A nanoindentation modeling of viscoelastic creep and relaxation behaviors of ligaments mechanical characteristics of biological tissues

Nanoindentation has recently appeared as a powerful tool for measuring nano and micro-scale mechanical properties of biological tissues. In biological engineering, the majority of soft tissues exhibit as viscoelastic materials with a time-dependent response. However, the viscoelastic constitutive effects of biological tissues during nanoindentation are seldom considered rigorously. The presented paper develops a mathematical contact approach for independently measuring of creep compliance and relaxation modulus of the periodontal ligaments from nanoindentation tests using the constant - rate displacement and loading histories, respectively. A proper curve - fitting method has been developed to measure these characteristics via the nanoindentation of rigid Berkovich tips. Generalized Voigt-Kelvin and Wiechert models have been used to model constitutive equations of ligaments, in which relaxation and creep functions are represented by sum of a series of decaying exponential functions of time. Relaxation and Creep moduli should be measured from two nanoindentation tests separately to improve accuracy. Stress relaxation proceeds more rapidly than creep in periodontal ligaments.