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4. For the same displacement field as in Q3, at X = (1, 0, -) what would be the difference in the (second Piola-Kirchoff) stress

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4. For the same displacement field as in Q3, at X = (1, 0, -) what would be the difference in the (second Piola-Kirchoff) stress tensor for the materials defined by the following hyperelastic constitutive laws? W1 = 5exp[3((E11)2 + (Ezz)2 + (E33)2)] W2 = 5exp[3((E11)2 + 2(E12)2 + 2(E13)2 + (Ezz)2 + 2(E23)2 + (E33)2)] Make sure to explain your reasons clearly and where appropriate. Hint: you can answer this without a long calculation. [6 marks] 5. Compare, and explain the significance of Cauchy stress tensor and the second Piola- Kirchoff stress tensor, which are defined in the theory of nonlinear elasticity. What are the equivalent quantities for these in the linear elasticity theory? [6 marks]

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