To develop some facility with application of the principles discussed in the preceding three chapters, some examples of classical problems are discussed in this chapter. The first problem involves the collapse of a cylindrical hole in ice. This solution is applied to problems of determining flow law constants from closure of tunnels and boreholes, ofclosure of water conduits in response to melting by energy dissipated in the flowing water. In the second, force balance calculations are used to study the role of seasonal and shorter-term variations in water pressure on glacier motion.Then, the need to consider longitudinal coupling in calculations of deformation rates is explored. In calculating velocity profiles at a point on a glacier, one needs to take into consideration not only the surface slope and ice thickness at that point, but also their variation up- and downglacier from that point.Finally, the theoretical basis for analysis of borehole deformation data to determine flow law constants is presented. Longitudinal strain rates and vertical advection need to be taken into consideration in analyzing borehole tilt data.

The behaviour of composite materials is often sensitive to changes in temperature. This arises for two main reasons. First, the response of the matrix to an applied load is often temperature-dependent; and second, changes in temperature can cause internal stresses to be set up as a result of differential thermal contraction and expansion of the two constituents. These stresses affect the thermal expansivity (expansion coefficient) of the composite. Furthermore, significant stresses are normally present in the material at ambient temperatures, since it has in most cases been cooled at the end of the fabrication process. Changes in internal stress state on altering the temperature can be substantial and may influence the response of the material to an applied load. Thermal cycling can thus have strong effects on, for example, creep characteristics. Finally, the thermal conductivity of composite materials is of interest, since many applications and processing procedures involve heat flow of some type. This property can be predicted from the conductivities of the constituents, although the situation may be complicated by poor thermal contact across the interfaces.