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Indentation of Nonlinearly Viscoelastic Solids

Published online by Cambridge University Press:  01 February 2011

Michelle L Oyen
Michelle L Oyen*
Affiliation:
mlo29@cam.ac.uk, Cambridge University, Engineering Department, Trumpington Street, Cambridge, N/A, United Kingdom
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Abstract

Much recent attention has been focused on the indentation of linearly viscoelastic solids, and analysis techniques have been developed for polymeric material characterization. However, there has been relatively little progress made in the development of analytical approaches for indentation of nonlinearly viscoelastic materials. Soft biological tissues tend to exhibit responses which are nonlinearly viscoelastic and are frequently modeled using a decomposition of the relaxation or creep function into a product of two functions, one time-dependent and the other stress- or strain-level dependent. Consideration here is for soft biological tissue-like responses, exhibiting approximately quadratic stress-strain behavior, which can be alternatively cast as linear dependence of elastic modulus on strain level. An analytical approach is considered in the context of indentation problems with flat punch, spherical and conical indenter shapes. Hereditary integral expressions are developed and solved for typical indentation experimental conditions including indentation creep, load-relaxation and monotonic constant load- or displacement-rate tests. Primary emphasis is on the deconvolution of material and geometrical nonlinearities during an indentation experiment. The simple analytical expressions that result from this analysis can be implemented for indentation characterization of soft biological tissues without the need for computationally- intensive inverse finite element approaches.

Keywords

viscoelasticitystress/strain relationshipbiological
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 1049: Symposium AA – Fundamentals of Nanoindentation and Nanotribology IV , 2007 , 1049-AA06-06
Copyright
Copyright © Materials Research Society 2008

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References

1 Field, JS and Swain, MV, J Mater Res 8 (1993) 297–306.Google Scholar
2 Oliver, WC and Pharr, GM, J Mater Res 7 (1992) 1564–83.Google Scholar
3 Oyen, ML, Philosophical Magazine 2006, 86 5625–5641.Google Scholar
4 Oyen, ML, Journal of Materials Research, 20 (2005) 2094–2100.Google Scholar
5 Oyen, ML, Bembey, AK, Bushby, AJ, in Mechanics of Biological and Bio-Inspired Materials, edited by C., Viney, K., Katti, C., Hellmich, U., Wegst (Mater. Res. Soc. Symp. Proc. 975E, Warrendale, PA, 2007), 0975–DD07.Google Scholar
6 Oyen, ML and Cook, RF: Journal of Materials Research, 18 (2003) 139–50.Google Scholar
7 Cook, RF and Oyen, ML, International Journal of Materials Research, 98 (2007) 370–8.Google Scholar
8 Oyen, ML and Ko, C-C, J. Mater. Sci. Mater. Med., 18 (2007) 623–8.Google Scholar
9 Lee, EH and Radok, JRM, J. Applied Mech. 27 (1960) 438–44.Google Scholar
10 Oyen, ML, Cook, RF, Stylianopoulos, T, Barocas, VH, Calvin, SE, and Landers, DL, Journal of Materials Research, 20 (2005) 2902–9.Google Scholar
11 Johnson, KL, Contact Mechanics. (Cambridge University Press, Cambridge UK, 1985).Google Scholar
12 Mattice, JM, Lau, AG, Oyen, ML, Kent, RW, J. Mater. Res. 21 (2006) 2003–10.Google Scholar
13 Findley, WN, Lai, J, and Onaran, K, Creep and Relaxation of Nonlinear Viscoelastic Materials, (Dover, New York, 1989).Google Scholar
14 Fung, YC, Biomechanics: Mechanical Properties of Living Tissues, 2nd edition, (Springer-Verlag, New York, 1993).Google Scholar