Problem $5$: Imagine you are a design engineer at an orthopedic implant

company and your task is to optimize a hip prosthesis in order minimize bone

loss due to stress$-$shielding and lack of bone loading. The ideal implant will

produce roughly the same axial stress in both the prosthesis and the bone

$($i$.$e$.,$ equal load sharing$).$

a$)$ Is there an optimal area or stiffness ratio between the cross$-$sectional

area of the implant and the cross$-$sectional area of the bone?

b$)$ Based on this criterion, which material from the following chart would

be the best candidate for the prosthesis?