Determination of Elastic Constants of Anisotropic Materials from Oblique Angle Ultrasonic Wave Measurements II: Experimental

Mignogna, R. B.; Batra, N. K.; Simmonds, K. E.

doi:10.1007/978-1-4615-3742-7_70

Cited by 4 publications

(3 citation statements)

References 5 publications

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“…If the solution does not satisfy these conditions, the problem is called badly-set and its treatment requires special methods. The numerical methods of minimization are generally based on Newton's algorithm [11,28]. It is well known that this algorithm requires a good initialization to converge towards the solution of the problem.…”

Section: Determination Of Elastic Constants From Immersion Measuremenmentioning

confidence: 99%

See 1 more Smart Citation

Magnetooptics of two-dimensional electrons in the ultraquantum limit

Кукушкин¹,

Тимофеев²

1991

Sov. Phys. Usp.

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For homogeneous materials, the ultrasonic immersion method, associated with a numerical optimization process mostly based on Newton's algorithm, allows the determination of elastic constants for various synthetic and natural composite materials. Nevertheless, a principal limitation of the existing optimization procedure occurs when the considered material is at the limit of the homogeneous hypothesis. Such is the case of the woven bidirectional SiC matrix and SiC fibre composite material. In this study, we have developed two numerical methods for the determination of the elastic constants of the 2D SiC/SiC composite material (2D SiC/SiC). The first one is based on Newton's algorithm: the elastic constants are obtained by minimizing the square deviation between experimental and calculated velocities. The second method is based on the Levenberg-Marquardt algorithm. We show that these algorithms give the same results in the case of homogeneous anisotropic composite materials. For the 2D SiC/SiC composite material, the two methods, using the same measured velocities, give different sets of elastic constants. We then note that the Levenberg-Marquardt algorithm enables a better convergence towards a global set of elastic constants in good agreement with the elastic properties, which can be measured using classical quasi-static methods.

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Section: Determination Of Elastic Constants From Immersion Measuremenmentioning

confidence: 99%

“…So, by using mode conversion at the liquid-solid interface, three bulk acoustical modes can be generated and transmitted in numerous directions in the material [7][8][9][10][11]. The phase velocities of these modes are related to the elastic constants of the material through the well-known Christoffel equation [12].…”

Section: Introductionmentioning

confidence: 99%

Magnetooptics of two-dimensional electrons in the ultraquantum limit

Кукушкин¹,

Тимофеев²

1991

Sov. Phys. Usp.

View full text Add to dashboard Cite

show abstract

“…It has been used successfully to determine the all elastic properties of orthotropic composites [3,4] and the complex viscoelastic constants [5,6] for lossy composite materials. So, by using mode conversion at the liquid-solid interface, three bulk acoustical modes can be generated and transmitted in numerous directions in the material [7][8][9][10][11]. The phase velocities of these modes are related to the elastic constants of the material through the well-known Christoffel equation [12].…”

Section: Introductionmentioning

confidence: 99%

Optimal determination of the elastic constants of woven 2D SiC/SiC composite materials

Mouchtachi

Guerjouma²,

Baboux³

et al. 2004

J. Phys. D: Appl. Phys.

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For homogeneous materials, the ultrasonic immersion method, associated with a numerical optimization process mostly based on Newton's algorithm, allows the determination of elastic constants for various synthetic and natural composite materials. Nevertheless, a principal limitation of the existing optimization procedure occurs when the considered material is at the limit of the homogeneous hypothesis. Such is the case of the woven bidirectional SiC matrix and SiC fibre composite material. In this study, we have developed two numerical methods for the determination of the elastic constants of the 2D SiC/SiC composite material (2D SiC/SiC). The first one is based on Newton's algorithm: the elastic constants are obtained by minimizing the square deviation between experimental and calculated velocities. The second method is based on the Levenberg–Marquardt algorithm. We show that these algorithms give the same results in the case of homogeneous anisotropic composite materials. For the 2D SiC/SiC composite material, the two methods, using the same measured velocities, give different sets of elastic constants. We then note that the Levenberg–Marquardt algorithm enables a better convergence towards a global set of elastic constants in good agreement with the elastic properties, which can be measured using classical quasi-static methods.

show abstract