Investigation of the Motion of a Spherical Object Located at Soft Elastic and Viscoelastic Material Interface for Identification of Material Properties

Article Sidebar

PDF
Published: Oct 17, 2024
DOI: https://doi.org/10.14416/j.asep.2023.12.002
Keywords:
Dynamic Hertz model Material properties Shear modulus Soft material Sphere Viscoelastic properties Viscosity

Main Article Content

Hasan Koruk
Faculty of Engineering, MEF University, Istanbul, Turkey
Antonios N. Pouliopoulos
Department of Surgical and Interventional Engineering, School of Biomedical Engineering and Imaging Sciences, King’s College London, London, United Kingdom

Abstract

Measuring the properties of soft viscoelastic materials is challenging. Here, the motion of a spherical object located at the soft elastic and viscoelastic material interface for the identification of material properties is thoroughly investigated. Formulations for different loading cases were derived. First, the theoretical models for a spherical object located at an elastic medium interface were derived, ignoring the medium viscosity. After summarizing the model for the force reducing to zero following the initial loading, we developed mathematical models for the force reducing to a lower non-zero value or increasing to a higher non-zero value, following the initial loading. Second, a similar derivation process was followed to evaluate the response of a spherical object located at a viscoelastic medium interface. Third, by performing systematic analyses, the theoretical models obtained via different approaches were compared and evaluated. Fourth, the measured and predicted responses of a spherical object located at a gelatin phantom interface were compared and the viscoelastic material properties were identified. It was seen that the frequency of oscillations of a spherical object located at the sample interface during loading was 10–15% different from that during unloading in the experimental studies here. The results showed that different loading cases have immense practical value and the formulations for different loading cases can provide an accurate determination of material properties in a multitude of biomedical and industrial applications.

Article Details

How to Cite
Koruk, H., & Pouliopoulos, A. N. (2024). Investigation of the Motion of a Spherical Object Located at Soft Elastic and Viscoelastic Material Interface for Identification of Material Properties. Applied Science and Engineering Progress, 17(4), 7277. https://doi.org/10.14416/j.asep.2023.12.002
Issue
Vol. 17 No. 4 (2024): Special Issue
Section
Research Articles

References

Y. A. Ilinskii, G. D. Meegan, E. A. Zabolotskaya, and S. Y. Emelianov, “Gas bubble and solid sphere motion in elastic media in response to acoustic radiation force,” The Journal of the Acoustical Society of America, vol. 117, no. 4, pp. 2338–2346, 2005, doi: 10.1121/1.1863672.

S. R. Aglyamov, A. B. Karpiouk, Y. A. Ilinskii, E. A. Zabolotskaya, and S. Y. Emelianov, “Motion of a solid sphere in a viscoelastic medium in response to applied acoustic radiation force: Theoretical analysis and experimental verification,” The Journal of the Acoustical Society of America, vol. 122, no. 4, pp. 1927– 1936, 2007, doi: 10.1121/1.2774754.

C.-C. Huang, C.-C. Shih, T.-Y. Liu and P.-Y. Lee, “Assessing the viscoelastic properties of thrombus using a solid-sphere-based instantaneous force approach,” Ultrasound in Medicine & Biology, vol. 37, no. 10, pp. 1722–1733, 2011, doi: 10.1016/j.ultrasmedbio.2011.06.026.

S. Yoon, S. R. Aglyamov, A. B. Karpiouk, S. Kim, and S. Y. Emelianov, “Estimation of mechanical properties of a viscoelastic medium using a laser-induced microbubble interrogated by an acoustic radiation force,” The Journal of the Acoustical Society of America, vol. 130, no. 4, pp. 2241–2248, 2011, doi: 10.1121/1.3628344.

S. Yoon, S. Aglyamov, A. Karpiouk, and S. Emelianov, “The mechanical properties of ex vivo bovine and porcine crystalline lenses: Age-related changes and location-dependent variations,” Ultrasound in Medicine & Biology, vol. 39, no. 6, pp. 1120–1127, 2013, doi: 10.1016/j.ultrasmedbio.2012.12.010.

B. E. Levy and A. L. Oldenburg, “Single magnetic particle motion in magnetomotive ultrasound: An analytical model and experimental validation,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency, vol. 68, no. 8, pp. 2635–2644, 2021, doi: 10.1109/TUFFC.2021.3072867.

A. Cebrecos, N. Jiménez, R. Tarazona, M. Company, J. M. Benlloch, and F. Camarena, “Characterization of viscoelastic media combining ultrasound and magnetic-force induced vibrations on an embedded soft magnetic sphere,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency, vol. 68, no. 12, pp. 3540–3548, 2021, doi: 10.1109/TUFFC.2021.3097883.

H. Koruk, A. E. Ghamrawy, A. N. Pouliopoulos, and J. J. Choi, “Acoustic particle palpation for measuring tissue elasticity,” Applied Physics Letters, vol. 107, no. 22, 2015, Art. no. 223701, doi: 10.1063/1.4936345.

