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After completion of this process length of a sample becomes equal lf so the difference of lengths (l — lf) is answered by vysokoelastichesky part of lengthening, and (lf – the l-lengthening which arose owing to a viscous current.

Let rheological properties of the environment be described by ratios of the linear theory of viscoelasticity and characterized by creep function ψ (t) or function of a relaxation φ (t). Then at deformation in the mode έ =έ0=const change of tension in time is described by a formula:

The definitions given above a component of full deformation and fullest deformation answer the direction of stretching and represent components of a tensor of deformations with an index 1 Other components find from a condition of constancy of volume.

This function reflects influence of the orientation of polymer leading to strengthening of intermolecular interaction on viscosity. Some examples of this function following from various rheological models were given above.

where D — a certain differential operator; σ’ij — components of a deviator of a tensor of tension; γ’ij — components of a tensor of speeds of deformations (the tensor { γ’ } represents a deviator because its first invariant is equal to zero).

Other modes of deformation of viscoelastic liquid which rheological properties are described by ratios of the linear theory of viscoelasticity, can be also analysed on the basis of the general ratios of the theory. So, at deformation in the V=Vo=const mode change of tension of speed of a natekaniye of irreversible deformation are described by formulas:

This conclusion is physically caused by that the effect of anomaly of viscosity in yaumannovsky model arises because of rotation of the coordinate system connected with this point at deformation of the environment. At uniform monoaxial stretching rotation of elements of a body is absent and therefore the viscoelastic environment behaves as the Newtonian liquid.

Thus, for model (1, generalized on big deformations on Oldroyda, viscosity at stretching λ, it is not equal viscosity at compression λ. This result shows that in principle for viscoelastic liquid with any rheological properties, despite kinematic reversibility of stretching and compression, the inequality can take place: λ =λ.

Let's consider a case of monoaxial compression, on kinematics the return to monoaxial stretching. For usual viscous liquid when replacing stretching with compression all rheological characteristics of the environment (to within a sign remain invariable. But for the viscoelastic environment compression is not process, the return to stretching. It is visible from the ratios given below. Compression is answered by a tensor of speeds of deformation

It is essential that at calculation of vysokoelastichesky deformation size 1 belongs not to the initial length of a sample 1o, and to size 1f, i.e. to that length which the sample gets as a result of the viscous current happening to development of vysokoelastichesky deformation. The specified choice of a way of definition of vysokoelastichesky deformation provides performance of a natural condition of equality of full relative deformation to the sum of irreversible and vysokoelastichesky components of deformation

Let stretching occur in the conditions of the constant speed of the movement of one end of a sample: V = V0 = const, and its second end remains motionless. This mode of deformation is most easily carried out in ordinary test cars. Then the longitudinal gradient of speed is variable in time