Nonmonotonicity and Nonnegativity Criteria for the Poisson Ratio of Isotropic Viscoelastic Materials Described by the Rabotnov Nonlinear Relation

摘要

General properties of the theoretic creep curves for volumetric, longitudinal, and lateral strains generated by the Rabotnov physically nonlinear constitutive equation for non-aging viscoelastic materials under uniaxial loading are studied analytically assuming four material functions of the relation are arbitrary. The expressions for Poisson's ratio via the strain state parameter and via four material functions of the model are derived. The Poisson ratio dependence on time, stress level and material functions are examined. General two-sided bound for its range is obtained. It is proved that the Rabotnov relation is able to simulate non-monotone behavior and sign changes of lateral strain and Poisson's ratio. The restrictions on material functions providing negative Poisson's ratio values are found and the criterion for its nondependence on time is formulated.