H. Koruk and J. J. Choi, “Displacement of a bubble by acoustic radiation force into a fluid–tissue interface,” The Journal of the Acoustical Society of America, vol. 143, no. 4, pp. 2535–2540, 2018, doi: 10.1121/1.5034175.

H. Koruk and J. J. Choi, “Displacement of a bubble located at a fluid-viscoelastic medium interface,” The Journal of the Acoustical Society of America, vol. 145, no. 5, pp. EL410–EL416, 2019, doi: 10.1121/1.5108678.

J. H. Bezer, H. Koruk, C. J. Rowlands, and J. J. Choi, “Elastic deformation of soft tissue-mimicking materials using a single microbubble and acoustic radiation force,” Ultrasound in Medicine & Biology, vol. 46, no. 12, pp. 3327–3338, 2020, doi: 10.1016/j.ultrasmedbio.2020.08.012.

H. Koruk, “Assessment of the models for predicting the responses of spherical objects in viscoelastic mediums and at viscoelastic interfaces,” IOP Conference Series: Materials Science and Engineering, vol. 1150, 2021, Art. no. 012016, doi: 10.1088/1757-899X/1150/1/012016.

H. Koruk, “Development of a model for predicting dynamic response of a sphere at viscoelastic interface: A dynamic Hertz model,” IOP Conference Series: Materials Science and Engineering, vol. 1150, 2021, Art. no. 012015, doi: 10.1088/ 1757-899X/1150/1/012015.

H. Koruk, A. Besli, H. O. Koc, and S. B. Yurdaer, “Identification of material viscoelastic properties using the motion of a rigid sphere located at tissue-mimicking material interface in response to a dynamic force,” Materials Science Forum, vol. 1066, pp. 73–78, 2022, doi: 10.4028/p-oum2c1.

H. Koruk, S. B. Yurdaer, H. O. Koc, and A. Besli, “Identification of the viscoelastic properties of soft materials using a convenient dynamic indentation system and procedure,” Materials Today: Proceedings, vol. 57, part 2, pp. 464–468, 2022, doi: 10.1016/j.matpr.2022.01.188.

H. Koruk and K. Y. Sanliturk, “Identification and removal of adverse effects of non-contact electromagnetic excitation in Oberst Beam Test Method,” Mechanical Systems and Signal Processing, vol. 30, pp. 274–295, 2012, doi: 10.1016/j.ymssp.2012.02.003.

K. Y. Sanliturk and H. Koruk, “A new triangular composite shell element with damping capability,” Composite Structures, vol. 118, pp. 322–327, 2014, doi: 10.1016/j.compstruct.2014.07.053.

H. Koruk and K. Y. Sanliturk, “Optimisation of damping treatments based on big bang-big crunch and modal strain energy methods,” Journal of Sound and Vibration, vol. 333, no. 5, pp. 1319– 1330, 2014, doi: 10.1016/j.jsv.2013.10.023.

H. Koruk, “Quantification and minimization of sensor effects on modal parameters of lightweight structures,” Journal of Vibroengineering, vol. 16, no. 4, pp. 1952–1963, 2014.

X. Zhang, B. Qiang, and J. Greenleaf, “Comparison of the surface wave method and the indentation method for measuring the elasticity of gelatin phantoms of different concentrations,” Ultrasonics, vol. 51, no. 2, pp. 157–164, 2011, doi: 10.1016/j.ultras.2010.07.005.

R. Han and J. Chen, “A modified Sneddon model for the contact between conical indenters and spherical samples,” Journal of Materials Research, vol. 36, pp. 1762–1771, 2021, doi: 10.1557/s43578-021-00206-5.

S. V. Kontomaris, A. Georgakopoulos, A. Malamou, and A. Stylianou, “The average Young’s modulus as a physical quantity for describing the depth- dependent mechanical properties of cells,” Mechanics of Materials, vol. 158, 2021, Art. no. 103846, doi: 10.1016/j.mechmat.2021.103846.

D. Xu, T. Harvey, E. Begiristain, C. Domínguez, L. Sánchez-Abella, M. Browne, and R. B. Cook, “Measuring the elastic modulus of soft biomaterials using nanoindentation,” Journal of the Mechanical Behavior of Biomedical Materials, vol. 133, 2022, Art. no. 105329, doi: 10.1016/j.jmbbm.2022.105329.

S. V. Kontomaris, A. Stylianou, A. Malamou, and K. S. Nikita, “An alternative approach for the Young’s modulus determination of biological samples regarding AFM indentation experiments,” Materials Research Express, vol. 6, 2019, Art. no. 025407, doi: 10.1088/2053-1591/aaef10.

L. Cheng, X. Xia, L. E. Scriven, and W. W. Gerberich, “Spherical-tip indentation of viscoelastic material,” Mechanics of Materials, vol. 37, no. 1, pp. 213–226, 2005, doi: 10.1016/j.mechmat. 2004.03.002.

