Fundamental of Continuum Mechanics

Abstract

Continuum mechanics is a branch of physical sciences concerned with the deformations and motions of continuous material media under the influence of external effects. External effects that influence bodies appear in the form of forces, displacements, and velocities that result from contact with other bodies, gravitational forces, thermal changes, chemical interactions, electromagnetic effects, and other environmental changes.

The theory of continuous media is built upon two strong foundations: (1) the basic laws of motion and (2) a constitutive theory. The basic laws of motion are the fundamental axioms of motion that are valid for all bodies irrespective of their constitution. They are the results of our experience with the physical world. The constitutive relations are constructed to take the nature of different materials into consideration. These relations also depend on the range of physical effects, which we wish to describe. Certain axioms are employed in the construction and restriction of the constitutive relations. The resulting equations nevertheless contain some unknown material parameters that must be determined through experiments and/or statistical mechanical considerations.

This chapter is a brief review of continuum mechanics devoted to a study of the basic laws of motions and the constitutive theory (cf. [Eringen, 1989]).