Mechanics is the study of the behavior of matter under the action of internal and external forces. In this introductory treatment of continuum mechanics, we accept the concepts of time, space, matter, energy, and force as the Newtonian ideals. Here our objective is the formulation of engineering problems consistent with the fundamental principles of mechanics. To paraphrase Professor Y. C. Fung–there are generally two ways of approaching mechanics: One is the ad hoc method, in which specific problems are considered and specific solution methods are devised that incorporate simplifying assumptions, and the other is the general approach, in which the general features of a theory are explored and specific applications are considered at a later stage. Engineering students are familiar with the former approach from their experience with “Strength of Materials” in the undergraduate curriculum. The latter approach enables them to understand an entire field in a systematic way in a short time. It has been traditional, at least in the United States, to have a course in continuum mechanics at the senior or graduate level to unify the ad hoc concepts students have learned in the undergraduate courses. Having had the knowledge of thermodynamics, fluid dynamics, and strength of materials, at this stage, we look at the entire field in a unified way.

Concept of a Continuum

Although mechanics is a branch of physics in which, according to current developments, space and time may be discrete, in engineering the length and time scales are orders (and orders) of magnitude larger than those in quantum physics and we use space coordinates and time as continuous.