3. A unit cube of neo-Hookean material characterised by the strain-energy density func- tion W 1 = (1, -3), where p > 0

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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 P 0 1 (38.16 KiB) Viewed 43 times

3. A unit cube of neo-Hookean material characterised by the strain-energy density func- tion W 1 = (1, -3), where p > 0 is constant and I, is the first principal strain invariant of the Cauchy-Green tensors, is deformed by the simple shear x1 = X1+kX2 29 = X2 23 = X3, where (21, 22, 23) are the current coordinates, (X1, X2, X3) are the reference coordi- nates, and k > 0 is constant. Evaluate the total energy E = sw WAV, where N is the domain occupied by the body in the undeformed state. I [10] 4. Show that, for a hyperelastic material characterised by the strain-energy function C2 ) W(41, 42, 4s) = (12 +13 + 13 – 3) + (17' +d3 + ;? – 3), + where C >0 and C2 > 0 are constants, necking instability may occur in the case that C2 > 64C (2C+C).