Elastic Constants Of Anisotropic Solids Research Articles

Determination of elastic constants of anisotropic solids from elastodynamic Green's functions

This paper describes a number of elastodynamic experiments that have been used to measure the elastic constants of anisotropic solids, or potentially could be used for that purpose. The inversion algorithms that are used to recover the elastic constants from measured data are discussed.

Analytical and optimization procedures for determination of all elastic constants of anisotropic solids from group velocity data measured in symmetry planes

Analytical and optimization methods of determining all elastic constants of elastically anisotropic solids from the group velocities measured in various directions in the symmetry planes are described. The group velocities in various directions of the specimen are measured, using broadband pointlike and line-type sources in combination with pointlike detectors, and changing a source-to-detector orientation. The mixed index elastic constants of the specimen are determined using analytic formulas that relate the elastic constants to the group velocity in an arbitrary direction on the symmetry plane. It is demonstrated that given the numerous group velocity data, one can efficiently determine the elastic constants by first converting them into phase velocity data and then applying the least-squares optimization methods to the phase velocity data. Examples are provided with specimens of transversely isotropic zinc, cubic silicon, and orthotropic fiber-reinforced poly ether ether kethon.

Determinations of anisotropic elastic constants using laser-generated surface waves

This paper studied the recovery of elastic constants of anisotropic solids from measured surface wave energy velocities. The calculations of surface wave phase and energy velocities of anisotropic solids were based on an efficient forward formalism. In the experiment, the surface waves were generated by a pulsed laser and detected by using the PS/PR technique, where the source and receiver were located on the same surface of a specimen. The inverse problem was solved successfully by the simplex optimization method. Following the simplex iteration rules, the orientation and the elastic constants can be recovered from the measured surface wave energy velocities. The wave fronts and the caustic effects of the skimming shear waves have also been observed in the laser ultrasound experiment.

Determination of the elastic constants of anisotropic solids

This article sets out to review the methods that are available for determining the elastic constants of anisotropic solids, with particular emphasis on techniques that involve the measurement of bulk acoustic wavespeeds. Some of the comparative advantages and disadvantages of the various methods are pointed out. In describing ultrasonic wave transmission, attention is given to the question of whether it is the phase or group velocity that is measured. Finally, the algorithms used for obtaining elastic constants from bulk acoustic wave phase and group velocity data are discussed.

48443 Determination of elastic constants of anisotropic solids from group velocity data : Every, A.G.; Sachse, W.; Kim, K.Y.; Niu, L. Review of Progress in Quantitative Nondestructive Evaluation, La Jolla, California (United States), 15–20 Jul. 1990. vol. 10B, pp. 1663–1668. Edited by D.O. Thompson and D.E. Chimenti. Plenum Press (1991). ISBN 0-306-43903-4

48443 Determination of elastic constants of anisotropic solids from group velocity data : Every, A.G.; Sachse, W.; Kim, K.Y.; Niu, L. Review of Progress in Quantitative Nondestructive Evaluation, La Jolla, California (United States), 15–20 Jul. 1990. vol. 10B, pp. 1663–1668. Edited by D.O. Thompson and D.E. Chimenti. Plenum Press (1991). ISBN 0-306-43903-4

44144 Optimized determination of elastic constants of anisotropic solids from wavespeed measurements : Castagnede, B.; Sachse, W. Proceedings of the 15th Annual Review of Progress in Quantitative Nondestructive Evaluation, La Jolla, California (USA), 31 Jul. – 5 Aug. 1988. vol. 8B, pp. 1855–1862. Edited by D.O. Thompson and D.E. Chimenti. Plenum Press (1989). ISBN 0-306-43209-9

44144 Optimized determination of elastic constants of anisotropic solids from wavespeed measurements : Castagnede, B.; Sachse, W. Proceedings of the 15th Annual Review of Progress in Quantitative Nondestructive Evaluation, La Jolla, California (USA), 31 Jul. – 5 Aug. 1988. vol. 8B, pp. 1855–1862. Edited by D.O. Thompson and D.E. Chimenti. Plenum Press (1989). ISBN 0-306-43209-9

