely isotropic about the fibre direction. This is directly correlated with the histological structure of these materials, which here predominates over the molecular structure in determining the nature of the elastic anisotropy.

The Elastic Anisotropy of Keratinous Solids

1955 ◽  
Vol 8 (2) ◽  
pp. 278
Author(s):  
K RacheI Makinson
Keyword(s):  
Molecular Structure ◽  
Elastic Constants ◽  
Elastic Waves ◽  
Radial Direction ◽  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
Histological Structure ◽  
Pulse Technique ◽  
Principal Axes

The rigidity constants of ram's horn have been determined by using a pulse technique to measure the velocities of propagation along the principal axes of transverse elastic waves of frequency 4 Mc/s. The results show that the conclusion, which was drawn previously from measurement of the dilatational constants, that ram's horn is transversely isotropic about the radial direction, is approximately though not exactly correct. The type of anisotropy and the relative magnitudes of the various elastic constants are directly correlated with the histological structure of the horn, which under the conditions of the measurements is more important than the molecular structure in determining the nature of the elastic anisotropy.

A continuum model for fibre-reinforced plastic materials

1967 ◽  
Vol 301 (1467) ◽  
pp. 473-492 ◽  
Keyword(s):  
Experimental Data ◽  
Continuum Model ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Rigid Plastic ◽  
Fibre Direction ◽  
Preferred Direction ◽  
Principal Axes ◽  
Theoretical Predictions ◽  
General Continuum

A simple, general continuum model is proposed for describing the plastic behaviour of a composite material consisting of a metal matrix reinforced by strong fibres. The model is that of an incompressible rigid/plastic continuum which is transversely isotropic—the single preferred direction at any point, and at all times, being the fibre-direction at that point—and which is inextensible in the preferred direction. The principal axes of anisotropy are therefore explicitly determined by the deformation history. The kinematics and general three-dimensional theory for the material are developed and then applied to two cases of plane strain and one of plane stress. The latter is employed in the analysis of previously published experimental data on the yielding of thin fibre-reinforced sheets; good agreement is obtained between the theoretical predictions and the experimental data.

On: “Weak elastic anisotropy,” by L. Thomsen (GEOPHYSICS, 52, 1954–1966, October, 1986).

Geophysics ◽  
1988 ◽  
Vol 53 (4) ◽  
pp. 558-559 ◽  
Author(s):  
Franklyn K. Levin
Keyword(s):  
Elastic Constants ◽  
Vertical Velocity ◽  
Elastic Waves ◽  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
P Wave ◽  
Sh Waves ◽  
The Individual ◽  
Transversely Isotropic Solids ◽  
Isotropic Solids

In a paper whose importance seems to have escaped notice, Thomsen (1) derived equations that give the moveout velocities of P, SV, and SH-waves when solids are weakly transversely isotropic and (2) tabulated experimentally determined elastic constants for a large number of rocks, crystals, and a few other solids. For rocks, one of the constants, delta, differed from zero by as much as 0.73 and −0.27. Delta is the fraction by which P-wave moveout velocity deviates from the vertical velocity [Thomsen’s equation (27a)]. Although some deltas indicated deviations from the vertical velocity smaller than 1 or 2 percent, most were larger and positive. Until the publication of Thomsen’s data, most of us concerned with elastic waves traveling in earth sections that act as transversely isotropic solids because the sections consist of thin beds had assumed the individual beds were isotropic solids, all with the same Poisson’s ratios. That assumption results in a zero value for delta and a moveout velocity equal to the vertical velocity. The validity of the assumption is now doubtful.

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