(Solved): Consider the following constant Cauchy stress tensor for all points (i.e., the body has a uniform ...

Consider the following constant Cauchy stress tensor for all points (i.e., the body has a uniform stress state) in a linearly elastic isotropic solid spherical body of radius \( R=2 \) in., \( E_{Y}=29000 \mathrm{ksi} \), and \( v=0.3 \) : \[ [T]=\left[\begin{array}{ccc} 10 & 4 & 6 \\ 4 & -20 & 0 \\ 6 & 0 & 20 \end{array}\right] \mathrm{ksi} \] a) Determine all the infinitesimal strain components, \( E_{i j}(i, j=1,2,3) \). b) Compute the dilatation, \( e \). c) Approximate the volume of the deformed sphere.