A Mathematical Approach for Describing Time-Dependent Poisson’s Ratios of Periodontal Ligaments

Periodontal ligament is a thin layer of soft tissue that connects root of a tooth tothe surrounding alveolar bone. these ligaments play an important role in initiatingtooth movement when loads are applied to teeth with orthodontic appliances. themajority of such soft tissues exhibit as viscoelastic bodies or have a time-dependentbehavior. due to the viscoelastic behavior of the periodontal ligaments, the mechanicalproperties are strongly affected by the loading history. poisson’s ratios for theviscoelastic materials are time-dependent (in time domain) or complex frequency-dependent(in frequency domain) quantities. moreover, three-dimensional stress fieldsdepend on these poisson’s ratios. the main objective of this work was to develop amathematical approach capable of determining the time-dependent poisson’s ratios ofthe periodontal ligaments based on experimental data of stress relaxation and creeptests. the resulting stress relaxation and creep curves are described by a three-parameterviscoelastic models. the time-dependent poisson’s ratios of the periodontalligaments have been obtained as increasing functions of time, because shear modulusof these ligaments relaxes much more than their bulk modulus.