Mechanics of Solids

The application of the principles of mechanics to bulk matter is conventionally divided into the mechanics of fluids and the mechanics of solids. The entire subject is often called continuum mechanics, particularly when we adopt the useful model of matter as being continuously divisible, making no reference to its discrete structure at microscopic length scales well below those of the application or phenomenon of interest. Solid mechanics is concerned with the stressing, deformation and failure of solid materials and structures. What, then, is a solid? Any material, fluid or solid, can support normal forces. These are forces directed perpendicular, or normal, to a material plane across which they act. The force per unit of area of that plane is called the normal stress. Water at the base of a pond, air in an automobile tire, the stones of a Roman arch, rocks at base of a mountain, the skin of a pressurized airplane cabin, a stretched rubber band and the bones of a runner all support force in that way (some only when the force is compressive). We call a material solid rather than fluid if it can also support a substantial shearing force over the time scale of some natural process or technological application of interest. Shearing forces are directed parallel, rather than perpendicular, to the material surface on which they act; the force per unit of area is called shear stress. For example, consider a vertical metal rod that is fixed to a support at its upper end and has a weight attached at its lower end. If we consider a horizontal surface through the material of the rod, it will be evident that the rod supports normal stress. But it also supports shear stress, and that becomes evident when we consider the forces carried across a plane through the rod that is neither horizontal nor vertical. Thus, while water and air provide no long term support of shear stress, normally granite, steel, and rubber do so, and are called solids. Materials with tightly bound atoms or molecules, like the crystals formed below melting temperature by most substances or simple compounds, or the amorphous structures formed in glass and many polymer substances at sufficiently low temperature, are usually considered solids.