4.2 Consider the LCE described by the following strain-energy function, = W(lce) (1) - (A +...

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4.2 Consider the LCE described by the following strain-energy function, = W(lce) (1) - (A + x + X 3) + (a + a + a 3), (2) - 2 2 where (1), (2) > 0 are constant model parameters, {1, 2, 3} denote the eigenvalues of the Cauchy- Green tensor FFT, where F is the deformation gradient from the reference cross-linking state, sat- isfying det F = 1, and {a, a, a} are the eigenvalues of AAT, where A = GFGo is the local elastic deformation tensor, such that det A = 1, with Go and G representing the 'natural' deforma- tion tensors due to the liquid crystal director in the reference and current configuration, respectively. Determine the stretch interval where shear stripes can form under the uniaxial deformation with X => and A2 = A3 = A-1/2, assuming that the nematic parameter a is constant and that the director n is initially aligned parallel to the second direction. 4.2 Consider the LCE described by the following strain-energy function, = W(lce) (1) - (A + x + X 3) + (a + a + a 3), (2) - 2 2 where (1), (2) > 0 are constant model parameters, {1, 2, 3} denote the eigenvalues of the Cauchy- Green tensor FFT, where F is the deformation gradient from the reference cross-linking state, sat- isfying det F = 1, and {a, a, a} are the eigenvalues of AAT, where A = GFGo is the local elastic deformation tensor, such that det A = 1, with Go and G representing the 'natural' deforma- tion tensors due to the liquid crystal director in the reference and current configuration, respectively. Determine the stretch interval where shear stripes can form under the uniaxial deformation with X => and A2 = A3 = A-1/2, assuming that the nematic parameter a is constant and that the director n is initially aligned parallel to the second direction.