Oyen Lab: Multiscale Mechanics of Biological Materials
Contact Mechanics and Nanoindentation
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Local contact probe "nanoindentation" experiments are ideally suited to the mechanical characterization of heterogeneous materials including biological tissues. While much recent effort has emphasized the correlation of local mechanical response (from indentation) with local structure and tissue composition, the data are typically analyzed assuming that the tissue is a homogeneous half-space and behaves in a time-independent manner. While such approximations came into routine use for nanoindentation of bulk engineering materials with dominant elastic or elastic-plastic responses, these assumptions are problematic for composite tissues with viscoelastic and/or poroelastic responses. |
| Biological materials are multi-phase composites with the potential for wide variations in the properties of the component phases. Since the indentation test is a local test, there are fundamental differences in the physics of the indentation process depending on the relative length-scale of the indentation event (as quantified by the indentation depth or contact radius) and the length-scale(s) of the material (as quantified by feature size or sizes). When the indentation length-scale is large compared with the material length scale, as illustrated here, the indentation test will probe the effective modulus of the material, as can be estimated from standard composites theory (e.g. Hashin-Shtrikman bounds). |
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However, for comparable indentation and material length-scales, as illustrated here, the placement of the indenter relative to the material microstructure (here, "P" for particle and "M" for matrix) is critical. This is often the case for small-scale contact testing using commercial nanoindentation equipment! |
"Viscoelastic" is frequently used as a generic term for time-dependent mechanical responses, although linearly viscoelastic responses are particularly associated with polymeric materials and represented mathematically by exponential decay functions. Viscoelastic stress analysis is typically considered using the elastic-viscoelastic correspondence principle, in which time-dependent material parameters are substituted for the elastic properties. There are two possibilities for the time-dependent functions: differential form and integral form, as illustrated here for an isotropic viscoelastic solid.
For experimental work, integral functions are most useful since a complicated loading history can be simply solved. In the context of indentation, the boundary conditions for flat-punch indenters are allowed within the elastic-viscoelastic correspondence problem directly, while the boundary conditions for spherical and conical/pyramidal indentation are not directly allowed. However, this subject was examined in the 1960s and following pioneering papers by Lee and Radok [J. Applied Mechanics 27 (1960) 438-44] and Ting [J. Applied Mechanics 88 (1960) 845-54] the routine use of viscoelastic correspondence for indentation analysis has been allowed within specific guidelines. Linearly viscoelastic responses have been seen under spherical nanoindentation while conical/pyramidal indentation appears to result in nonlinearly viscoelastic responses. The basic construction of single integral equations for spherical indentation is shown below; these expressions are simply integrated for standard experimental protocols such as ramp-hold creep tests.
- Oyen ML and Cook RF, Load-displacement behavior during sharp indentation of viscous-elastic-plastic materials. Journal of Materials Research, 18 (2003) 139-50.
- Oyen ML, Cook RF, Moody NR, Emerson JA, Indentation responses of time-dependent films on stiff substrates. Journal of Materials Research, 19 (2004) 2487-97. Erratum in Journal of Materials Research 19 (2004) 3120-1.
- Oyen ML, Spherical indentation creep following ramp loading. Journal of Materials Research, 20 (2005) 2094-2100.
- Oyen ML and Ko C-C, Examination of local variations in viscous, elastic and plastic indentation responses in healing bone. Accepted for publication, Journal of Materials Science: Materials in Medicine, 2005.
- Oyen ML, Nanoindentation hardness measurements of mineralized tissues. Journal of Biomechanics, 39 (2006) 2699-702.
- Bembey AK, Bushby AJ, Boyde A, Ferguson VL and Oyen ML, Hydration effects on bone micro-mechanical properties. Journal of Materials Research, 21 (2006) 1962-8.
- Bembey AK, Oyen ML, Bushby AJ, Boyde A, Viscoelastic properties of bone as a function of hydration state determined by nanoindentation. Philosophical Magazine, 86 (2006) 5691-703.
- Mattice JM, Lau AG, Oyen ML, Kent RW, Spherical indentation load-relaxation of soft biological tissues. Journal of Materials Research, 21 (2006) 2003-10.
- Oyen ML, Analytical techniques for indentation of viscoelastic materials. Philosophical Magazine, 86 (2006) 5625-41.
- (Invited review) Oyen ML and Bushby AJ, Viscoelastic effects in small-scale indentation of biological materials. International Journal of Surface Science and Engineering, In press (2007).
- Cook RF and Oyen ML, Nanoindentation behavior and mechanical properties measurement of polymeric materials. International Journal of Materials Research, In press (2007).
- Oyen ML, Sensitivity of polymer nanoindentation creep properties to experimental variables. Acta Materialia, In press (2007).