Module 4 : Nonlinear elasticity
  Lecture:23 : Homogeneuos Strain
   

 

We can use the relation for in equations (23.16) and (23.17), , which yields for (23.16)

  (23.18)

Similarly, for equation (23.17), we obtain,

 

and
(23.19)

These results then suggest that if ,  and  are satisfied then all three necessary and sufficient conditions as in equations (23.18) and (23.19) will be satisfied and the corresponding equilibrium state is stable. If is negative, the equilibrium state is uniquely determined.