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RELATIONS IN VISCOELASTICITY

RELATIONS IN VISCOELASTICITY
Elena Artamonova, professor, doctor of technical science, full professor

Saratov State Technical University, Russia

Svetlana Shatokhina, applicant

Саратовский государственный технический университет

Championship participant: the National Research Analytics Championship - "Russia";

the Open European-Asian Research Analytics Championship;

Some aspects of the development and the theory of viscoelasticity describes the results to incorporate the impact to integrate environmental impact. Discusses the integral form of stress strain constitutive relations. The text describes the mathematical framework to predict material behavior. It discusses the problems to which integral transform methods do not apply.

Keywords: thermodynamic, relationship, mathematical modelof deformation, strain

 

All materials exhibit some viscoelastic  response. In common metals such as steel or aluminum, as well as in quartz, at room temperature and at small strain, the behavior does not deviate much from linear elasticity. Synthetic polymers, wood, and human tissue as well as metals at high temperature display significant viscoelastic effects. In some applications, even a small viscoelastic response can be significant. To be complete, an analysis or design involving such materials must incorporate their viscoelastic behavior.  Knowledge of the viscoelastic response of a material is based on measurement.  The mathematical formulation of viscoelasticity theory is presented in the following chapters with the aim of enabling prediction of the material response to arbitrary load histories. Viscoelasticity is of interest in materials science, metallurgy, and solid state physics since it is causally linked to a variety of microphysical processes and can be used as an experimental probe of those processes. Viscoelasticity is of interest in materials science, metallurgy, and solid state physics since it is causally linked to a variety of microphysical processes and can be used as an experimental probe of those processes. Interdisciplinary aspects.

Engineering mechanics: Materials used in aircraft and spacecraft have viscoelastic response.

Wood is viscoelastic. The beams of old wooden houses can often be seen to sag, but this creeping under the weight of the roof and gravity can take many decades or centuries to be noticeable. Concrete and soils are other materials which creep, as is ice, which has consequences for glacial movements.In such applications as shoe insoles to reduce impact force in running, or wrestling mats to reduce impact force in falls.

Biomedical engineering: Tissues in the body are all viscoelastic.Bone exhibits viscoelastic behavior. The disks in the human spine are viscoelastic. Under normal body weight, the disks creep, that is they get shorter with time. Lying down allows the spinal disks to recover and this means that most people are taller in the morning than in the evening. Skin tissue is viscoelastic. Materials science: Viscoelasticity results from physical processes such as dislocation motion, grain boundary slip, molecular motions, domain motion, or diffusion, Metal matrix composites of silicon carbide. Viscoelasticity is of use as a probe into such processes.  

Mechanical engineering: Viscoelastic materials are used for control of vibration in machinery.Viscoelastic damping of materials can reduce noise. Creep and relaxation of materials can affect their performance in machinery. For example, viscoelastic shoe insoles are useful in reducing mechanical shocks transmitted to the bones and joints.

Civil engineering: Viscoelasticity of soil and other earth materials is relevant to settlement of buildings.

Electrical engineering:

Creep is also one of the principal causes of failure in the electric lightbulb. Vibration control in computer disk drives improves their performance.

Fig. 1.  In the Fort Point Channel Tunnel in Boston, 12 tons of concrete fell on a car due to creep in the epoxy that was used to support anchoring bolts for the ceiling panels [1].

Viscoelastic can imagine in such a way as if the materialIt consists of two elements: the elastic (spring) and viscous (resistance movement of the piston in the liquid). Combining various combinations of elasticity and viscous drag, you can build a lot of so-called mechanical models describing quite well rheological behavior of materials. This line of research has been proposed mid-19th century - the work of Maxwell, Voigt, Calvin and many others scientists. The elements may be connected in series or in parallel but. Later it was shown that this type of model bad behavior describe the entire range of materials and may be suitable only for a description of creep or relaxation, but more general do not allow an impression. There may be some other non-mentioned above, the relation between stress, strain and time.It is therefore necessary to build models such that could be used in operating conditions the same set of parameters creep, relaxation, loading in various operating conditions, taking into account the aggressive effects of the environment. The only known approach in constructing equations which satisfy all requirements, is to use the principle of heredity.The corresponding functional form is

J(t) = j(t) H (t),

with j(t) as a function defined over the entire time scale. This functional form for J(t) follows from the physical concept of causality, that the effect does not precede the cause. The phenomenological theory of viscoelasticity which permits interrelation of the results of different types of experiments is presented first, with many useful approximation procedures for calculations given. Physical relationships between stress and strain(constitutive equations) follow the principle of macroscopic definability [1, p. 295] and specified as the operator communication:

or

.

To close the equationsof continuum mechanics must use the laws of thermodynamics, and other laws of physics for non-mechanical thermodynamic parameters.

