A tissue engineered heart valve is mechanically loaded in a physiological salt solution.(pressure = 0 MPa). The response

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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.
Direction 1, 2 and 3 are mutually perpendicular. Direction 1
is the loading direction. A strain of 4 % is imposed in the
direction 1 in a ramp of 2 ms duration, where after 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 the direction 1. After 8
hours the stress stabilizes and the strain is measured in the 2 and
3 direction. Both strains equal -1 % relative to the unloaded
state. Assume that the tissue is isotropic and linear elastic.
Infinitesimal deformation theory applies, the solid and fluid are
both incompressible.
a. Calculate the Young’s modulus E and the Poisson’s
ratio of the tissue engineered sample. [8 marks]
b. Calculate the total normal stress in the 1-direction at t = 6
h. [4 marks]
c. Calculate the total normal stress in the 3-direction at t = 2
ms.[4 marks]
d. Calculate the effective normal stress in the 2-direction at t
= 2 ms.[4 marks]