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Indentation method for measuring the viscoelastic kernel function of nonlinear viscoelastic soft materials

Published online by Cambridge University Press:  08 February 2013

Yan-Ping Cao*
Affiliation:
AML & CMM, Institute of Biomechanics and Medical Engineering, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Man-Gong Zhang
Affiliation:
AML & CMM, Institute of Biomechanics and Medical Engineering, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
Xi-Qiao Feng
Affiliation:
AML & CMM, Institute of Biomechanics and Medical Engineering, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
*
a)Address all correspondence to this author. e-mail: [email protected]
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Abstract

The indentation method of nonlinear viscoelastic materials is investigated through combined numerical and experimental efforts to reveal the correlation between the viscoelastic kernel function and the indentation responses. It is shown that the viscoelastic kernel function of a nonlinear viscoelastic solid with viscous response characterized by a linear rate constitutive equation scales with the normalized relaxation load in an indentation relaxation test. This scaling relation does not depend on the geometry of the indented solid and the profile of the indenter. Therefore, it may serve as a fundamental relation for characterizing the viscoelastic properties of some biological soft tissues and artificial soft materials with regular/irregular surface morphology.

Type
Articles
Copyright
Copyright © Materials Research Society 2013

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References

REFERENCES

Fung, Y.C.: Biomechanics: Mechanical Properties of Living Tissues (Springer, New York, NY, 1993).CrossRefGoogle Scholar
Taber, L.A.: Nonlinear Theory of Elasticity: Applications in Biomechanics (World Scientific Publishing, River Edge, NJ, 2004).CrossRefGoogle Scholar
Levental, I., Georges, P.C., and Janmey, P.A.: Soft biological materials and their impact on cell function. Soft Matter 3, 299 (2007).CrossRefGoogle ScholarPubMed
DiSilvestro, M.R. and Suh, J.K.F.: A cross-validation of the biphasic poroviscoelastic model of articular cartilage in unconfined compression, indentation, and confined compression. J. Biomech. 34, 519 (2001).CrossRefGoogle ScholarPubMed
Korhonen, R.K., Laasanen, M.S., Töyräs, J., Lappalainen, R., Helminen, H.J., and Jurvelin, J.S.: Fibril reinforced poroelastic model predicts specifically mechanical behavior of normal, proteoglycan depleted and collagen degraded articular cartilage. J. Biomech. 36, 1373 (2003).CrossRefGoogle ScholarPubMed
Crosby, A.J. and Macmanus, J.J.: Blowing bubbles to study living material. Phys. Today 64, 62 (2011).CrossRefGoogle Scholar
Shimizu, S., Yanagimoto, T., and Sakai, M.: Pyramidal indentation load-depth curve of viscoelastic materials. J. Mater. Res. 14, 4075 (1999).CrossRefGoogle Scholar
Lu, H., Wang, B., Ma, J., Huang, G., and Viswanathan, H.: Measurement of creep compliance of solid polymers by nanoindentation. Mech. Time-Depend. Mater. 7, 189 (2003).CrossRefGoogle Scholar
Fischer-Cripps, A.: Multiple-frequency dynamic nanoindentation testing. J. Mater. Res. 19, 2981 (2004).CrossRefGoogle Scholar
Ngan, A.H.W. and Tang, B.: Response of power-law-viscoelastic and time-dependent materials to rate jumps. J. Mater. Res. 24, 653 (2009).CrossRefGoogle Scholar
Tang, B. and Ngan, A.H.W.: A rate-jump method for characterization of soft tissues using nanoindentation techniques. Soft Matter 8, 5974 (2012).CrossRefGoogle Scholar
Oyen, M.L. and Cook, R.F.: Load–displacement behavior during sharp indentation of viscous–elastic–plastic materials. J. Mater. Res. 18, 139 (2003).CrossRefGoogle Scholar
Oyen, M.L.: Spherical indentation creep following ramp loading. J. Mater. Res. 20, 2094 (2005).CrossRefGoogle Scholar
Cheng, Y.T. and Cheng, C.M.: Scaling, dimensional analysis, and indentation measurements. Mater. Sci. Eng., R. 44, 91 (2004).CrossRefGoogle Scholar
