3) The strain energy function U of a linearly elastic isotropic material is given by the...

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3) The strain energy function U of a linearly elastic isotropic material is given by the relation U = ( + G)J 2GJ2, where (A,G) are the Lam elastic constants and (J1, J2) are the first and second strain invariants (same mathe- matical form as the stress invariants). a) Employing the relation between U and the stress components, derive the constitutive relations for a state of plane strain 22 = Eyz = Exz = 0. b) Repeat part (a) for a state of plane stress zz = xz = yz = 0. 3) The strain energy function U of a linearly elastic isotropic material is given by the relation U = ( + G)J 2GJ2, where (A,G) are the Lam elastic constants and (J1, J2) are the first and second strain invariants (same mathe- matical form as the stress invariants). a) Employing the relation between U and the stress components, derive the constitutive relations for a state of plane strain 22 = Eyz = Exz = 0. b) Repeat part (a) for a state of plane stress zz = xz = yz = 0.