Sinusoidally-driven flat-ended indentation of time-dependent materials: Asymptotic models for low and high rate loading

In recent years, a sinusoidally-driven indentation test was shown to be effective for viability characterization of articular cartilage. The mathematical analysis of dynamic indentation experiments for a time-dependent material requires a complete understanding of the material damping characteristics. It is assumed that the mechanical response of the articular cartilage layer can be described in the framework of viscoelastic model with time-independent Poisson’s ratio such that the overall constitutive behavior is expressed in terms of the complex modulus. Based on the elastic-viscoelastic correspondence principle, the governing integral equation of the associated dynamic contact problem is formulated, and closed-form analytical solutions for the integral characteristics of the indentation test are obtained. An asymptotic modeling approach is then applied for analyzing and interpreting the results of the dynamic indentation test in terms of the storage modulus and the loss angle of the viscoelastic material. The behavior of the dynamic and pulsatile indentation moduli has been studied in detail.

► Cartilage is modeled as viscoelastic material with time-independent Poisson’s ratio.
► Incomplete storage modulus and incomplete loss angle are introduced.
► Asymptotic modeling is applied for analyzing dynamic indentation tests.