Optimal determination of the material symmetry axes and associated elasticity tensor from ultrasonic velocity data

Abstract

A simultaneous identification of the angular parallax locating the higher symmetry coordinate system and the associated optimal stiffness tensor from wave speed measurements of obliquely ultrasonic bulk waves in an arbitrarily oriented coordinate system is presented. The property used in classifying a material with regard to its elastic symmetry is the existence and the number of planes of reflective or mirror symmetry. That leads to considering the problem of determining the symmetry class and the directions of the elements of symmetry. To consider the uncertainties of the experimental data, the wave speed measurements are only used to determine the symmetry frames and the optimal stiffness tensor. The proposed inverse propagation algorithm consists of minimizing a functional where the unknowns are the elasticity constants and the Euler angles between the geometric coordinate system and the frame of higher symmetry. Stability of the used least-square algorithm to the initial guesses and to the noise in the wave speed measurements is shown by using simulated data for materials with the most general anisotropy. The applicability of the method is demonstrated using experimental data for arbitrarily oriented but known composite materials.

Towards real-time assessment of anisotropic plate properties using elastic guided waves

“…To ensure physically acceptable solutions, thermodynamics constraints requiring the elasticity tensor to be positive-definite were adopted. 41 For the isotropic, cubic and transverse isotropic cases, this, respectively, lead to c 11 > 4 3 c 44 > 0 È É ; c 11 > c 12 > 0; c 44 > 0 f g , and fc 11 > c 66 > 0; c 44 > 0; c 33 ðc 11 À c 66 Þ > c 2 13 g. For all tests, the inverse procedure was solved using a random initial population of N p ¼ 20 chromosomes within the genetic algorithms. The number of generations N g was adaptive in the sense that the algorithm stopped if the optimal solutionĥ remained unchanged along 50 generations.…”

“…Initially, the anisotropic elastic properties of a number of materials have been determined through bulk waves measurements. 1,2 Nonetheless, these experiments require the measurements to be performed along many propagation directions. In addition, for wave speed data processing, the correct identification of the two transverse waves is not trivial and some additional information is usually required for this purpose.…”

Ultrasonic Field Computation into Multilayered Composite Materials Using a Homogenization Method Based on Ray Theory

“…A fast optimization procedure is then used in order to find the effective stiffness constants leading to the best fit of slowness surfaces. Assuming that the homogenized medium symmetry is known (for example transversely isotropic or hexagonal) a function derived from the Christoffel equation 2is minimized, following [5].…”

Excitation and Reception of Higher-Order Guided Lamb Wave’s A1 and S1 Modes in Plastic and Composite Materials

“…In most cases, the dispersion curves for particular materials are not known in advance, and therefore they should be calculated or measured beforehand. For that, elastic constant of the materials is necessary to know, which usually is found from the measured phase velocities in investigated plastic or composite materials [ 23 , 24 , 25 , 26 , 27 , 28 ]. It is necessary to point out that in the case of materials with high attenuation, phase velocities are frequency-dependent even in bulk specimens, and therefore methods based on reconstruction of the phase velocity dispersion curves should be used [ 17 , 18 ].…”

“…It is necessary to point out that in the case of materials with high attenuation, phase velocities are frequency-dependent even in bulk specimens, and therefore methods based on reconstruction of the phase velocity dispersion curves should be used [ 17 , 18 ]. In our case, attenuation is not very high, and therefore the elastic constants of the materials were determined using methods described in [ 25 , 26 , 27 , 28 ].…”