Introduction

We will now mention a wide range of important solid mechanics phenomena that warrant discussion even in a mathematically-oriented book but have been ignored or scarcely mentioned so far.

A phenomenon of interest in industries ranging from food to glass is that of viscoelasticity. Here the molecular structure of the material is such that it flows under any applied stress, no matter how small. As we will see in Section 9.2, viscoelastic materials are quite unlike plastic materials. Their behaviour depends critically on the time-scale of the observer; for example when a ball of “silly putty” or suitably dilute custard impacts a wall, it rebounds almost elastically but, if left on a table, it will slowly spread horizontally under the action of gravity.

Yet another attribute of solids is well-known to be of great practical importance in the kitchen, when glass can be observed to break in hot water, and in the railway industry, where track can distort in high summer. This is thermoelasticity, which describes the response of elastic solids to temperature variations. To model this response ab initio, even at a macroscopic scale, requires more thermodynamics than is appropriate for this text, and in Section 9.3 we will only present the simplest ad hoc model that can give useful realistic results.

Even the above list of diverse phenomena only relates to solids that are fairly homogeneous on a macroscopic scale. Hence this book would certainly not be a fair introduction to the mathematics of solid mechanics without some discussion of the increasingly important properties of composites.