Application of the Principal Stretch Approach

Rivlin adopted a formulation for the strain energy function U that involved the squares of the extension ratios because he envisaged that negative values of these quantities were 

The use of the invariant approach, which is closely linked to Rivlin s use of strain in the form of even powers of the extension ratios as exemplified in Equation (3.40), now appears to be unnecessarily restrictive. In this section, we give examples of applications using the approach to the strain energy function listed as (2) in Section 3.4.2. We shall again restrict the discussion to incompressible materials. 

Valanis and Landel [13] have introduced a strain energy function of the form 

This form has the essential property specified in (2) in Section 3.4.2, that 17 is a symmetric function of the principal extension ratios. Stresses are derived using Equation (3.55) that gives 

Valanis and Landel used the expression for the stress difference in the I-II plane 

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