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The paper studies the viscoelastic body described by the generalized Maxwell model. This model consists of several parallel-connected simple models of Maxwell. Assuming the interaction of atoms of the body with embedded nanoparticles leads to a change in model parameters. It is shown that with the addition of nanoparticles with a specific property, it can change the value of the deformation points of a viscoelastic body. This change depends on the number of elements.

This paper highly evaluated the creation of efficient technologies on the basis of nanotechnologies in the areas of oil industry, automobile industry, shipbuilding, construction, aviation and examples. For example, the application of nanotechnologies in oil industry is connected with the increasing of oil productive rate of high-viscous oil deposits. There are many efforts carried out in this direction [1-5].

It is known that one of the most important directions of nanotechnologies in the paint-and-lacquer coating is developing new special materials on the basis of sol-gel technology [

Effectiveness of suggested technology is connected with changing of physical chemical properties of paint-andlacquer systems. Taking into consideration that such systems are described by viscoelastic and visco-plastic models, there is a task of describing the model medium with interaction on atomic and molecular level. To describe such a medium, no nanoparticle is taken as a model that is detailed studied [

The presented work is considered the generalized model of viscoelastic liquid [4,7] based on simple Maxwell model.

Let us consider the generalized model of viscoelastic liquid that is known as generalized Maxwell model (

As have been above mentioned the generalized Maxwell model consists of parallel-connected -numbered models of Maxwell. Simple -model of Maxwell is described by successively jointed elastic -element with the ratio is true and viscous -element with ratio.

Here is taken the following designations: indexes “1”

and “2” relate to elastic and viscous element of i-model correspondingly, and tension and deformation of each above mentioned elements, -elastic modulus, is viscosity factor of corresponding simple -model of Maxwell. The dot indicates the time derivative.

At successive joining in simple -model of Maxwell we accept and designate, i.e. . Then for generalized model on the assumption of elements joining follows, , where -tension, applied to whole body, -number of simple models (

where -lump sum deformation of -model of Maxwell (

Then accept for definition at time:

This equation is solved at the following initial condition:

i.e. at initial moment the viscous element does not work.

The decision of Equation (2), satisfying to initial condition (3) is:

Based on obtained equation and dependence of from:

,(5)

where: generalized elastic modulus,: generalized fluidity nuclei.

This expression makes possible to establish the dependence between and. Usually such correlations describe the behavior of viscoelastic “liquid” medium [

Assume that elastic element of Maxwell model can be presented like one-dimensional “chain” of atoms, interacting to each other (

Assume that each embedded nanoparticle take intermediate position between atoms (possibility of embedding several nanoparticles). The structure of elastic element does not change it is still rectilinear (not branched) “chain”. It follows from assumption of Maxwell model preservation at nanoparticles addition. Assume that particles interact only with neighboring particles. Then without consideration of nanoparticles follow

; (6)

where: atom interactions force,: distance between atoms after deformation,: before deformation,: elasticity factor,: characteristic size of cross-sectional area of atom exposed to force, stroke—

shows coordinate derivative, and: tension and deformation of each of above mentioned elements.

Then have the following correlation:

.

Using formula (8) let us generalize for case with nanoparticles consideration.

Assume that each of embedded nanoparticle takes intermediate position between atoms (

Then with consideration of nanoparticles we have

Hence we have correlation of “chain” elasticity with consideration of nanoparticles.

where “i” and “N”: mean, that given value relates to -model of Maxwell and to nanoparticle. Here assumed that nanoparticle is between atoms in the middle of “chain”. Note that this position is efficient in terms of energy.

Let us present the viscous element of -model of Maxwell as cylinder filled by viscous liquid compressed by piston. Assume nanoparticles are distributed in viscous liquid that leads to prevention of Maxwell model element. In this case the influence of nanoparticles is similar to the influence of solid particles in viscous liquid [

.

So, based on correlation (1), defining the equation of Maxwell model with nanoparticles is:

where introduced the following designations:

.

The decision of Equation (8) is:

or

.

Due to the essence of initial condition does not change the Equation (9), satisfying to initial condition (3), is:

Taking into consideration that lump sum tension is equal to sum of tensions, based on (10), we receive:

where E_{0N}: generalized elasticity modulus,: generalized fluidity nuclei with nanoparticles.

So on example of generalized Maxwell model it is shown that presence of nanoparticles in constituent elements leads to change of parameters of model. The character of these changes and its values are described in the frame of assumptions about interactions of nanoparticles with atoms of elastic element and viscous liquid.

Accepting, , , , then from (11) we receive:

.(12)

Differentiate the Equation (12), we receive the following differential equation:

The decision of differential Equation (13) with condition, for any is:

Define the influence of number of elements n on deformation value. For, based on (14) follow:

.

then

.

for different values.

From diagram follows at, the deformation steadily increases, and at, deformation steadily decreases. The increasing of elements number leads to decreasing of deformation value.

So if elastic bonds of nanoparticles satisfy the following inequality, i.e., then addition of nanoparticles in visco-elastic liquids leads to increasing of deformation. Otherwise, i.e. if, then addition of nanoparticles in visco-elastic liquids leads to decreasing of deformation. Thereby the addition of nanoparticles with specific properties to Maxwell model of viscoelastic liquid can change the deformation value, i.e. can change the properties of model.

This work carries out the model generalization of the viscoelasticity theory with nanoparticle consideration. The type of model preserved for Maxwell model generalization equates the basic correlations. This model shows the influence of number of elements and nanoparticles on mechanic properties.