The Fundamental Equations of Continuum Mechanics

Abstract

Continuum mechanics draws its equations from three sources of physical information. In Section 4.2 we have already discussed the constitutive equations, which describe the empirical properties of the material. The kinematic relations between the displacement vector and the strain tensor have been explained in Chapter 2, but the treatment given there had a preliminary character because we approached the subject before we had learned how to differentiate a vector. We shall have to come back to this subject. The equilibrium conditions and their dynamic counterpart, the equations of motion, have not yet been touched upon. All this will be done now, and then we shall see how one can condense all these equations to a single one for one surviving unknown.