5. (a) In finite elasticity, the Green-Lagrange strain tensor is defined as E = (C-1)/2, where C is the right Cauchy-Gre

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5 A In Finite Elasticity The Green Lagrange Strain Tensor Is Defined As E C 1 2 Where C Is The Right Cauchy Gre 1 (37.99 KiB) Viewed 73 times

5. (a) In finite elasticity, the Green-Lagrange strain tensor is defined as E = (C-1)/2, where C is the right Cauchy-Green tensor. Show that, in the linear elastic limit, this is equal to the infinitesimal strain tensor €. [10] (b) For an elastic body made from a linear elastic material which is homogeneous (i.e. the material properties are independent of position) and isotropic (i.e. the behaviour of the material is the same in all directions), given the displacement: u = 022 0 0 where a > 0 is constant, find the corresponding linear strain, linear stress, and strain-energy density (10) (c) How is the strain-energy density at the previous point modified when aty is replaced by a(x2 + x3)? [5]