Chapter 8 - Incompressibility and Thermal Expansion

Abstract

In this chapter, we develop thermomechanical models for (i) incompressible viscous fluids, (ii) incompressible nonlinear elastic solids, and (iii) viscous fluids that thermally expand and contract. A material is referred to as incompressible if, within a certain class of loadings, only isochoric or volume-preserving motions are possible. In other words, the volume of the material cannot be changed appreciably by any means, be they thermal or mechanical. In the same vein, for certain classes of loadings, some materials are mechanically incompressible, yet experience significant thermal expansion, i.e., thermally induced volume change. For instance, polymer melts are relatively insensitive to changes in pressure, but can experience significant volume shrinkage (sometimes 30 percent or more) as they cool from their melt-processing temperature to room temperature.