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Hand written explanation required 3. A unit cube of neo-Hookean material characterised by the strain-energy density func- tion W = = ( 1 1 -

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3. A unit cube of neo-Hookean material characterised by the strain-energy density func- tion W = = ( 1 1 - 3 ) , where u > 0 is constant and I, is the first principal strain invariant of the Cauchy-Green tensors, is deformed by the simple shear $1 = XI+ KX2, 12 = X2, 23 = X3, where (I1, Ta, 0 is constant. Evaluate the total energy E = | Wav, where ? is the domain occupied by the body in the undeformed state. [10] 4. Show that, for a hyperelastic material characterised by the strain-energy function W(1, A2, As) = 2 ( X7 + 13 + 13- 3) + , ( di ' + Az) + As] - 3) , where C, > 0 and C2 > 0 are constants, necking instability may occur in the case that (2 > 640, (20, + C2)

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