B. Qiang, J. Greenleaf, M. Oyen, and X. Zhang, “Estimating material elasticity by spherical indentation load-relaxation tests on viscoelastic samples of finite thickness,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency, vol. 58, no. 7, pp. 1418–1429, 2011, doi: 10.1109/ TUFFC.2011.1961.

I. Argatov and G. Mishuris, Indentation Testing of Biological Materials. Cham: Springer, 2018, doi: 10.1007/978-3-319-78533-2.

M. Mizukami, H. -Y. Ren, H. Furukawa, and K. Kurihara, “Deformation of contacting interface between polymer hydrogel and silica sphere studied by resonance shear measurement,” The Journal of Chemical Physics, vol. 149, no. 16, 2018, Art. no. 163327, doi: 10.1063/1.5037326.

S. -V. Kontomaris and A. Malamou, “Exploring the non-linear oscillation of a rigid sphere on an elastic half-space,” European Journal of Physics, vol. 42, no. 2, 2021, Art. no. 025011, doi: 10.1088/1361-6404/abce1d.

H. Koruk, “Modelling small and large displacements of a sphere on an elastic half-space exposed to a dynamic force,” European Journal of Physics, vol. 42, no. 5, 2021, Art. no. 055006, doi: 10.1088/1361-6404/ac0e42.

H. Koruk, “Development of an improved mathematical model for the dynamic response of a sphere located at a viscoelastic medium interface,” European Journal of Physics, vol. 43, no. 2, 2022, Art. no. 025002, doi: 10.1088/1361- 6404/ac4647.

H. Koruk, H. O. Koc, S. B. Yurdaer, A. Besli, and A. N. Pouliopoulos, “A new approach for measuring viscoelastic properties of soft materials using the dynamic response of a spherical object placed at the sample interface,” Experimental Mechanics, 2023, doi: 10.1007/s11340-023-01004-2.

D. J. Inman, Engineering Vibrations. New Jersey: Pearson Education, 2013.

S. Chen, M. W. Urban, C. Pislaru, R. Kinnick, Y. Zheng, A. Yao, and J. F. Greenleaf, “Shearwave dispersion ultrasound vibrometry (SDUV) for measuring tissue elasticity and viscosity,” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency, vol. 56, no. 1, pp. 55–62, 2009, doi: 10.1109/TUFFC.2009.1005.

S. H. Crandall, “The role of damping in vibration theory,” Journal of Sound and Vibration, vol. 11, no. 1, pp. 3–18, 1970, doi: 10.1016/S0022- 460X(70)80105-5.

J. P. Holman, Experimental Methods for Engineers. New York: McGraw Hill, 2012.

H. Koruk, J. T. Dreyer, and R. Singh, “Modal analysis of thin cylindrical shells with cardboard liners and estimation of loss factors,” Mechanical Systems and Signal Processing, vol. 45, no. 2, pp. 346–359, 2014, doi: 10.1016/j.ymssp.2013.10.026.

H. Koruk and K. Y. Sanliturk, “A novel definition for quantification of mode shape complexity,” Journal of Sound and Vibration, vol. 332, no. 14, pp. 3390–3403, 2013, doi: 10.1016/j. jsv.2013.01.039.

B. D. Siva Deeraj, K. Joseph, J. S. Jayan, and A. Saritha, “Dynamic mechanical performance of natural fiber reinforced composites: A brief review,” Applied Science and Engineering Progress, vol. 14, no. 4, pp. 614–623, 2021, doi: 10.14416/j.asep.2021.06.003.

A. E. Ghamrawy, F. de Comtes, H. Koruk, A. Mohammed, J. R. Jones, and J. J. Choi, “Acoustic streaming in a soft tissue microenvironment,” Ultrasound in Medicine & Biology, vol. 45, no. 1, pp. 208–217, 2019, doi: 10.1016/j.ultrasmedbio. 2018.08.026.

A. C. Ozcan, K. Y. Sanliturk, G. Genc, and H. Koruk, “Investigation of the sound absorption and transmission loss performances of green homogenous and hybrid luffa and jute fiber samples,” Applied Science and Engineering Progress, vol. 14, no. 4, pp. 668–679, 2021, doi: 10.14416/j.asep.2021.04.005.

H. Koruk, “Assessment of the measurement and prediction methods for the acoustic properties of natural fiber samples and evaluation of their properties,” Journal of Natural Fibers, vol. 19, no. 13, pp. 6283–6311, 2022, doi: 10.1080/15440478.2021.1907835.

S. M. Rangappa, S. Siengchin, and H. N. Dhakal, “Green-composites: Ecofriendly and sustainability,” Applied Science and Engineering Progress, vol. 13, no. 3, pp. 183–184, 2020, doi: 10.14416/j.asep. 2020.06.001.