Особенности поведения поперечной деформации и коэффициента Пуассона изотропных реономных материалов при ползучести, описываемые линейной теорией вязкоупругостистатья
Статья опубликована в журнале из списка RSCI Web of Science
Статья опубликована в журнале из перечня ВАК
Дата последнего поиска статьи во внешних источниках: 21 мая 2019 г.
Аннотация:А. V. Khokhlov. Behavior types, characteristic features and peculiarities of lateral strain and Poisson’s ratio of isotropic linear viscoelastic materials under creep conditions
The Boltzmann-Volterra linear constitutive equation for isotropic non-aging visco-elastic materials (with an arbitrary shear and volumetric creep compliances) is studied analytically in order to find out its capabilities to provide an adequate qualitative description of rheological phenomena related to creep under uni-axial loading and types of evolution of the Poisson ratio (lateral contraction ratio in creep) and to outline the control scopes of the material functions. The constitutive equation doesn’t involve the third invariants of stress and strain tensors (or the Lode-Nadai coefficients) and implies that their hydrostatic and deviatoric parts don’t depend on each other. It is governed by two material functions of a positive real argument (that is shear creep compliance and volumetric creep compliance); they are implied to be positive, differentiable, increasing and convex up functions. General properties of the creep curves for volumetric, longitudinal and lateral strain generated by the model under uni-axial loading are investigated. Conditions for creep curves monotonicity and for existence of extrema and sign changes of strains, the Poisson ratio evolution in time are studied and the influence of qualitative restrictions imposed on its material functions is analyzed. The expressions for Poisson’s ratio via the strain triaxiality ratio and in terms of creep compliances are derived. Assuming creep compliances are arbitrary (permissible), general accurate two-sided bounds for the Poisson ratio range are obtained, it is proved that the lateral contraction ratio in creep is greater than -1 and less than 0.5 at any time moment. Additional restrictions on material functions and stress levels are derived to provide negative values of Poisson’s ratio. Criteria for the Poisson’s ratio increase or decrease and for its non-dependence on time are found. In particular, it is proved that the linear relation is able to simulate non-monotone behavior and sign changes of lateral strain and Poisson’s ratio under constant axial load.
***** Keywords: viscoelasticity, compressibility, volumetric creep, longitudinal creep, lateral contraction ratio in creep, non-monotone lateral strain, negative Poisson’s ratio