Page 174 - Introduction to Continuum Mechanics

Kinematics of a Continuum 159

so that

When the current configuration is used as the reference, it is customary also to denote
tensors based on such a reference with a subscript t, e.g.,

etc. All the formulas derived earlier, based on a fixed reference configuration, can be easily
rewritten for the case where the current configuration is used as the reference. For example,
let (r ', 0 ', z ',T ) denote the cylindrical coordinates for the position x' at time r for a material
point which is at (r ,0, z) at time t i.e.,

then, with respect to the current bases (e f , e#, e z)

We will have more to say about relative deformation tensors in Chapter 8 where we shall
discuss the constitutive equations for Non-Newtonian fluids.