Mechanics of Continua-A Brief Review

Abstract

The objective of this chapter is to review the major principles of continuum mechanics and to record the governing equations for future reference. It is well-known that the equations of continuum mechanics fall into four basic categories: 1) kinematics, 2) kinetics and the mechanical balance laws, 3) thermodynamics, and 4) constitution. Kinematics, of course, is a study of the geometry of motion and deformation without regard to the agents which caused them, and by kinetics we mean the collection of mechanical ideas that includes the notion of force and stress, plus the axioms of physics which have to do with conservation of mass and balances of momenta. The thermodynamics of continua gives us global laws very important to the development of a variational theory for problems in mechanics, and the equations of constitution, of course, involve relations between the kinematic variables (or temperatures) and their duals, and define the constitution of the material under study.