EGM 4592 BioSolid Mechanics Problem Set #3
Assigned: February 27th, 2007
Due: March 20th, 2007
1. Explain the differences between elasticity, pseudo-elasticity, and quasi-linear
viscoelasticity. Comment on why these concepts are useful?
2. Look at Figure 7.6:5. a) For the Maxwell, Voigt, and Kelvin models describe why the
hysteresis changes with frequency as shown in the second row of the figure.
b) Suggest an experiment to determine which model (Maxwell, Voigt or Kelvin)
would be best to use for a particular tissue.
3. We saw an example in class using MATLAB to examine the stress-strain relationship
for blood vessels based on an exponential strain-energy function and a 4 parameter
(constant coefficients) model:
eww = (0:99)/99;
ezz = .1*ones(1,100);
for i = 1:100
sww(i) = 2.93*(2.5*eww(i)+.176*ezz(i))*exp(2.5*eww(i)*eww(i)+...
.46*ezz(i)*ezz(i)+2.*.176*eww(i)*ezz(i));
end
plot(eww,sww)
xlabel('strain Eww, Ezz = .1')
ylabel('stress S11 (KPa)')
hold on
for i = 1:100
sww(i) = …
3.39*(2.8*eww(i)+.58*ezz(i))*exp(2.8*eww(i)*eww(i)+.52*ezz(i)*ezz(i)+…
2.*.58*eww(i)*ezz(i));
end
plot(eww,sww)
This model assumes that the longitudinal strain is constant at 0.1. Starting from this
code, plot a family of curves (using the same values for C, a1, a2, a4) showing the
stress/ strain relationships for Ezz = [0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1.0]
4. Suppose you have a strain-energy function:
Derive the equations for the stress components (Sθθ, SZZ, SθZ) in terms of the strain
components. Make up two values for each of the required constant coefficients and use
MATLAB to plot the stress/strain curves for Sθθ as a function of Eθθ (0 1) with EZZ=0.1,
and SZZ as a function of EZZ (0 1), with Eθθ=0.3.
5. Do problem 8.2 in Fung.