A note on the Mooney-Rivlin material model

In finite elasticity, the Mooney-Rivlin material model for the Cauchy stress tensor T in terms of the left Cauchy-Green strain tensor B is given by T = -pI + s(1)B + s(2)B(-1), where p is the pressure and s (1), s (2) are two material constants. It is usually assumed that s (1) > 0 and s (2) <= 0, known as E-inequalities, based on the assumption that the free energy function be positive definite for any deformation. In this note, we shall relax this assumption and with a thermodynamic stability analysis, prove that s(2) need not be negative so that some typical behavior of materials under contraction can also be modeled.