Mechanical models generalized Kelvin

When the examination was over and the report submitted, a new tumult was raised. Kelvin opposed the theory in general. He could -understand nothing, he said, which could not be translated into a mechanical model. For this reason he had likewise rejected Maxwell s electromagnetic theory of light. Only the Dane submitted an enthusiastic judgment of the... 

The theory of non-isothermal viscoelastic behavior as developed by Hopkins [2] and Haugh [3] may be based on the representation of linear viscoelastic behavior by mechanical models. The linear viscoelastic behavior of polymers in simple shear at constant temperature and prescribed stress history may be expressed in terms of the deformation of a generalized Kelvin model. Spring constants and dashpot viscosity constants of the model have to be appropriately chosen the choice depends on temperature. For the non-isothermal treatment, the elasticity of the springs and the viscosities of the dashpots have to be inserted as functions of temperature. Due to the prescribed temperature history, they become functions of time. 

It is possible using transform methods to convert viscoelastic problems into elastic problems in the transformed domain, allowing the wealth of elasticity solutions to be utilized to solve viscoelastic boundary value problems. Although there are restrictions on the applicability of this technique for certain types of boundary conditions (discussed further in Chapter 9), the method is quite powerful and can be introduced here by building on the framework provided by mechanical models. Recall the differential equation for a generalized Maxwell or Kelvin model,... 

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