Body and Surface Forces

      When a structure is subjected to applied external loadings, internal forces are induced inside the body. Following the philosophy of continuum mechanics, these internal forces are distributed continuously within the solid. In order to study such forces, it is convenient to categorize them into two major groups, commonly referred to as body forces and surface forces.
     Body forces are proportional to the body’s mass and are reacted with an agent outside of the body. Examples of these include gravitational-weight forces, magnetic forces, and inertial forces. Figure 3-1(a) shows an example body force of an object’s self-weight. By using continuum mechanics principles, a body force density (force per unit volume) F(x) can be defined such that the total resultant body force of an entire solid can be written as a volume integral over the body

     Surface forces always act on a surface and result from physical contact with another body. Figure 3-1(b) illustrates surface forces existing in a beam section that has been created by sectioning the body into two pieces. For this particular case, the surface S is a virtual one in the sense that it was artificially created to investigate the nature of the internal forces at this location in the body. Again the resultant surface force over the entire surface S can be expressed as the integral of a surface force density function T^n (x).

    The surface force density is normally referred to as the traction vector and is discussed in more detail in the next section. In the development of classical elasticity, distributions of body or surface couples are normally not included. Theories that consider such force distributions have been constructed in an effort to extend classical elasticity for applications in micromechanical modeling. Such approaches are normally called micropolar or couple-stress theory (see Eringen 1968) and are briefly presented in Chapter 14.