Curve Fitting Young's Modulus for Stress Strain Curve

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Ella
Ella 2025-3-6
编辑： Ella 2025-3-8
Hello everyone! I am trying to find the elastic modulus for all my datasets (6 total split across two donors) and I am struggling to implement it into my code. I have been advised to use the 0.002 offset to find the yield point and then fit a line to that point on my stress-strain curve. I know I should probably sue polyfit but I have been struggling to get it to look right and so I have my code for my stress-strain curves below. Any help would be great!
% load files
files =
legend;
hold off;
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Sam Chak
Sam Chak 2025-3-7
Hi @Ella
Originally, you used polyfit, but the fitting appeared unsatisfactory. I wonder if this fitting topic is covered by the mechanical professor or the numerical analysis professor. It is true that any continuous curve can be fitted by a polynomial of arbitrary order, provided certain conditions are met, according to the Weierstrass approximation theorem. If a stress–strain curve exhibits elasto-plastic behavior, you may consider using the Ramberg–Osgood model.
By the way, if the .CSV file or the .ZIP file is too large, you may upload only one set of data so that the experts here can demo how the fitting can be performed.
Sam Chak
Sam Chak 2025-3-7
Hi @Ella, could you please share your code for using the polyfit() function to fit the stress–strain curve? This will allow us to evaluate whether you wish to analyze both the linear and nonlinear regions.

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回答（1 个）

Star Strider
Star Strider 2025-3-7
Ran in:
I am not certain what you want to do. To fit the initial linear portion of the curve, you can either usee polyfit or mldivide, \
Try something liike this —
% load files
files = dir('*.csv');
d1_files = files(contains({files.name}, 'D1'));
d2_files = files(contains({files.name}, 'D2'));
d64 = 257 * 10^(-3); % mm
d93 = 255 * 10^(-3); % mm
A64 = (pi/4)*d64^2 ; %mm^2
A93 = (pi/4)*d93^2 ; %mm^2
l0 = 40 ; %mm
%% stress strain curves
% donor 1
figure;
hold on;
for i = 1:length(d1_files)
data = readmatrix(d1_files(i).name); % Load data
strain = data(:,1) / l0; % Calculate strain
stress = data(:,2) / A64; % Calculate stress
plot(strain, stress, 'DisplayName', strrep(d1_files(i).name,'_','\_')); % Plot strain vs stress
dssdsn = gradient(stress, strain);
hold on
% plot(strain, dssdsn)
% hold off
idx = find(diff(sign(dssdsn-5E+5))); % Use ‘gradient’ To Deteermine Linear Portion
% xline(strain(idx(end)))
idxrng = 1:idx(end);
DM = [strain(idxrng) ones(size(strain(idxrng)))];
B = DM \ stress(idxrng);
lrline = DM * B;
plot(strain(idxrng), lrline, '--r', DisplayName=sprintf('Linear Regression: stress = %9.3E \\times strain %+.3f', B))
end
xlabel('Strain');
ylabel('Stress (MPa)');
title('Stress-Strain Curve for Donor 1');
legend(Location='best')
hold off;
% donor 2
figure;
hold on;
for i = 1:length(d2_files)
data = readmatrix(d2_files(i).name); % Load data
strain = data(:,1) / l0; % Calculate strain
stress = data(:,2) / A93; % Calculate stress
plot(strain, stress, 'DisplayName', d2_files(i).name); % Plot strain vs stress
end
xlabel('Strain');
ylabel('Stress (MPa)');
title('Stress-Strain Curve for Donor 2');
legend;
hold off;
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