A mathematical approach for describing the time-dependent Poisson's ratio of viscoelastic ligaments mechanical characteristics of biological tissues

In biological engineering, the majority of soft tissues exhibit as viscoelastic materials with a time-dependent response. Therefore, the Poisson's ratios for viscoelastic materials are time dependent (in time domain) or complex frequency dependent (in frequency domain) quantities. In particular, three-dimensional stress fields depend on the Poisson's ratios. In a viscoelastic material, a time-dependent Poisson's ratio will be associated with time-dependent stress and deformation, thus stress concentration factors and interfacial stresses will depend on time and frequency. The main aim of this work is to develop a mathematical model capable of determining the time-dependent Poisson's ratios based on the stress relaxation and the creep tests for viscoelastic ligaments. The Poisson's ratios of periodontal ligaments have been obtained as increasing functions of time, because their shear modulus relaxes much more than their bulk modulus.