B) in) model Maxwell; d) model visco-plastic body Shvedova - Bingham; d) the Bingham model; (e) model Shvedova

Model body Kelvin - Voigt reflects the phenomenon of elastic aftereffect, which represents a change of elastic deformation in time when it or constantly grows to a certain point after the application loads, or decremented after its removal.

The mechanical model of a viscous-elastic relaxing body Maxwell (Fig. 2, C) is a serial connection gook with modulus G and Newton viscosity ETA. On both elements have the same voltage is t.

Body Maxwell behaves like elastic or viscous depending on the relationship of the relaxation time material to the duration of the experiment. So, if under instant efforts spring is stretched, and then immediately load is removed, the piston does not have time to move and the system behaves as an elastic body. However, on the other hand, if you keep the spring, regular, she gradually relaxed, moving the piston up, and the system behaves as a Newtonian fluid. Rheological equation of the body Maxwell is:

Two-mechanical model of a viscous-plastic body Shvedova - Bingham (Fig. 2, d) consists of elements connected in parallel Newton viscosity ETA and Saint-Venant with a yield strength τТ. If t ≤ τТ, the system behaves as a rigid unde body. Rheological equation of that body when t > τТ is:

In nature there are materials, which in the first approximation can be considered as the body of the Saint-Venant. They start to flow when the shear stress reaches this limit. If not viscous resistance, speed of flow of the material will become arbitrarily large. This shows that such materials can only as a first approximation, considered as the body of Saint-Venant. In the second approximation, they should have a viscosity. All this leads to polulitrovye ideal body Bingham, combining elasticity, viscosity and plasticity.

Mechanical Bingham model (Fig. 2, d) consists of elements gook with modulus G, Newton viscosity ETA and Saint-Venant with a yield strength τТ. Elements of Newton and Saint-Venant mutually connected in parallel and in series with the element gook.

With voltage t < τТ the Bingham model has only elastic deformation. Rheological equation of this model when t > τТ is:

Mechanical model Shvedova consists of elements gook with modulus GН, Saint-Venant with a yield strength τТ and Maxwell with modulus of DM and viscosity n (Fig. 2, e). In the 80-ies of the 19th century F.. Swedes have studied relaxation processes in colloid solutions and for the first time found their elasticity, and viscosity. The model of this body differs from model Bingham fact that in parallel models of Saint-Venant attached model Maxwell, and the model Bingham - element Newton.

When t ≤ τТ deformation model Shvedova's only because of the element gook. When t > τТ deformed all elements in the model. Rheological equation model Shvedova in the differential form is:

The desire of researchers to more accurately show the behavior of food materials under load led to the creation of complex models that have significantly increased the complexity of the calculations. Models that have a small number of elements, seldom give satisfactory convergence of experimental data calculated from the equations. At the same time increasing the number of items in excess of four does not lead to significant qualitative change in the model because the model containing four elements, inclusive, to settle all variety of mechanical behavior of this material.

Modeling of the deformation behavior food materials can be carried out not only on the basis of mechanical models, but also electric. The voltage is correlated with voltage of the electric circuit, the strain-rate - with electric current, module of elasticity with feedback capacitance value, and the viscosity is the resistance. Series connection of elements of a mechanical model is equivalent to the parallel connection of elements of electric circuits, and in parallel a mechanical model - serial connection to the electric. Electrical simulation enables to use computer modeling when studying the elastic-visco-plastic properties of food materials, and also for the calculation of processes of processing.

Checklist

1. Relate the mechanical model of a viscous-elastic bodies with relaxation deformations (body Maxwell).

2. Relate the mechanical model of a viscous-elastic bodies with relaxations stress (body of Voigt-Kelvin).

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

Date: 2015-12-24; view: 689