 - notation indicating the argumentsin parentheses is in accordancewith the postulate ofthe theory of simplematerials, also satisfies therequirement of "decaying memory", iematerials, viscoelastic.

Operators 

 -  is the potentialthat isthere arescalar operatorsthat:

, (1)

 

.(2)

Physical relations (1, 2) – nonlinear, for description the strain state and fracture in the framework of a generalized model of inelasticity is necessary to consider the history of deformation of the sample depends on the loading path and on time.

Figure 2

Creep curves may exhibit three regions (fig.2) [4], primary creep in which the curve is concave down (when plotted on a linear, not logarithmic time scale), secondary creep in which deformation is proportional to time, and tertiary creep in which deformation accelerates until creep rupture occurs. Tertiary creep is always a manifestation of nonlinear viscoelasticity, and secondary creep is usually nonlinear as well.Analysis of experimental data suggests characteristics of the temperature dependence of relaxation processes and fracture for viscoelastic polymers with the same value of energy  activation for each material. Combining different approaches to describing these processes, i.e. formulation of a general mathematical theory of deformation and fracture of polymers depends on the study of the relationship of deformation, destruction and action of strain, temperature, aggressive factors in the whole time interval of operation of the element. Viscoelastic behavior reflects the combined viscous and elastic responses, under mechanical stress, of materials which are intermediate between liquids and solids in character. Viscoelastic Properties of Polymers examines, in detail, the effects of the many variables on which the basic viscoelastic properties depend. These include temperature, pressure, and time; polymer chemical composition, molecular weight and weight distribution, branching and crystallinity; dilution with solvents or plasticizers; and mixture with other materials to form composite systems.

According to (1, 2)can be written:

U -voltage potential(free energy).

Deformation potential Фis determinedby means ofthe Legendre transformation.

Way to represent U according to the hypothesisof memory: 

Usingthe combined ratio of the basic laws of thermodynamics represent:

Consider different views U. From theStone-Weierstrass theorem continuousintegral can be uniformly approximated by polynomials

, (3)

where the functional U(n), U(m) can be represented asStieltjes integrals:

, (4)

- integrand.  

 

Substituting (4)  (3) anddifferentiating with respect toe, we can obtain the relation between theoryof Volterra-Frechet. The number of state parameters  can be infinite, but the state of a thermodynamic system is defined by a finite number of parameters.

 

References:

  • 1. William N. FindleyFrancis A. Davis. Creep and Relaxation of Nonlinear Viscoelastic Materials.-New York: Dover Publication, 2013.-384 p.
  • 2. Suvorova J.V., Ohlson N.G., Alexeeva S.I. An approach to the description of time-dependent materials // Materials and Design, Vol.24. Issue 4, June 2003. - P. 293-297.
  • 3. Biing-Lin Lee, Lawrence E.N. Temperature Dependence of the Dynamic Mechanical Properties of Filled Polymers // J. of Polymer Science, Vol.15, 1977. - P.683-692.
  • 4. YoungJ.F.,MindnessS., GrayR.J. and BenturA.The science and technology of civil engineering materials // Prentice Hall, 1998. - P.10-19.
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Comments: 2

Svetlana Pavlikova

The article the curve fit program developed, the generalized model is identified based on the master curve. This program is designed to completely fulfil the constraint conditions discussed in the initial section of the article.

Simonian Geworg

Уважаемая Елена Николаевна! Отличная статья. Известно, что все материалы- металлы в том числе сталь и алюминий, кварц дерево ткани человека,биополимери и синтетические полимери а обладают некоторой вязкоупругостью. Вязкоупругое поведение отражает комбинированные вязкие и упругие реакции, под механическим напряжением, из материалов, которые являются промежуточными между жидкостей и твердых тел в характере. Вами вязкоупругостние свойства полимеров анализируется в зависимости от температуры, давления и времени, химического состава, молекулярной масси и распределение веса, разветвленности и кристалличности, разбавление растворителями или пластификаторов. Успехов в дальнейшем.С уважением к.х.н. Г.С.Симонян.
Comments: 2

Svetlana Pavlikova

The article the curve fit program developed, the generalized model is identified based on the master curve. This program is designed to completely fulfil the constraint conditions discussed in the initial section of the article.

Simonian Geworg

Уважаемая Елена Николаевна! Отличная статья. Известно, что все материалы- металлы в том числе сталь и алюминий, кварц дерево ткани человека,биополимери и синтетические полимери а обладают некоторой вязкоупругостью. Вязкоупругое поведение отражает комбинированные вязкие и упругие реакции, под механическим напряжением, из материалов, которые являются промежуточными между жидкостей и твердых тел в характере. Вами вязкоупругостние свойства полимеров анализируется в зависимости от температуры, давления и времени, химического состава, молекулярной масси и распределение веса, разветвленности и кристалличности, разбавление растворителями или пластификаторов. Успехов в дальнейшем.С уважением к.х.н. Г.С.Симонян.
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