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The objective of this project is to determine the aggregate modulus (HA) and the permeability coefficient (k) of a cartilage sample by curve-fitting theoretical prediction with the experimental data that were obtained from a stress-relaxation confined compression test. The geometry of the cartilage specimen and the experimental data are included in the file ‘project_data.dat’ that can be downloaded from Blackboard. In the file, the first row includes the number of time points, the height of the specimen (mm), and the diameter of the specimen (mm). Experimental data start from the second row of the file with three columns. The first column is the time (sec), the second column is the applied displacement (mm), and the last column is the load response (kg). Curve-fitting can be performed using the LSQCURVEFIT function in Matlab. Figure 1 Experimental setup of the stress relaxation test In the stress-relaxation experiment (Figure 1), the displacement applied on the specimen was uz = { -0.05h !! t/t0 t ? t0, at z = h, -0.05h t > t0 where h is the height of specimen and t0 = 451 sec. The total stress at the surface z=h can be evaluated by the equation: ? = HA ?uz/?z |z=h = { - HAV0t/h - (2V0h/k?^2) ? (1/n^2) (1 - e^-(n^2?^2HAkt/h^2)) 0 ? t < t0 - HAV0t0/h - (2V0h/k?^2) ? (1/n^2) e^-(n^2?^2HAk(t-t0)/h^2) (1 - e^-(n^2?^2HAkt0/h^2)) t0 ? t where V0 = 0.05h/t0. HA and k of cartilage can be determined by curve-fitting the total stresses of specimen measured at the surface z=h with the corresponding theoretical prediction. Two types of curve-fitting should be performed: 1. HA is determined from the equilibrium state and then k is determined by curve-fitting; 2. Both HA and k are determined by curve-fitting. The quality of curve-fitting is assessed by calculating the coefficient of determination r^2: r^2 = 1 - ?(y - yi)^2 / ?(y - y?)^2 where y and yi represent the experimental and theoretical variables, respectively, and y? is the mean value of y.

          The objective of this project is to determine the aggregate modulus (HA) and the permeability coefficient (k) of a cartilage sample by curve-fitting theoretical prediction with the experimental data that were obtained from a stress-relaxation confined compression test. The geometry of the cartilage specimen and the experimental data are included in the file ‘project_data.dat’ that can be downloaded from Blackboard. In the file, the first row includes the number of time points, the height of the specimen (mm), and the diameter of the specimen (mm). Experimental data start from the second row of the file with three columns. The first column is the time (sec), the second column is the applied displacement (mm), and the last column is the load response (kg). Curve-fitting can be performed using the LSQCURVEFIT function in Matlab.

Figure 1 Experimental setup of the stress relaxation test
In the stress-relaxation experiment (Figure 1), the displacement applied on the specimen was
uz = { -0.05h !! t/t0  t ? t0, at z = h,
-0.05h  t > t0
where h is the height of specimen and t0 = 451 sec. The total stress at the surface z=h can be evaluated by the equation:
? = HA ?uz/?z |z=h = {
- HAV0t/h - (2V0h/k?^2) ? (1/n^2) (1 - e^-(n^2?^2HAkt/h^2)) 0 ? t < t0
- HAV0t0/h - (2V0h/k?^2) ? (1/n^2) e^-(n^2?^2HAk(t-t0)/h^2) (1 - e^-(n^2?^2HAkt0/h^2)) t0 ? t
where V0 = 0.05h/t0. HA and k of cartilage can be determined by curve-fitting the total stresses of specimen measured at the surface z=h with the corresponding theoretical prediction. Two types of curve-fitting should be performed:
1. HA is determined from the equilibrium state and then k is determined by curve-fitting;
2. Both HA and k are determined by curve-fitting.

The quality of curve-fitting is assessed by calculating the coefficient of determination r^2:
r^2 = 1 - ?(y - yi)^2 / ?(y - y?)^2
where y and yi represent the experimental and theoretical variables, respectively, and y? is the mean value of y.

The objective of this project is to determine the aggregate modulus (HA) and the permeability coefficient (k) of a cartilage sample by curve-fitting theoretical prediction with the experimental data that were obtained from a stress-relaxation confined compression test. The geometry of the cartilage specimen and the experimental data are included in the file ‘projectdata.dat’ that can be downloaded from Blackboard. In the file, the first row includes the number of time points, the height of the specimen (mm), and the diameter of the specimen (mm). Experimental data start from the second row of the file with three columns. The first column is the time (sec), the second column is the applied displacement (mm), and the last column is the load response (kg). Curve-fitting can be performed using the LSQCURVEFIT function in Matlab.

Figure 1 Experimental setup of the stress relaxation test
In the stress-relaxation experiment (Figure 1), the displacement applied on the specimen was
uz = -0.05h !! t/t0 t ? t0, at z = h,
-0.05h t > t0
where h is the height of specimen and t0 = 451 sec. The total stress at the surface z=h can be evaluated by the equation:
? = HA ?uz/?z |z=h =
- HAV0t/h - (2V0h/k?^2) ? (1/n^2) (1 - e^-(n^2?^2HAkt/h^2)) 0 ? t < t0
- HAV0t0/h - (2V0h/k?^2) ? (1/n^2) e^-(n^2?^2HAk(t-t0)/h^2) (1 - e^-(n^2?^2HAkt0/h^2)) t0 ? t
where V0 = 0.05h/t0. HA and k of cartilage can be determined by curve-fitting the total stresses of specimen measured at the surface z=h with the corresponding theoretical prediction. Two types of curve-fitting should be performed:
1. HA is determined from the equilibrium state and then k is determined by curve-fitting;
2. Both HA and k are determined by curve-fitting.

The quality of curve-fitting is assessed by calculating the coefficient of determination r^2:
r^2 = 1 - ?(y - yi)^2 / ?(y - y?)^2
where y and yi represent the experimental and theoretical variables, respectively, and y? is the mean value of y.

Added by Gregorio H.

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