I have a code that I would like to modify to plot multiple items all together

I have this code

% Matrix properties (Al2O3)
Em = 380E3; % Young's modulus
num = 0.22; % Poisson's ratio
Vv_vals = [0.01, 0.35, 0.47]; % different porosity volumes
KIc = 3.63; % MPa*sqrt(m) fracture toughness
% Dv = 1E-3; % void diameter
%
Porous_AL2O3;
% Crack density parameter (from Budiansky and O'Connel, IJSS 12:81-97, 1976)
cdp0 = 0;
cdp = cdp0;
a = 1;
%
%%
% MECHANISMS OF CYCLIC FATIGUE-CRACK PROPAGATION IN A FINE-GRAINED ALUMINA
% CERAMIC: THE ROLE OF CRACK CLOSURE C. J. Gilbert, R. O. Ritchie 2008
C = 1.3E-18; % Paris law coefficient
m = 23; % material exponent
delta_gmcv = 2.5;
%
%%
N_cycles = 1E7;
sigma_avg = [569, 59, 13]; % average strength
sigma_max = [0.9*sigma_avg 0.8*sigma_avg 0.7*sigma_avg 0.6*sigma_avg; 0 0 0; 0 0 0; 0 0 0; 0 0 0; 0 0 0]; % max stress
% needs to be 0.9, 0.8, 0,7, and 0.6 of sigma_avg for the three Vv_vals

R = sigma_min/sigma_max; % stress ratio
%%

%% Critical eneergy release rate for matrix
GIc = KIc^2/Em*1000;
% eps_step = zeros(6,6);
rmcv = 2/3*(1-Vv_vals)*pi*GIc/a;
% Stiffness and compliance matrices of uncracked material (6 x 6)
[S2m,C2m] = S2_C2_ortho(Em,Em,Em,num,num,num,Em/2/(1+num),Em/2/(1+num),Em/2/(1+num)); % matrix
%
num_Vv = length(Vv_vals);
for Vv_idx = 1 : num_Vv
    Vv = Vv_vals(Vv_idx);
    for k = 1:N_cycles
        % F tensor for crakcs
        Fc = F_tens_penny_iso(num);
        %
        % Swap axis 3 with axis 1 (so axis 3 of the crack is aligned with material axis 1)
        Fc = Fc([3 2 1 6 5 4],[3 2 1 6 5 4]);
        %
        % Strain concentration tensor for voids
        [~,SE2v] = eshelby_tens_sph_iso(num); % Eshelby tensor for voids
        inv_Tv = eye(6)-SE2v; % inverse T tensor for voids
        Tv = inv_Tv\eye(6); % T tensor for voids
        % Homogenised stiffness and compliance with voids and cracks
        inv_Am = (1-Vv)*eye(6) + Vv*Tv + cdp*Fc; % inverse absolute strain concentration tensor for the matrix
        Am = inv_Am\eye(6); % absolute strain concentration tensor for the matrix
        C2 = (1-Vv)*C2m*Am; % stiffness tensor of matrix + cracks + voids
        S2 = C2\eye(6); % compliance tensor of matrix + cracks + voids
        %
        %
        % Equivalent elastic moduli from compliance matrix
        %
        [E1,E2,E3,nu12,nu13,nu23,G12,G13,G23] = moduli_ortho(S2);

        eps_max = S2*sigma_max;
        s_mcv = C2*eps_max;
        eps_mcv_max = Am*eps_max;
        s_mcv_max = Am*s_mcv;
        gmcv_max = 1/2*(1-Vv)*eps_mcv_max'*C2*Am*Fc*Am*eps_mcv_max;
        cdp = cdp + C * (delta_gmcv)^m * k;
        eps_mcv_step(:,k) = eps_mcv_max;
        s_mcv_step(:,k) = s_mcv_max;



    end
end
loglog(s_mcv_step(1,:),'r','LineWidth',2)
hold
loglog(AL01_SIGMA08(:,1),AL01_SIGMA08(:,2),'bo','MarkerSize',8,'MarkerFaceColor',[0 0 1])
loglog(meanAL0108(:,1),meanAL0108(:,2),'bo','MarkerSize',8,'MarkerFaceColor',[0 1 1])

there is one material which has three varying porosities (0.01, 0.35, and 0.47). Each case is being loaded to 0.9,0.8,0.7, and 0.6 of their average respective strengths. the test data is found in

Porous_AL2O3

Which has 12 data sets. I would like to take the mean of each data set and then plot all of it against each other to generat a graph that resembles this one but with the 12 different data sets, their means and the respective comparison all on the same plot

I realise that this maybe a bit of a huge ask but any help is greatly welcomed.

Thanks

Alex

[Govind KM]

Since you have used hold, you can continue plotting data for each of the datasets and they will appear on the same plot.

[A Poyser]

Thanks for the input. To add a little more clarity. I have yet to generate all of the 12 lines I need. So I need a line of a material with a porosity of 0.01, and an average strength of 569MPa being loaded to 0.9 of its average strength, 0.8 of its average strength, ... Then I have a material with 0.35 porosity with an average strength that is lower than that is being loaded to 0.9, ... Finally I have a material with 0.47 porosity with an average strength of a different value again being loaded to 0.9, 0.8,0.7, and 0.6. I just can't figure out the logic of how to make my code do all of that.

[Chris Burschyk]

You could multiply your average Strength with [0.9:-0.1:0.6] and adjust your code to use piecewise multiplication and devision (just add a "." before "*" and "/").

But I don't fully understand your code. A lot of the calculations inside the loops seem to be the same every time, maybe do these outside of the loop.

[A Poyser]

Thanks Chris. It is calling, other pieces of code. I have updated the code editor so it is hopefully a little more clear what I am trying to acheive

[Chris Burschyk]

Everything in the loop before the line

inv_Am = (1-Vv)*eye(6) + Vv*Tv + cdp*Fc;

is calculated everytime but it doesnt get changed because the variable "num" stays at 0.22.

For your plotting problem I could suggest to put one more loop between the two which iterates over the different loads

figure()

hold on

for Vv_idx = 1 : num_Vv

for idx_load = 0:4

Vv = Vv_vals(Vv_idx) * (1-(idx_load/10);

for k = 1:N_cycles

...

end

loglog(s_mcv_step(1,:),'r','LineWidth',2)

end

end

hold off

This will give you only the red lines for each Iteration. As for the means I do not know how your dataset looks like so its hard to give you advice on that.

[A Poyser]

The Vv value does stay the same, however the cdp value increments but only by a very small amount at first however. It is exponential so cdp*Fc eventually starts to cause a fatigue response in the material

Answer 1

[Tushar]

Hi Alex,

I think we can do it like this.Try adding this to your code.

% calculate the mean value for each data set in Porous_AL2O3
mean_values = zeros(12,1);
for i = 1:12
    mean_values(i) = mean(Porous_AL2O3(:,i+1));
end

% plot the mean values against each other
figure
hold on
for Vv_idx = 1:num_Vv
    plot(mean_values, s_mcv_step(Vv_idx,:))
end

% plot the mean values of the data set and the mean of all data sets
mean_all = mean(mean_values);
plot(mean_all,mean(s_mcv_step,2),'ks','MarkerSize',10,'LineWidth',2,'MarkerFaceColor',[1 0.5 0])

% add labels and a legend to the plot
xlabel('Mean strength of each data set')
ylabel('Maximum stress during cyclic loading')
title('Comparison of cyclic loading behavior for porous Al2O3')
legend({'0.01 Vv','0.35 Vv','0.47 Vv','Mean of all data sets'})

[A Poyser]

I forgot to add that each porosity material has a different sigma average