A tissue-engineered heart valve is mechanically loaded in a physiological salt solution (pressure = 0 MPa). The response of the fibroblasts depends on the mechanical load that the tissue senses. For this reason, knowledge of the exact stress history is vital. A strain of 4% is imposed in direction 1 in a ramp of 2 ms duration, whereafter the strain is maintained constant in that direction. Immediately after the ramp, the stress in the 1-direction is measured: 3 MPa. After that time, the stress decreases progressively in direction 1. After 8 hours, the stress stabilizes and the strain is measured in the 2 and 3 directions. Both strains equal -1% relative to the unloaded state. Assume that the tissue is isotropic and linear elastic. Infinitesimal deformation theory applies, and the solid and fluid are both incompressible.
A) Calculate Young's modulus E using the Poisson's ratio of the tissue-engineered sample.
B) Calculate the total normal stress in the 1-direction at t = 6h.
C) Calculate the total normal stress in the 3-direction at t = 2 ms.
D) Calculate the effective stress in the 2-direction at t = 2 ms.
E) Calculate the total normal stress in the 2-direction at t = 6h.