Q1. For the deformation describe below, address in much detail as possible the following.

x1= X ₁ + 2X ₃ ,x2= X ₂ 2X ₃ ,x3= 2X ₁ + 2X ₂ + X ₃

a) Consider the two line elements dX⁽¹⁾ =It is1 , dX⁽²⁾ =It is2 emanating from the the origin (0, 0, 0). Use the Right Cauchy Green strain tensor to determine whether these elements in the current configuration (dx(1),dx(2)) are perpendicular.

b) Use the Right Cauchy-Green strain tensor to evaluate the stretch of the line element dX =It is1 + It is2, and hence determine whether the element contract, stretches, or stays the same length after deformation.

c) Decompose the deformation into a stretching and rotation tensors. Describe what kind of deformation the body is undergoing by including what the principal stretches area and the type of rotation the body is undergoing.