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 Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 2018, Volume 10, Issue 4, Pages 65–77 (Mi vyurm394)

Mechanics

Behavior types and features of lateral strain and Poisson's ratio of isotropic rheonomous materials under creep conditions described by the linear theory of viscoelasticity

A. V. Khokhlov

Lomonosov Moscow State University, Institute of mechanics, Moscow, Russian Federation

Abstract: The Boltzmann–Volterra linear constitutive equation for isotropic non-aging viscoelastic materials (with an arbitrary shear and bulk 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's 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 controlled by two material functions of a positive real argument (that is shear creep compliance and bulk creep compliance); they are implied to be positive, differentiable, increasing and convex functions. General properties of the creep curves for volumetric, longitudinal and lateral strain generated by the model under uni-axial loading are studied. Conditions for creep curves monotonicity and for existence of extrema and sign changes of strains and the Poisson's ratio evolution in time are studied. The influence of qualitative restrictions imposed on its material functions is analyzed. The expressions for Poisson's ratio through 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's 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 moment of time. 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-monotonic behavior and sign changes of lateral strain and Poisson's ratio under constant axial load.

Keywords: viscoelasticity, compressibility, axial creep, volumetric creep, non-monotonic lateral strain, negative Poisson's ratio.

 Funding Agency Grant Number Russian Foundation for Basic Research 17-08-01146_à

DOI: https://doi.org/10.14529/mmph180408

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Document Type: Article
UDC: 539.37

Citation: A. V. Khokhlov, “Behavior types and features of lateral strain and Poisson's ratio of isotropic rheonomous materials under creep conditions described by the linear theory of viscoelasticity”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 10:4 (2018), 65–77

Citation in format AMSBIB
\Bibitem{Kho18} \by A.~V.~Khokhlov \paper Behavior types and features of lateral strain and Poisson's ratio of isotropic rheonomous materials under creep conditions described by the linear theory of viscoelasticity \jour Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz. \yr 2018 \vol 10 \issue 4 \pages 65--77 \mathnet{http://mi.mathnet.ru/vyurm394} \crossref{https://doi.org/10.14529/mmph180408} \elib{http://elibrary.ru/item.asp?id=36313218}