The generalized definition of strain

In this introduction to finite elasticity it is only necessary to develop the most elementary definition of finite strains (for a more comprehensive discussion, see [3], chapter 3). 

The quantities Ai, A2 and A3 that define the deformation are called the deformation ratios, because they define the ratio of the length of lines in the x, y and z directions in the deformed body to their length in the undeformed body. Note 

Finite strain is most conveniently defined by these three deformation ratios, although we can equally well define the three components of extensional finite strain , Eyy and e z (in bold type to distinguish them from the small strain components defined in Section 2.4.1 above) as 

This generalized definition of strain, which is not limited to small strains, is compatible with our definition of strain in Section 2.2 above. For example, for 

A deformation in which lines of material along the three coordinate axes x, y and z in the undeformed state remain mutually perpendicular is called normal strain (often normal homogeneous strain, to include the idea that it is also uniform throughout the body) because the shear strain components are zero. We will always develop the theories of rubber elasticity with this simplification because it involves no loss of generality, as can be appreciated from the following. 

---