Abstract
Elastic-viscoelastic correspondence was used to generate displacement–time solutions for spherical indentation testing of soft biological materials with time-dependent mechanical behavior. Boltzmann hereditary integral operators were used to determine solutions for indentation load-relaxation following a constant displacement rate ramp. A “ramp correction factor” approach was used for routine analysis of experimental load-relaxation data. Experimental load-relaxation tests were performed on rubber, as well as kidney tissue and costal cartilage, two hydrated soft biological tissues with vastly different mechanical responses. The experimental data were fit to the spherical indentation ramp-relaxation solutions to obtain values of short- and long-time shear modulus and of material time constants. The method is used to demonstrate linearly viscoelastic responses in rubber, level-independent indentation results for costal cartilage, and age-independent indentation results for kidney parenchymal tissue.
Similar content being viewed by others
References
A. Cooper, B. Barlow, C. Discala, D. String: Mortality and truncal injury: The pediatric perspective. J. Pediatr. Surg. 29(1), 33 (1994).
M.L. Nance, N. Lutz, K.B. Arbogast, R.A. Cornejo, M.J. Kallan, F.K. Winston, D.R. Durbin: Optimal restraint reduces the risk of abdominal injury in children involved in motor vehicle crashes. Ann. Surg. 239(1), 127 (2004).
M. Farshad, M. Barbezat, P. Flueler, F. Schmidlin, P. Graber, P. Niederer: Material characterization of the pig kidney in relation with the biomechanical analysis of renal trauma. J. Biomech. 32, 417 (1999).
A. Tamura, K. Omori, K. Miki, J. Lee, K. Yang, and A. King: Mechanical characterization of porcine abdominal organs, in Proc. 46th Stapp Car Crash Conference SAE Paper No. 2002-22-0003, (Point Verdra Beach, FL, 2002), edited by Stapp advisory committee, (SAE International: Warrendale, PA, 2002), p. 55.
H. Yamada: Strength of Biological Materials (Kreiger, Huntingdon, NY, 1971), pp. 205, 207.
S. Nasseri, L. Bilston, N. Phan-Thein: Viscoelastic properties of pig kidney in shear, experimental results and modeling. Rheol. Acta 41, 180 (2002).
J. Snedeker, M. Barbezat, P. Niederer, F. Schmidlin, M. Farshad: Strain energy density as a rupture criterion for the kidney: Impact tests on porcine organs, finite element simulation, and a baseline comparison between human and porcine tissues. J. Biomech. 38, 993 (2005).
L. Rosenberg, B. Johnson, M. Schubert: Proteinpolysaccharides from human articular and costal cartilage. J. Clin. Invest. 44, 1647 (1965).
W. Hukins, D.P. Knight, J. Woodhead-Galloway: Amianthoid change: Orientation normal collagen fibrils during aging. Science 194, 622 (1976).
R. Mallinger, L. Stockinger: Amianthoid (asbestoid) transformation: Electron microscopial studies on aging human costal cartilage. Am. J. Anat. 181(1), 23 (1988).
R. Roy, S.S. Kohles, V. Zaporojan, G.M. Peretti, M.A. Randolph, J. Xu, L.J. Bonassar: Analysis of bending behavior of native and engineered auricular and costal cartilage. J. Biomed. Mater. Res. A 68, 597 (2004).
J.Y. Rho, T.Y. Tsui, G.M. Pharr: Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials 18, 1325 (1997).
A.J. Bushby, V.L. Ferguson, A. Boyde: Nanoindentation of bone: Comparison of specimens tested in liquid and embedded in polymethylmethacrylate. J. Mater. Res. 19, 249 (2004).
A.K. Bembey, M.L. Oyen, A.J. Bushby, A. Boyde: Viscoelastic properties of bone as a function of hydration state determined by nanoindentation. Philos. Mag. (2006) (in press).
A. Gefen, N. Gefen, Q. Zhu, R. Raghupathi, S. Margulies: Age-dependent changes in material properties of the brain and braincase of the rat. J. Neurotrauma. 20, 1163 (2003).
K. Miller: Constitutive modeling of abdominal organs. J. Biomech. 33, 367 (2000).
S. Lai-fook, T. Wilson, R. Hyatt, J. Rodarte: Elastic constants of inflated lobes of dog lungs. J. Appl. Physiol. 40, 508 (1976).
Y. Zheng, A. Mak, B. Lue: Objective assessment of limb tissue elasticity: Development of a manual indentation procedure. J. Rehabil. Res. Dev. 36(2), 71 (1999).
W.C. Hayes, L.F. Mockros: Viscoelastic properties of human articular cartilage. J. Appl. Physiol. 31, 562 (1971).
W. Hayes, L. Keer, G. Herrmann, L. Mockros: A mathematical analysis for indentation tests of articular cartilage. J. Biomech. 5, 541 (1972).
J. Parsons, J. Black: The viscoelastic shear behavior of normal rabbit articular cartilage. J. Biomech. 10, 21 (1977).
A.F. Mak, W.M. Lai, V.C. Mow: Biphasic indentation of articular cartilage—I. Theoretical analysis. J. Biomech. 20, 703 (1987).
M. Beek, J. Koolstra, T. Van Eijden: Human temporomandibular joint disc cartilage as a poroelastic material. Clin. Biomech. (Bristol, Avon) 18, 69 (2003).
E.H. Lee, J.R.M Radok: Contact problem for viscoelastic bodies. J. Appl. Mech. 27, 438 (1960).
K.L. Johnson: Contact Mechanics (Cambridge University Press, Cambridge, UK, 1985).
M.L. Oyen: Spherical indentation creep following ramp loading. J. Mater. Res. 20, 2094 (2005).
L. Cheng, X. Xia, L.E. Scriven, W.W. Gerberich: Spherical-tip indentation of viscoelastic material. Mech. Mater. 37, 213 (2005).
M. Sakai: Time-dependent viscoelastic relation between load and penetration for an axisymmetric indenter. Philos. Mag. A 82, 1841 (2002).
W.C. Oliver, G.M. Pharr: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).
Author information
Authors and Affiliations
Corresponding author
Additional information
This author was an editor of this focus issue during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs.org/publications/jmr/policy.html.
Rights and permissions
About this article
Cite this article
Mattice, J.M., Lau, A.G., Oyen, M.L. et al. Spherical indentation load-relaxation of soft biological tissues. Journal of Materials Research 21, 2003–2010 (2006). https://doi.org/10.1557/jmr.2006.0243
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/jmr.2006.0243