Spatial equations of mechanics of composite solid for viscoelasticity models containing in one-dimensional case of two elastic and one viscous element

Abstract

Spatial equations of mechanics of composite solid for viscoelasticity models containing in one-dimensional case of two elastic and one viscous element

Kravchuk A.S., Kravchuk A.I., Smaluk A.F.

Incoming article date: 09.09.2018

For the first time, in the generalization to the spatial case of a one-dimensional viscoe-lasticity model for one viscous and two elastic elements, the stress deviators, deformations, and also the stress and strain rates were used. It is established that the model of a standard viscoelastic body (standard linear solid model) is more universal. The second model cannot be used to solve problems for a weighty body, or dynamic problems, since leads to the solution of an auxiliary physically unjustified boundary or initial-boundary value problem for doubled values of the accelerations. It means that the second model can be applied only to the solution of quasistatic problems for weightless bodies. It is established that the model of a standard viscoelastic body (standard linear solid model) is applicable only to the study of unsteady creep, while the second model is suitable for investigating the steady rheological behavior of a weightless material. Generalization of both models viscoelasticity for composite body was created. The effective Kravchuk-Tarasyuk values of the Poisson ratio, the Young's modulus, and the viscosity of composite material were defined.

Keywords: deviator of stresses, deviator of strains, deviator of stress rates, deviator of strain rates, viscosity, standard linear solid model