Page 494 - Introduction to Continuum Mechanics

478 Relative Deformation Tensors

In cylindrical coordinates, with pathline equations given by

the two point components of F f, with respect to (e',, e'g, e' 2) at time T and (e n %, e 2) at the
current time t are given by the matrix

In spherical coordinates, with pathline equations given by

the two point components of ¥ t, with respect to (eV, e'g, e'^) at time T and (e^ e^, e^) at the
current time t are given by the matrix

8.7 Relative Deformation Tensors

The descriptions of the relative deformation tensors (using the current time t as reference
time) are similar to those of the deformation tensors using a fixed reference time. [See
Chapter 3, Section 3.18 to 3.29]. Indeed by polar decomposition theorem (Section 3.21)

where U, and V f are relative right and left stretch tensor respectively and R, is the relative
rotation tensor. Note