NEW FUNCTIONAL RELATIONS FOR LINEAR RHEOLOGICAL MODELS OF MAXWELL AND KELVIN-VOIGT

The article proposes new functional relationships for deformations and stresses within the framework of the linear rheological Maxwell and Kelvin-Vogt models. The relations obtained are valid for the entire time interval, which allows one to consider numerous special cases of creep and relaxation tension, in particular the following practical regimes: constant tension, constant deformation, constant strain rate. In calculations, the Heaviside step function, the Dirac delta function, and the solution of the Cauchy problem proposed by E.M. Kartashov were used. Using of generalized functions allows us to consider more complex three-element models, for example, with two springs and one damper and vice versa. At the same time, the principal aspect of the approach does not change, the mathematical calculations are practically not complicated. The proposed relations can be used in rheology as a generalizing form of the record containing known special cases. This work presents a methodological interest for the departments of polymeric profile.

relaxation, creep, tension, deformation, polymers, Maxwell model, Kelvin-Voigt model, Cauchy problem, elasticity, viscosity, differential equations

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