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.