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Rod Lakes
University of Wisconsin
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We use ultrasonic methodology as a tool for characterizing the elastic and viscoelastic properties of materials. The purposes are to better understand the relationship between structure and properties of complex heterogeneous materials including those of biological origin, and materials that undergo phase transformations, and to guide the synthesis of new kinds of materials with extreme properties. For viscoelastic studies we also use broadband viscoelastic spectroscopy in which the same specimen can be examined at ultrasonic frequency up to 100 kHz or at audio or sub-audio frequency.

Selected research involving ultrasonics.

D. Li, L. Dong and Lakes, R. S., The resonant ultrasound spectroscopy method for determining the Poisson's ratio of spheres over the full range, Materials Letters, 143 31-34 (2015).
The method for determining the Poisson's ratio of isotropic spheres was studied via resonant ultrasound spectroscopy (RUS). To that end, the mode structure maps for freely vibrating isotropic spheres were obtained via finite element method over the full range of Poisson's ratio (-1 to +0.5). RUS measurements for spherical samples (indium, steel, SiO2, 13.5 wt% In-Sn, and copper foam) were compared with the numerical results and the Poisson's ratios were determined as +0.4, +0.3, +0.2, -0.08, and -0.3, respectively. The effects of slight shape imperfection upon the first 12 modes were analyzed for various Poisson's ratios, and were found to be negligible in interpretation of the experimental results.
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Li, D., Dong, L., and Lakes, R. S., "The properties of copper foams with negative Poisson's ratio via resonant ultrasound spectroscopy", Physica Status Solidi , 250(10), 1983-1987 (2013). DOI number: 10.1002/pssb.201384229 (2013). The Poisson's ratios of re-entrant Cu foams with different initial relative densities were studied by resonant ultrasound spectroscopy (RUS). Slight anisotropy in foam was detected by RUS and removed by a small unidirectional compression. The transformation into the re-entrant foam was accomplished by applying a sequence of permanent triaxial compression deformations. The Poisson's ratio first decreases and then increases with increasing compression strain. A minimum in Poisson's ratio of approximately -0.7 for all initial densities was achieved with an appropriate permanent compression strain, compared with -0.6 at similar density determined earlier via optical methods. Foams with higher values of initial density attained minima in Poisson's ratio at lower permanent volumetric compression. The shear modulus increased with increasing volumetric compression ratio, and showed a small hump near the point corresponding to Poisson's ratio minimum. get pdf

Li, D., Jaglinski, T. M., Stone, D. S. and Lakes, R. S., "Temperature insensitive negative Poisson's ratios in isotropic alloys near a morphotropic phase boundary, Appl. Phys. Lett, 101, 251903, Dec. (2012). Poisson's ratio, shear modulus, and damping of polycrystalline indium-tin (In-Sn) alloys in the vicinity of the morphotropic gamma-gamma + beta phase boundary were measured with resonant ultrasound spectroscopy. Negative Poisson's ratios were observed from 24 C to 67 C for alloys near the phase boundary. Properties were unaffected by annealing at 100 C for 2 days. This isotropic fully dense negative Poisson's ratio material is temperature insensitive, in contrast to other materials that undergo phase transformation. get pdf.

Li, D., Dong, L., and Lakes, R. S., "Resonant ultrasound spectroscopy of cubes over the full range of Poisson's ratio", Rev. Sci. Instr. 83, 113902 (2012). get pdf.

Jaglinski and Lakes, R. S., "Resonant ultrasound spectroscopy of cylinders over the full range of Poisson's ratio" Rev. Sci. Instr. 82, 035105 (2011). get pdf. Journal link, online version.

Lakes, R. S., "Viscoelastic measurement techniques", Review of Scientific Instruments, 75, 797-810, April (2004).

Wang, Y. C. and Lakes, R. S., "Resonant ultrasound spectroscopy in shear mode", Review of Scientific Instruments, 74, 1371-1373, Mar. (2003). download pdf

Lee, T., Lakes, R. S., and Lal, A., "Investigation of bovine bone by resonant ultrasound spectroscopy and transmission ultrasound", Biomechanics and Modeling in Mechanobiology, 1, 165-175, October (2002). (download pdf)

Lee, T. and Lakes, R. S., "Damping properties of lead metaniobate", IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 48, 48-52, Jan. (2001). download pdf

Lee, T., Lakes, R. S., Lal, A. , "Resonant ultrasound spectroscopy for measurement of mechanical damping: comparison with broadband viscoelastic spectroscopy", Rev. Sci. Instr. 71 (7) 2855-2861, July (2000). This article compares resonant ultrasound spectroscopy (RUS) and other resonant methods for the determination of viscoelastic properties such as damping. RUS scans from 50 kHz to 500 kHz were conducted on cubical specimens of several materials including brass, aluminum alloys and PMMA, a glassy polymer. Comparison of damping over the frequency ranges for broadband viscoelastic spectroscopy (BVS) and RUS for indium tin alloy in shear modes of deformation discloses a continuation of the tan delta power-law trend for ultrasonic frequencies up to 300 kHz. For PMMA, resonant peaks were sufficiently broad that higher modes in RUS began to overlap. Tan delta via RUS and BVS for PMMA agreed well in the frequency range where the methods overlap. RUS is capable of measuring tan delta as high as several percent at the fundamental frequency. Since higher modes are closely spaced, it is impractical to determine tan delta above 0.01 to 0.02 at frequencies other than the fundamental. download pdf

Resonant ultrasound spectroscopy setup Lakes, R. S., Yoon, H. S. and Katz, J. L., "Ultrasonic wave propagation and attenuation in wet bone," J. Biomed. Engng., 8 143-148 (1986). The propagation of ultrasonic longitudinal waves in bovine plexiform and wet human Haversian bone has been studied over the range 0.5 - 16 MHz. Little velocity dispersion was observed, in contrast to the results of earlier studies on dry bone. Large values of attenuation were observed.

Lakes, R. S., Yoon, H. S. and Katz, J. L., "Slow compressional wave propagation in wet human and bovine cortical bone", Science, 220 513-515, (1983). A slow compressional wave as well as the usual fast wave is observed in wet bone. The slow wave is attributed to stress-induced fluid motion in bone. Download pdf from jstor or here.

Selected teaching involving ultrasonics.
Advanced Mechanical Testing class, EMA611, including links to pages on nondestructive testing and resonant ultrasound spectroscopy. Ultrasonic wave velocity, inference of moduli, isotropy and anisotropy, and attenuation of waves.
Viscoelastic Solids class, EMA630, including measurement and interpretation of attenuation and experimental methods.
Biomechanics class, BME 315.