49873 Numerical simulation of the instabilities associated to the recovery of elastic constants of anisotropic solids from quasi-longitudinal velocities alone : Castagnede, B.; Every, A.G.; Sachse, W. Comptes Rendus de R'Academie des Sciences, Series II, vol. 314, no. 9, pp. 865–871 (23 Apr. 1992)

The present Note describes instabilities observed in the use of numerical simulations for recovering the elastic constants of anisotropic solids when only bulk quasi-longitudinal (qL) velocities are taken into account. Both 2-D and 3-D versions of the simulation are discussed, and a number of numerical examples are presented. The influence of the angular range of the data, the density of the simulated data, as well as the addition of a few transverse wavespeeds are discussed in some detail. Some practical implications related to laser generation experiments are pointed out.

Sensitivity of inversion algorithms for recovering elastic constants of anisotropic solids from longitudinal wavespeed data

This paper discusses the sensitivity of inversion algorithms for recovering the elastic constants of moderately anisotropic solids using only ultrasonic longitudinal wavespeed data measured for various directions in a medium. This investigation is motivated, in part, by experience with the recently developed point source/point receiver technique, in which longitudinal wave arrivals are clearer and easier to measure accurately than the later transverse wave arrivals. A perturbation method is presented which shows that for a medium of triclinic symmetry, the longitudinal wavespeeds are most sensitive to the partial set of elastic constants C 11, C 22, C 33, ( C 12 + 2 C 66), ( C 23 + 2 C 44) and ( C 13 + 2 C 55), and it is these constants which can therefore be most accurately recovered from longitudinal wavespeed data. A number of illustrative numerical examples are presented which demonstrate the lack of sensitivity to certain constants and illustrate the recovery of elastic constants from simulated longitudinal mode data. These show that there is good convergence for the partial set of elastic constants, whereas the remaining elastic constants are much less accurately recovered.

Determination of the elastic constants of anisotropic solids from acoustic-wave group-velocity measurements.

A method is proposed for determining the elastic constants of an anisotropic solid from acoustic-wave group velocities measured in off-symmetry directions in a specimen. The method corresponds to a two-stage optimization procedure in which the elastic constants are varied so as to obtain a least-squares fit of measured to calculated group velocities. At each iterative step a numerical minimization process is employed to find the wave normals and velocities of waves having the required ray directions. The method is demonstrated with synthetic data generated for a number of cubic crystals, and to experimental data obtained on single crystals of silicon using the ultrasonic point-source/enpoint-receiver technique. When provided with longitudinal- and transverse-mode velocity data, the method is able to accurately recover all three independent elastic constants. When only longitudinal mode data are provided, ${\mathit{C}}_{11}$ and the combination ${\mathit{C}}_{12}$+2${\mathit{C}}_{44}$ can be accurately recovered, but not ${\mathit{C}}_{12}$ and ${\mathit{C}}_{44}$ individually.

Optimal determination of the elastic constants of composite materials from ultrasonic wave-speed measurements

A method is described to optimally determine the elastic constants of anisotropic solids from wave-speeds measurements in arbitrary nonprincipal planes. For such a problem, the characteristic equation is a degree-three polynomial which generally does not factorize. By developing and rearranging this polynomial, a nonlinear system of equations is obtained. The elastic constants are then recovered by minimizing a functional derived from this overdetermined system of equations. Calculations of the functional are given for two specific cases, i.e., the orthorhombic and the hexagonal symmetries. Some numerical results showing the efficiency of the algorithm are presented. A numerical method is also described for the recovery of the orientation of the principal acoustical axes. This problem is solved through a double-iterative numerical scheme. Numerical as well as experimental results are presented for a unidirectional composite material.

Elastic Constants of Anisotropic Solids. Group-theoretical Treatment

Elastic Constants of Anisotropic Solids. Group-theoretical Treatment