Herbert, E., Oliver, W., Lumsdaine, A., and Pharr, G.: Measuring the constitutive behavior of viscoelastic solids in the time and frequency domain using flat punch nanoindentation. J. Mater. Res. 24, 626 (2009).CrossRefGoogle Scholar
Cao, Y.P., Ma, D., and Raabe, D.: The use of flat punch indentation to determine the viscoelastic properties in the time and frequency domains of a soft layer bonded to a rigid substrate. Acta Biomater. 5, 240 (2009).CrossRefGoogle ScholarPubMed
Cheng, Y.T. and Yang, F.Q.: Obtaining shear relaxation modulus and creep compliance of linear viscoelastic materials from instrumented indentation using axisymmetric indenters of power-law profiles. J. Mater. Res. 24, 3013 (2009).CrossRefGoogle Scholar
Galli, M. and Oyen, M.L.: Fast identification of poroelastic parameters from indentation tests. CMES: Comput. Model. Eng. Sci. 48, 241(2009).Google Scholar
Kalcioglu, Z.I., Mahmoodian, R., Hu, Y.H., Suo, Z.G., and Van Vliet, K.J.: From macro- to microscale poroelastic characterization of polymeric hydrogels via indentation. Soft Matter 8, 3393 (2012).CrossRefGoogle Scholar
Li, B., Cao, Y.P., Feng, X.Q., and Gao, H.: Mechanics of morphological instabilities and surface wrinkling in soft materials: a review. Soft Matter 8, 5728 (2012).CrossRefGoogle Scholar
Goh, S.M., Charalambides, M.N., and Williams, J.G.: Characterisation of non-linear viscoelastic foods by the indentation technique. Rheol. Acta 44, 47(2004).CrossRefGoogle Scholar
Rauchs, G., Bardon, J., and Georges, D.: Identification of the material parameters of a viscous hyperelastic constitutive law from spherical indentation tests of rubber and validation by tensile tests. Mech. Mater. 42, 961973 (2010).CrossRefGoogle Scholar
Cao, Y.P., Ji, X.Y., and Feng, X.Q.: Geometry independence of the normalized relaxation functions of viscoelastic materials in indentation. Philos. Mag. 90, 1639 (2010).CrossRefGoogle Scholar
ABAQUS: ABAQUS Theoretical Manual, Version 6.9 (2009).Google Scholar
ANSYS: ANSYS Theory Reference, Ansys, Version 10 (2010).Google Scholar
Simo, J.C.: On a fully three-dimensional finite-strain viscoelastic damage model: Formulation and computational aspects. Comput. Meth. Appl. Mech. Eng. 60, 153 (1987).CrossRefGoogle Scholar
Pipkin, A. and Rogers, T.: A non-linear integral representation for viscoelastic behaviour. J. Mech. Phys. Solids 16, 59 (1968).CrossRefGoogle Scholar
Holzapfel, G.A.: On large strain viscoelasticity: Continuum formulation and finite element applications to elastomeric structures. Int. J. Numer. Methods Eng. 39, 3903 (1996).3.0.CO;2-C>CrossRefGoogle Scholar
Reese, S. and Govindjee, S.: A theory of finite viscoelasticity and numerical aspects. Int. J. Solids Struct. 35, 3455 (1998).CrossRefGoogle Scholar
Lion, A. and Kardelky, C.: The Payne effect in finite viscoelasticity: Constitutive modelling based on fractional derivatives and intrinsic time scales. Int. J. Plasticity 20, 1313 (2004).CrossRefGoogle Scholar
Shim, V.P.W., Yang, L.M., Lim, C.T., and Law, P.H.: A visco-hyperelastic constitutive model to characterize both tensile and compressive behavior of rubber. J. Appl. Polym. Sci. 92, 523 (2004).CrossRefGoogle Scholar
Arruda, E.M. and Boyce, M.C.: A three-dimensional model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41, 389 (1993).CrossRefGoogle Scholar
Cao, Y.P. and Lu, J.: Depth-sensing instrumented indentation with dual indenters: Stability analysis and corresponding regularization schemes. Acta Mater. 52, 1143 (2004).CrossRefGoogle Scholar
Zang, J.F., Zhao, X.H., Cao, Y.P., and Hutchinson, J.W.: Localized ridge wrinkling of stiff films on compliant substrates. J. Mech. Phys. Solids 60, 1265 (2012).CrossRefGoogle Scholar
Findley, W.N., Lai, J.S., and Onaran, K.: Creep and Relaxation of Nonlinear Viscoelastic Materials (North-Holland Publishing Company, New York, 1976).Google Scholar
Duenwald, S.E., Vanderby, R., and Lakes, R.S.: Stress relaxation and recovery in tendon and ligament: Experiment and modeling. Biorheology 47, 1 (2010).CrossRefGoogle ScholarPubMed
Ciambella, J., Paolone, A., and Vidoli, S.: A comparison of nonlinear integral-based viscoelastic model through compression tests on filled rubber. Mech. Mater. 42, 932 (2010).CrossRefGoogle Scholar