Since the strain energy has physical meaning that is independent of the choice of coordinate axes, it must be invariant to all coordinate transformations. Because U is a quadratic form in the strains or stresses, it cannot depend on the third invariants III_e or I₃, and so it must depend only on the first two invariants of the strain or stress tensors. Show that the strain energy can be written in the following forms:

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U=(2/2 + ) 1 - 2lle = 2/(1-2(1 + v) 12)