An elastic medium subjected to a state of stress ij deforms incompressibly (???? = 0). Consider

An elastic medium subjected to a state of stress σij deforms incompressibly (???? ̅ଵ = 0). Consider rectangular Cartesian coordinate axes (x, y, z). 

(a) Assume that σ ₁₁ + σ ₂₂ + σ ₃₃ ≠ 0. Determine the value of ν, Poisson’s ratio, for the material. 

(b) Assume additionally that ε33 = 0. Show that two values of ν are theoretically possible. Determine these two values of ν.