Filled region between three functions

I would like to shade the region inbetween [sigma1, Friction], [sigma1, Friction2] and [sigma2, Tension_failure]. I have shaded the area between the two first functions but I don'tknow how to restrict the curve to the third function.

Forhold = 1/2 ;

Forhold2 = 54/228;

f_vk0 = 0.4 ; % Klæbningsbidrag [MPa]

mu_k = 0.65 ; % Friktionskoefficient

f_bt = 1.00 ; % Trækstyrke af sten [MPa]

f_k = 10.00 ; % Trykstyrke af sten [MPa]

sigma1 = -0.0:0.1:1.4 ;

sigma2 = 0.1:0.1:10 ;

sigma3 = 8.5:0.1:10 ;

sigma23 = 9.2:0.1:10 ;

Friction = (f_vk0 + mu_k * sigma1) / (1 + mu_k * 2 * Forhold) ;

Tension_failure = f_bt / 2.3 * sqrt(1 + sigma2/f_bt) ;

Compression_failure = (f_k - sigma3) * 1/Forhold*(1/2) ;

Friction2 = (f_vk0 + mu_k * sigma1) / (1 + mu_k * 2 * Forhold2) ;

Tension_failure = f_bt / 2.3 * sqrt(1 + sigma2/f_bt) ;

Compression_failure2 = (f_k - sigma23) * 1/Forhold2*(1/2) ;

figure()

hold on

plot(sigma1, Friction,'--','Color',[0.4660 0.6740 0.1880])

plot(sigma2, Tension_failure,'--','Color',[0.9290 0.6940 0.1250])

plot(sigma3, Compression_failure,'--','Color',[0.4940 0.1840 0.5560])

plot(sigma1, Friction2)

plot(sigma2, Tension_failure,'Color',[0.6350 0.0780 0.1840])

plot(sigma23, Compression_failure2,'Color',[0.8500 0.3250 0.0980])

% Shade the area between [sigma1, Friction] and [sigma1, Friction2]

fill([sigma1, fliplr(sigma1)], [Friction, fliplr(Friction2)], [0.7 0.7 0.7], 'EdgeColor', 'none');

grid on;

Answer 1

[Mathieu NOE]

hello

you need to compute the intersections points - for that I am using the function in attachment (intersections.m , found that on the FEX page but may not be the only solution)

Fast and Robust Curve Intersections - File Exchange - MATLAB Central (mathworks.com)

then use those points to redefine the area to fill

Forhold = 1/2 ;
Forhold2 = 54/228;
f_vk0 = 0.4 ; % Klæbningsbidrag [MPa]
mu_k = 0.65 ; % Friktionskoefficient
f_bt = 1.00 ; % Trækstyrke af sten [MPa]
f_k = 10.00 ; % Trykstyrke af sten [MPa]
sigma1 = -0.0:0.1:1.4 ;
sigma2 = 0.1:0.1:10 ; 
sigma3 = 8.5:0.1:10 ;
sigma23 = 9.2:0.1:10 ;
Friction = (f_vk0 + mu_k * sigma1) / (1 + mu_k * 2 * Forhold) ;
Tension_failure = f_bt / 2.3 * sqrt(1 + sigma2/f_bt) ;
Compression_failure = (f_k - sigma3) * 1/Forhold*(1/2) ;
Friction2 = (f_vk0 + mu_k * sigma1) / (1 + mu_k * 2 * Forhold2) ;
Tension_failure = f_bt / 2.3 * sqrt(1 + sigma2/f_bt) ;
Compression_failure2 = (f_k - sigma23) * 1/Forhold2*(1/2) ;
figure()
hold on
plot(sigma1, Friction,'--','Color',[0.4660 0.6740 0.1880])
plot(sigma2, Tension_failure,'--','Color',[0.9290 0.6940 0.1250])
plot(sigma3, Compression_failure,'--','Color',[0.4940 0.1840 0.5560])
plot(sigma1, Friction2)
plot(sigma2, Tension_failure,'Color',[0.6350 0.0780 0.1840])
plot(sigma23, Compression_failure2,'Color',[0.8500 0.3250 0.0980])

% Shade the area between [sigma1, Friction] and [sigma1, Friction2]
[x0,y0,~,~] = intersections(sigma1,Friction,sigma2, Tension_failure);
ind = (sigma1<x0);
sigma1b = [sigma1(ind) x0]; % add x0 of true intersection point
Frictionp = [Friction(ind) y0]; % add y0 of true intersection point
[x1,y1,~,~] = intersections(sigma1,Friction2,sigma2, Tension_failure);
ind = (sigma1<x1);
sigma1c = [sigma1(ind) x1]; % add x1 of true intersection point
Friction2p = [Friction2(ind) y1]; % add y1 of true intersection point

% fill([sigma1, fliplr(sigma1)], [Friction, fliplr(Friction2)], [0.7 0.7 0.7], 'EdgeColor', 'none');
fill([sigma1b, fliplr(sigma1c)], [Frictionp, fliplr(Friction2p)], [0.7 0.7 0.7], 'EdgeColor', 'none');
grid on;