A note on the Mooney–Rivlin material model

AbstractIn 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 s1, s2 are two material constants. It is usually assumed that s1 > 0 and s2 ≤ 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 s2 need not be negative so that some typical behavior of materials under contraction can also be modeled.