MATHEMATICAL MODELING OF TIME-DEPENDENT POISSON’S RATIO IN LINEAR VISCOELASTIC SOLID-LIKE FOODS

The viscoelastic bodies have a time-dependent response since simultaneously store and dissipate mechanical energy when subjected to the applied forces. Therefore, Poisson’s ratio in viscoelastic solids generally is a time dependent (in time domain) or a complex frequency dependent (in frequency domain) quantity. In particular, three-dimensional stress fieldssuch as those associated with stress concentration depend on the Poisson’s ratio. In a viscoelastic material, a time-dependent Poisson’s ratio will be associated with time-dependent stress and deformation, so stress concentration factors and interfacestresses can depend on time and frequency. In biological engineering, the majority of solid-like foods exhibit as viscoelastic solids. For viscoelastic solids, the shear modulus relaxes much more than the bulk modulus, therefore, the Poisson's ratio isan increasing function of time. The main aim of this work is to develop a mathematical model capable of determining timedependent Poisson’s ratio based on the relaxation tests in viscoelastic food materials. A generalized Maxwell model is usedto model the viscoelastic behavior of solid- like foods. At the end of this work, as a case study, the Poisson’s ratio of food texture specimens of apple flesh is given which give rise to modelled time-dependent Poisson’s ratios

Keywords:

mathematical modeling , viscoelasticity , time-dependent Poisson’s ratio , solid-like foods