Code Error on Line 39 and 41

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]')

Answer 1

[Cris LaPierre]

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]')

[Briana Canet]

Can you explain why the dots go there?

[Cris LaPierre]

For the same reason you use a ".^" at the end of each expression.

You can read more about array vs matrix operations here.

A = 1:3;

% with the dot
3./A

ans = 1×3

3.0000 1.5000 1.0000

% without the dot
3/A

Error using /
Matrix dimensions must agree.

[Steven Lord]

Do you want to perform array or matrix operations?