Modelling of the Frequency Response to Dynamic Nanoindentation of Soft Hydrated Anisotropic Materials: Application to Articular Cartilage

Dynamic nanoindentation is a novel nanomechanical testing that is being increasingly used to characterize the frequency response of viscoelastic materials and of soft hydrated biological tissues at the micrometric and nanometric length scales. This technique is able to provide more information than those obtained by simple indentation; however, its interpretation is still an open issue for complex materials such as the case of anisotropic biological tissues that generally have a high water content. This work presents a numerical model to characterize the frequency response of poro-elastic tissues subjected to harmonic indentation loading with particular regard to the effect of geometrical characteristic lengths (i.e. penetration depth and indenter radius) and to the effect of tissue anisotropy. The analysis is performed by a frequency domain finite element axi-symmetric model of harmonic spherical indentation. Under the basic hypotheses of poro-elastic response of the material and of strain-independent isotropic permeability, this work shows that anisotropic properties of the tissue can be obtained from one single dynamic indentation experiment. In particular, we show that anisotropy of the tissue is a necessary property to correctly predict the experimental frequency response in terms of drained to undrained ratio and of tangent of phase lag.