ABSTRACT
In this chapter we provide a condensed review of basic solid mechanics typically presented in upper-level undergraduate courses. Our emphasis is on formal relations as well as examples.
Figure 5.1 depicts a body in both its reference and current configurations. The former is considered to be the undeformed configuration, and the latter is called the deformed configuration-it reflects the deformation induced by the forces applied to the undeformed configuration. Consider a material particle occupying ‘‘point’’ P in the undeformed position and point Q in the deformed position. In the undeformed configuration its position determined the undeformed position vector, given in rectilinear coordinates as
X ¼ X1iþ X2jþ X3k (5:1)
while the same particle in the deformed configuration gives rise to the deformed position vector
x ¼ x1iþ x2jþ x3k (5:2)
referred to the same base vectors i, j, k. It is assumed that xi are functions of Xj and time t.
