ABSTRACT
CHAPTER 2
KINEMATICS OF DEFORMATION
2.1. Material and Spatial Description of Motion
The locations of material points of a three-dimensional body in its initial,
undeformed conguration are specied by vectors X. Their locations in
deformed conguration at time t are specied by vectors x, such that
x = x(X; t): (2.1.1)
The one-to-one deformation mapping from X to x is assumed to be twice
continuously dierentiable. The components of X are the material coordi-
nates of the particle, while those of x are the spatial coordinates. They can
be referred to the same or dierent bases. For example, if the orthonormal
base vectors in the undeformed conguration are e
J
, and those in the de-
formed conguration are e
i
, then X = X
J
e
J
and x = x
i
e
i
. Often, the same
basis is used for both congurations (common frame).
