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First Order Ogden Stress Strain Plot

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Tom Arnstein
Tom Arnstein on 16 May 2024 at 16:21
Edited: Hussam on 30 May 2024 at 20:51
Hello,
I have the material constants mu and alpha to fit a first order ogden material model. Mu = 8000, alpha = 5.
I am trying to plot the stress strain curve. However, I would expect that the curve would intersect stress and strain at 0,0. Owing to the ogden formula, intersecting at 0,0 is not possible, which contradicts normal and expected material behaviour.
It would be great if someone could explain and help me understand where I am going wrong.
Thanks,
Tom
%%
close all;
clear all;
% Parameters
mu1 = 8000; % Shear modulus
alpha1 = 5; % Material parameter
% Strain range for compression
strain_comp = linspace(-1, 1, 1000); % From -0.5 to 0
% Stress calculation for compression
stress_comp = (mu1/alpha1) * (strain_comp.^alpha1 + strain_comp.^alpha1 + strain_comp.^alpha1 - 3);
% Plot compression
figure;
plot(strain_comp, stress_comp, 'LineWidth', 2);
xlabel('Strain (Compression)');
ylabel('Stress');
title('First Order Ogden Model - Compression');
grid on;
  1 Comment
Hussam
Hussam on 30 May 2024 at 20:42
Edited: Hussam on 30 May 2024 at 20:51
Hi,
Please correct me if I am wrong, but I believe you are using the strain energy function to calculate stress? I am not entirely sure, but the stress equation is different.
Also, in order to subsitute the stretch with strain, if it is uniaxial data, then stretch = 1 + strain.
I am trying to do a similar problem using the Ogden 3 parameter, but I think your math is not exactly correct?
Your feedback would be beneficial to me as well.
Best,
Hussam

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Answers (1)

Mathieu NOE
Mathieu NOE on 17 May 2024 at 8:07
hello
I believe parentheses are missing for the last term
% Stress calculation for compression
stress_comp = (mu1/alpha1) * (strain_comp.^alpha1 + strain_comp.^alpha1 + strain_comp.^alpha1 - 3);
should probably be :
stress_comp = (mu1/alpha1) * (strain_comp.^alpha1 + strain_comp.^alpha1 + strain_comp.^(alpha1 - 3));
full code :
% Parameters
mu1 = 8000; % Shear modulus
alpha1 = 5; % Material parameter
% Strain range for compression
strain_comp = linspace(-1, 1, 1000); % From -0.5 to 0
% Stress calculation for compression
stress_comp = (mu1/alpha1) * (strain_comp.^alpha1 + strain_comp.^alpha1 + strain_comp.^(alpha1 - 3));
% Plot compression
figure;
plot(strain_comp, stress_comp, 'LineWidth', 2);
xlabel('Strain (Compression)');
ylabel('Stress');
title('First Order Ogden Model - Compression');
grid on;

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