Data on the yield strain and yield stress for a cylindrical sample of cortical bone and a cylindrical sample

of cancellous bone from mechanical testing in compression are provided in the table below. Specimen

dimensions and a typical stress$-$strain curve obtained during testing are provided.

Questions

$1-1.(2$ points$).$ Find the apparent density $(,$ in units of $\frac{g}{c}{m}^3)$ of each bone specimen.

$1-2.(3$ points$).$ If the cancellous bone sample is determined to have a porosity of $75\%$ what is its tissue$-$

level density $({}_t,$ in units of $\frac{g}{c}{m}^3)?$

$1-3.(6$ points$).$ Based on the results of testing and assuming linear stress$-$strain behavior, compute the

apparent elastic modulus of cancellous bone and the apparent elastic modulus of cortical bone in

compression prior to yielding. Give answers in units of MPa.

$1-4.(10$ points$).$ Assuming a power relationship between elastic modulus $($ E $)$ and apparent density $()$ :

$E=A{}^B(MPa)$

holds for all bone, find the coefficient A and exponent $B.$

Using the power relationship with the A and $B$ values you found, determine the elastic modulus $(E,$

in units of MPa$)$ for a sample of bone with an apparent density of $0\mathrm{.}9\frac{g}{c}{m}^3.$

$1-5.(4$ points$).$ When the bone samples reach the yield point, what is happening to the material at the

tissue scale? How is this yielding behavior different from that in ductile metals?