Question

What is the answer to this question?

Imagine if an artificial cartilage is fully made of chondrocytes which has a compression modulus 0.41 KPa and apparent viscosity of 3.0 KPa.s.

a) If such a artificial cartilage is under a sudden load stress of 0.1 KPa, use a simple Kelvin model, can you give an estimate of the time period needed to equilibrium from the given mechanical properties?
b) What is the final equilibrium strain?

c) Plot out the creep function (strain/load stress) of this cartilage under a sudden load stress of 0.1 MPa at time t=0.
You can modify the sample Matlab skeleton code below.
syms sig0 eps emod mvis

dsolve('Deps + (emod/mvis)*eps = sig0/mvis') emod=0.1;
mvis=1.0;
sig0=1.0;

C5=1.0;
t=0:1:100;
epsresult=(sig0 - C5*exp(-(emod*t)/mvis))/emod plot(epsresult,t);

d) Comment on why a good artificial cartilage can not be made with only chondrocytes and what is missing.

Answer 1

a) For a step load, the strain relation for Kelvin model is

Where

= initial stress=0.1 kPa

= relaxation time constant

Here

= apparent viscosity=3 kPa.s

k=compression modulus=0.41 kPa

From the above relation, it is seen that the strain will reach about 99% of steady state value after a time of =36.59 s

The Kelvin model is shown below:

b) The equilibrium strain is given as

c) The creep function is given as

The above is plotted below:

The workspace screenshot is given below:

d) For any applied stress, it will take a very long time for the strain to reach the steady state value and in the meanwhile the cartilage is under deformation. This may affect the stability of the particular body part under load. Hence a good cartilage can not be made with chondrocytes. Also the relaxation of stress property (for an applied constant strain) is missing from this model.