ABSTRACT
Consider a differential tetrahedron enclosing the point x in the deformed configuration. The area of the inclined face is dS, and dSi is the area of the face whose exterior normal vector is −ei. Simple vector analysis serves to derive that ni=dSi/dS (see Exercise 1 in Chapter 1). Next, let dP denote the force on a surface element dS, and let dP(i) denote the force on area dSi. The traction vector is introduced by τ=dP/dS. As the tetrahedron shrinks to a point, the contribution of volume forces, such as inertia, decays faster than surface forces. Balance of forces on the tetrahedron now requires that
(5.1)
The traction vector acting on the inclined face is defined by
(5.2)
from which
(5.3)
