Right Cauchy-Green Tensor

Dear All,

I want to calculate  the limit of the fraction (J-1)/(1-2*nu) when material approach to incompressibility, where nu is the Poisson's ratio and J is the third invariant of the Cauchy-Green deformation tensor. In this case J->1 and nu->0.5, but I can't find any reference, how J depends on nu.

Intuitively, this limit has to be a finite value, as it is known that (J-1)^2/(1-2*nu) -> 0 (under the assumption that there is no hydrostatic pressure). Thanks in advance for any suggestions