En -introduction to continuum mechanics

Preface

Matter is formed of molecules, which in turn consist of atoms and subatomic particles. Thus, matter is not

continuous. However, there are many aspects of everyday experience regarding the behaviors of materials,

such as the deflection of a structure under loads, the rate of discharge of water in a pipe under a pressure gradient,

or the drag force experienced by a body moving in the air, that can be described and predicted with

theories that pay no attention to the molecular structure of materials. The theory that aims to describe relationships

among gross phenomena, neglecting the structure of material on a smaller scale, is known as continuum

theory. The continuum theory regards matter as indefinitely divisible. Thus, within this theory, one accepts

the idea of an infinitesimal volume of materials, referred to as a particle in the continuum, and in every neighborhood

of a particle there are always neighboring particles.

Whether the continuum theory is justified or not depends on the given situation. For example, although the

continuum approach adequately describes the behaviors of real materials in many circumstances, it does not

yield results that are in accord with experimental observations in the propagation of waves of extremely small

wavelength. On the other hand, a rarefied gas may be adequately described by a continuum in certain circumstances.

At any rate, it is misleading to justify the continuum approach on the basis of the number of molecules

in a given volume. After all, an infinitesimal volume in the limit contains no molecules at all. Neither is

it necessary to infer that quantities occurring in a continuum theory must be interpreted as certain particular

statistical averages. In fact, it has been known that the same continuum equations can be arrived at by different

hypotheses about the molecular structure and definitions of gross variables. Though molecular-statistical

theory, whenever available, does enhance understanding of the continuum theory, the point to be made is simply

that whether the continuum theory is justified in a given situation is a matter of experimental test and of

philosophy. Suffice it to say that more than 200 years of experience have justified such a theory in a wide

variety of situations.

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