Material properties of bone tissue are often determined by mechanical testing. B
ID: 3788621 • Letter: M
Question
Material properties of bone tissue are often determined by mechanical testing. Bone samples1 from a healthy male donor 21 years of age, an osteoarthritic female donor 65 years of age, and an osteoporotic female donor 85 years of age were subjected to a compression loading test. Cuboid bone samples with a height of 4 mm and cross-sectional dimensions of 4.9 mm by 4.9 mm were cut from vertebrae. The samples were compressed in increments of approximately 0.05 mm. The force required to produce each amount of deformation was measured. The file ‘bone_comp_data.xls’ contains the deformation and force measurements. From this data, mechanical properties such as stress, strain, and ultimate compressive strength can be computed. Stress, (N/m2 or Pascals), is calculated as force divided by the original cross sectional area of the material tested. The ultimate compressive strength is the maximum stress. Strain, (%), is calculated as change in length divided by the original length.
(N/mm2 or MPa) = force / cross-sectional area (%) = [(deformed length – original length) / original length] 100%
NOTE: Deformation as shown in the data file ‘bone_comp_data.xls’ is the same as (deformed length – original length) in the equation for strain.
Write a MATLAB script that (1) imports the compression test data for each bone sample, (2) uses custom functions to compute the stress and strain, (3) overlays plots of stress vs. strain (strain on the x-axis and stress on the y-axis) for each bone sample, and (4) displays the ultimate compression strength for each bone sample.
In order to receive full credit you must: 1. Begin your script file with a comments section including the following: a. The name of the program and a brief description of the purpose of the program. b. The date created and the creator’s name in the second line. c. The definitions of the variable names for every input and output variable. Include definitions of variables used in the calculations and units of measurement for all input and all output variables. d. The name of every user-defined function called by the program. 2. Include comments describing the calculations in the program. 3. Include comments describing details of each section as appropriate. 4. Use custom functions. 5. Display results as directed. Include units and axes labels where appropriate. 6. Publish your main MATLAB program to html. Note that you cannot publish your function file to html because it is not executable on its own. Note that .png files are also created for your plot. One .png is a thumbnail size graphic of your plot. The other .png is a larger size graphic of your plot.
DATA
deformation_healthy force_healthy deformation_porotic force_porotic deformation_arthritic force_arthritic 0.00 0.00 0.00 0.00 0.00 0.00 0.10 35.43 0.11 16.35 0.11 20.33 0.15 51.48 0.16 18.84 0.12 22.90 0.21 65.62 0.20 20.36 0.21 34.39 0.27 76.91 0.25 19.68 0.25 37.48 0.31 82.34 0.29 19.23 0.30 37.40 0.35 87.23 0.33 19.36 0.34 36.35 0.38 91.52 0.38 20.20 0.38 37.91 0.42 94.80 0.43 20.80 0.44 38.42 0.44 95.96 0.48 21.50 0.46 38.42 0.48 93.46 0.49 21.60 0.49 38.42 0.54 88.24 0.55 21.41 0.53 37.84 0.57 86.87 0.58 21.17 0.59 36.04 0.62 85.14 0.63 20.52 0.61 36.02 0.66 84.22 0.65 20.06 0.67 36.02 0.71 86.04 0.70 19.21 0.68 36.02 0.74 88.29 0.74 19.57 0.74 35.80 0.79 92.08 0.78 20.93 0.77 35.28 0.81 94.59 0.82 22.46 0.81 34.62Explanation / Answer
>> n = 5; % number of small trapeziums formed after splitting
a = 1.0; % starting point or lower limit of the area
b = 2.0; % end point or upper limit of the area
sum = 0.0; % to find the sum
dx = (b-a)/(n-1); % to find step size or height of trapezium
% Generating the samples
for i = 1:n
x(i) = a + (i-1)*dx;
end
% to generate the value of function at different values of x or sample
for i = 1:n
y(i) = x(i).^2;
end
% computation of area by using the technique of trapezium method
for i = 1:n
if ( i == 1 || i == n) % for finding the sum of fist and last ordinate
sum = sum + y(i)./2;
else
sum = sum + y(i); % for calculating the sum of other ordinates
end
end
area = sum * dx; % defining the area
area