Code Error on Line 39 and 41

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Briana Canet
Briana Canet on 21 Mar 2022
Edited: Cris LaPierre on 22 Mar 2022
There is an error in my code in Line 39 and 41 in K_a2 and Mu_a2, respectively. Maybe a dot/period is missing.
% Approach 1
E_m = 70000; % Elastic modulus of matrix, MPa
v_m = .33; % Poisson ratio of matrix
E_i = 250000; % Elastic modulus of inclusion, MPa
v_i = .2; % Poisson ratio of inclusion
% Fiber volume fraction
f_i = 0:0.01:1;
% 0 is 0% fiber and 1 is 100% fiber content
% points to be plotted
K_m = (E_m)/(3*(1-2*(v_m))); % Bulk modulus of matrix, MPa
K_i = (E_i)/(3*(1-2*(v_i))); % Bulk modulus of inclusion, MPa
Mu_m = (E_m)/(2*(1+v_m));
Mu_i = (E_i)/(2*(1+v_i));
% Iteration 1
s1_a1 = (1+v_m)/(3*(1-v_m));
s2_a1 = (2*(4-5*v_m))/(15*(1-v_m));
K_a1 = K_m*((1+f_i*(K_m/(K_m-K_i)-s1_a1)^-1)).^-1;
Mu_a1 = Mu_m*((1+f_i*(Mu_m/(Mu_m-Mu_i)-s2_a1)^-1)).^-1;
% Iteration 2
v_a2 = (3*K_a1-2*Mu_a1)/(2*(3*K_a1+Mu_a1));
s1_a2 = (1+v_a2)/(3*(1-v_a2));
s2_a2 = (2*(4-5*v_a2))/(15*(1-v_a2));
K_a2 = K_m*(1+(f_i*((K_i/K_m)-1)*(1+((K_i/K_a1)-1)*s1_a2).^-1));
Error using /
Matrix dimensions must agree.
Mu_a2 = Mu_m*(1+(f_i*((Mu_i/K_m)-1)*(1+((Mu_i/Mu_a1)-1)*s1_a2).^-1));
% Reuss and Voigt
K_Reuss = (((1-f_i)/K_m) + (f_i/K_i)).^-1;
K_Voigt = (((1-f_i)*K_m) + (f_i*K_i));
% Plotting
figure(1)
plot(f_i,K_a1, 'Color', 'red', 'LineWidth', 2.5);
hold on;
plot(f_i,K_a2, 'Color', 'blue', 'LineWidth', 2.5);
hold off;
grid off;
legend('K_a1', 'K_a2','K_a3', 'K_a4', 'K_a5')
legend('Location','northwest','FontSize',12)
title('Comp1: Bulk Modulus vs. Inclusion Volume Fraction')
xlabel('Inclusion Volume Fraction, f_i')
ylabel('Bulk Modulus, K [MPa]')

Answers (1)

Cris LaPierre
Cris LaPierre on 21 Mar 2022
You are correct on how to fix it.
f_i and K_a1 are both 1x101 vectors. Use elementwise operators to preserve the vectors.
K_a2 = K_m*(1+(f_i*((K_i/K_m)-1).*(1+((K_i./K_a1)-1)*s1_a2).^-1));
Mu_a2 = Mu_m*(1+(f_i*((Mu_i/K_m)-1).*(1+((Mu_i./Mu_a1)-1)*s1_a2).^-1));
% add elementwise operators ^* ^*
% Approach 1
E_m = 70000; % Elastic modulus of matrix, MPa
v_m = .33; % Poisson ratio of matrix
E_i = 250000; % Elastic modulus of inclusion, MPa
v_i = .2; % Poisson ratio of inclusion
% Fiber volume fraction
f_i = 0:0.01:1;
% 0 is 0% fiber and 1 is 100% fiber content
% points to be plotted
K_m = (E_m)/(3*(1-2*(v_m))); % Bulk modulus of matrix, MPa
K_i = (E_i)/(3*(1-2*(v_i))); % Bulk modulus of inclusion, MPa
Mu_m = (E_m)/(2*(1+v_m));
Mu_i = (E_i)/(2*(1+v_i));
% Iteration 1
s1_a1 = (1+v_m)/(3*(1-v_m));
s2_a1 = (2*(4-5*v_m))/(15*(1-v_m));
K_a1 = K_m*((1+f_i*(K_m/(K_m-K_i)-s1_a1)^-1)).^-1;
Mu_a1 = Mu_m*((1+f_i*(Mu_m/(Mu_m-Mu_i)-s2_a1)^-1)).^-1;
% Iteration 2
v_a2 = (3*K_a1-2*Mu_a1)/(2*(3*K_a1+Mu_a1));
s1_a2 = (1+v_a2)/(3*(1-v_a2));
s2_a2 = (2*(4-5*v_a2))/(15*(1-v_a2));
K_a2 = K_m*(1+(f_i*((K_i/K_m)-1).*(1+((K_i./K_a1)-1)*s1_a2).^-1));
Mu_a2 = Mu_m*(1+(f_i*((Mu_i/K_m)-1).*(1+((Mu_i./Mu_a1)-1)*s1_a2).^-1));
% Reuss and Voigt
K_Reuss = (((1-f_i)/K_m) + (f_i/K_i)).^-1;
K_Voigt = (((1-f_i)*K_m) + (f_i*K_i));
% Plotting
figure(1)
plot(f_i,K_a1, 'Color', 'red', 'LineWidth', 2.5);
hold on;
plot(f_i,K_a2, 'Color', 'blue', 'LineWidth', 2.5);
hold off;
grid off;
legend('K_a1', 'K_a2')
legend('Location','northwest','FontSize',12)
title('Comp1: Bulk Modulus vs. Inclusion Volume Fraction')
xlabel('Inclusion Volume Fraction, f_i')
ylabel('Bulk Modulus, K [MPa]')
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