The General Equations of Spatial and Planar Problems of Solid Mechanics in the Case of the Model of Quasielastic Behavior of Isotropic Viscoelastic Material

Abstract

The existing methods of experimental identification of the rheological properties for the normal component of the strain and stress allow to solve the problem only for the most simple and on the opinion of the authors the most adequate special case viscoelasticity equations – a quasi-elasticity: when two kernels in Starovoitov’s equations of viscoelasticity are equals. It corresponds to the application of the Arutyunyan’s hypothesis about constant Poisson's ratio (independent from the time) in the hereditary part of Rzhanitsin’s equations. The equations of a quasi-elasticity are investigated and applied in general equations of solid mechanics in the paper. The solutions of mixed problems for quasi-elastic bodies provide the appearance in a solid two mutually conditioned processes (creep and relaxation). Another way for obtaining in the solution of any boundary value problem of both processes for quasi-elastic model is the rejection of the hypothesis of the immutability of the solid border (small displacement in comparison with body size) when a load is applied.