We construct and study analytically the exact solution of the boundary value problem for a hollow cylinder (a tube) made of physically non-linear viscoelastic material obeying the Rabotnov constitutive equation with arbitrary material functions. We suppose that a material is homogeneous, isotropic and incompressible and that a tube is loaded with constant internal and external pressures and a plain strain state is realized, i.e. zero axial displacements are given on the edge cross sections of the tube. We obtain explicit closed form expressions for displacement, strain and stress fields via the single unknown function of time and integral operators involving this function, two material functions of the constitutive relation, preset pressure values and radii of the tube and derive functional equation to determine this unknown resolving function. Assuming material functions are arbitrary, we prove that strains (creep curves) increase with time but the axial force at cross section doesn’t depend on time and material functions although stresses and strains do. The axial force proved to be equal to the one calculated for linear elastic tube although axial stress depends on radial coordinate in the case of non-linear viscoelastic material. We show that for special choices of material functions the strain and stress fields coincide with classical solutions in the frames of linear viscoelasticity, elasticity or elastoplasticity with hardening or without it. Fixing the material function governing non-linearity to be power function with any positive exponent and assuming creep function is arbitrary, we construct exact solution of the resolving functional equation, calculate all the integrals involved in the general representation for strain and stress fields and reduce it to simple algebraic formulas convenient for analysis. The stresses in this case don’t depend on time and creep function and coincide with classical solution for elastoplastic material with power hardening. We obtain criteria for increase, decrease or constancy of stresses with respect to radial coordinate in form of inequalities for the exponent value.

axial force, CREEP, creep curves, elastoplasticity, incompressible material, non-linear viscoelasticity, stress field properties, the Rabotnov constitutive equation, нелинейная вязкоупроугость, несжимаемый материал, определяющее соотношение Работнова, ползучесть, продольная сила, свойства поля напряжений, семейство кривых ползучести, упругопластичность

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