TO THE ISSUE OF THE VALID FORM OF HEREDITARY VISCOELASTICITY WITH ONE CREEP KERNEL

Abstract

It is established that if the original equations of hereditary viscoelasticity in the traditional form contained two independent viscoelastic operators corresponding to the axial and transverse creep strains, then the record in the components of the deviators of the state equations will already contain three different viscoelastic kernels defined by the compositions of the original two operators. These three operators can coincide up to a real factor only when the Harutyunyan hypothesis about the constancy of transverse deformation (i.e., the constancy of the Poisson's ratio) during creep is fulfilled. Body with a similar viscoelastic behavior are called quasi-elastic. Taking into account the results of studies, as well as the fact that until now only the creep kernel has been experimentally established under axial tension and the transverse creep kernel has never been defined, it is currently not possible to solve the problems of hereditary creep beyond the application of the Harutyunyan hypothesis. It is also obvious that the volumetric strain operator cannot be identical, since it is determined by the composition of the creep operators. The application by some authors in their studies of the hypothesis of the identity of the operator has no mathematical or physical grounds. In the case of nonlinear viscoelasticity (or viscoelastic plasticity), with sufficient accuracy for practice, one should simply linearize the equation of state using the secant module and reduce these problems to the case of linear viscoelasticity already studied in this article.