Basic equations of the complex rheological tel

Plan of the lecture:

1. The mechanical model of a viscous-elastic bodies with relaxation deformations

(body Maxwell).

2. The mechanical model of a viscous-elastic body with a stress relaxation (body of Voigt-Kelvin).

3. The mechanical model of a viscous-plastic body Shvedova-Bingham.

Purpose of the lecture: get acquainted with rheological models and main complex rheological equations tel.

To describe the rheological behavior of a complex body depending on the properties of its components can be combined in various combinations of the above model is the simplest perfect bodies, each of which has only one physical-mechanical properties. These elements can be combined in parallel or sequentially.

The main complex models are: elastic-plastic body; visco-elastic bodies Kelvin - Volga and Maxwell; visco-plastic body Bingham, Shvedova and Shvedova - Bingham).

The model of elastic-plastic body (Fig. 2.,a) obtained by the sequential connection of the elastic element gook with modulus G and plastic element of Saint-Venant with a yield strength τт. When t < τт is elastic deformation of the material, and when t = τт - plastic flow.

Visco-elastic body Kelvin - Voigt presents a mechanical model, obtained with a parallel connection of the elastic element gook with modulus G and viscous element Newton viscosity n (Fig. 2.,b). Under the action of traction spring longer and the piston will move in a fluid. This movement of the piston is connected with viscous fluid resistance, thus giving full the spring comes not at once. When the load is removed, the spring is compressed to the original length, but it takes time due to the viscous fluids resistance.

For the issuing of a mathematical model of the body Kelvin - Voigt use the fact that in parallel elements deformation of complex body γКФ equal deformation of each element, and voltage total item τКФ is the sum of the voltages in the separate elements τГ and τН. On the basis of this system of equations:

We will use the previously recorded mathematical models for items gook (G) and Newton (N):

Having considered together, get finally mathematical rheological model body Kelvin - Voigt:

,

where: G - module of elasticity in shear, PA;

γ angular deformation;

ETA - Newtonian viscosity, PA * S.

Date: 2015-12-24; view: 904