Combination of Rheological Models

A characteristic regime that manifests the speciflcs of the mechanical behavior of this model is the regime in which the strain first instantaneously reaches the value of Yo and then stays at that level, that is, Y = Yo= const. At the initial moment, t = 0, the strain in the viscous element is zero, so the entire deformation (and the entire work) is concentrated within the elastic element. Consequently, the initial stress is Tq = Gyo- This stress further causes the deformation of the viscous element. Since the total deformation is constant, the deformation of the elastic element decreases, resulting in a decrease in the stress. Under conditions of constant net strain, y = const. Equation 3.2 can be written as 

Integrating this expression, using the initial condition x(f = 0) = Tq= G/q, yields 

The relaxation period defines the behavior of the system, in accordance with the Maxwell model with respect to the timescale of the applied stress. If the time t during which stress is applied is greater than the relaxation period, that is, t t the system has properties similar to those of a viscous liquid, while at t t the system behaves like an elastic solid. The flow of glaciers and other processes of strain development in mountains and cliffs are representative examples of such behavior. In rheology, the ratio of a material s characteristic relaxation time to the characteristic flow time is referred to as the Deborah number. This parameter plays an important role in describing the response of various materials to different stresses. 

The integration of the aforementioned expression yields deformation as a function of time, namely, 

Physical-Chemical Mechanics of Disperse Systems and Materials 

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