Thermoviscoelastic Boundary Value Problems

Abstract

As pointed out in Sect. 1.7, the viscoelastic functions of many materials depend strongly on temperature. The simplest realistic way of incorporating this dependence is to assume that the material is thermorheologically simple (TRS) in the sense defined in Sect. 1.7. This implies a non-linear dependence on the temperature field which renders the solution of most problem categories very difficult, in particular those where the temperature field is not given a priori but must be determined as part of the solution. A way out of this is to adopt a fully linear theory, as developed for example by Christensen (1982), Chap. 3. The assumption behind such a theory is that the effects of temperature variation on the viscoelastic functions is sufficiently small that its product with the field variables can be neglected. In many cases, this is very restrictive on the allowed range of temperature variation. A fully linear theory will not be considered here. We remark however that such a theory is susceptible to treatment by the Correspondence Principle-based methods, discussed in Chap. 2.