In the theory of elasticity and thermoelasticity, one way for reducing the problem of isotropic hereditary elasticity to solving a group of comparable quasi-static problems is proposed. The representability of the solution of the problem of linear hereditary elasticity in the form of the sum of solutions of three problems is proven: the linear theory of elasticity for imaginary bodies that are incompressible and have a zero Poisson’s ratio, and stationary uncoupled thermoelasticity for a body whose properties are not temperature dependent. The shear and bulk relaxation kernels are thought to be independent, but the viscoelastic Poisso n’s ratio is time dependent.

Two theorems are demonstrated that reduce solutions of the general quasistatic problem of linear viscoelasticity theory to a similar problem of elasticity theory. If one of the following requirements is met: 1) the material is near to becoming mechanically uncompressible; 2) the mean stress is zero; and 3) the shift and volume hereditary functions are equal, these theorems hold. The theorems allow for free direct and inverse transforms between solutions of viscoelasticity and elasticity issues, making them useful in practise. They’ve been used to solve difficulties with pure torsion in a prismatic viscoelastic solid with any simply linked cross section. Some examples of the results achieved have been considered.

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**Author (S) Details**

**Latif Kh. Talybly
**Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku Az 1141, Azerbaijan.

**Mehriban A. Mamedova
**Institute of Mathematics and Mechanics, Academy of Sciences of Azerbaijan, Baku Az 1141, Azerbaijan.

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