Abstract
The Rabotnov physically non-linear (quasi-linear) constitutive equation for non-aging elasto-viscoplastic materials with four material functions is studied analytically in order to outline the set of basic rheological phenomena which it can simulate, to clarify the material functions governing abilities, to indicate application field of the relation and to develop identification and verification techniques. General properties of the theoretic creep curves for volumetric, longitudinal and lateral strain generated by the model under uni-axial loading are investigated assuming material functions of the relation are arbitrary. Intervals of creep curves monotonicity and conditions for existence of extrema and sign changes are considered and the influence of minimal qualitative restrictions imposed on its material functions is analyzed. It is proved that the Rabotnov relation is able to simulate non-monotone behavior and sign changes of lateral strain and Poisson's ratio (lateral contraction ratio in creep). The expressions for Poisson's ratio via the strain state parameter (equal to volumetric strain divided by deviatoric strain) and via four material functions of the model are derived. The Poisso'n ratio dependence on time, stress level and material functions is examined. Assuming material functions are arbitrary, general two-sided bound for the Poisson's ratio range is obtained. Additional restrictions on material functions providing negative Poisson's ratio values are found and the criterion for its non-dependence on time is formulated. Taking into account volumetric creep (governed by two material functions of the model) is proved to affect strongly the qualitative behavior and characteristic features of longitudinal creep curves and the Poisso'n ratio evolution.
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