Hysteresis curve and envelope

I am trying to plot the backbone curve of the hysteresis curve shown in the figure below. I roughly sketched a black line showing what the backbone curve should look like. The curve plots the minimum force for displacement<0 and the maximum force for displacement>0. I attached the data force (column 1) and displacement (column 2) data. I think a for loop would work for the curve, but I don't know how to structure it. *Code is below

%Column 2 Force vs Displacement
clc;clear;close all;
%Transverse Force
h=load('InputForceDisp.txt');
f=h(:,1); %force
d=h(:,2); %displacement

for i=min(d):max(d)
    x=linspace(min(d),max(d),length(d));
    if x<=0
        y=min(f(i))
    else 
        y=max(f(i))
    end
end
%Values used to sketch approximate curve
xapp=[-5.484, -4.021, -2.655, -0.6775, -0.1959, 0, 0.1914, 1.582, 1.993, 2.29, 2.526];
yapp=[-27.69, -26.23, -25.17, -21.04, -10.25, 0, 11.88, 16.73, 17.09, 14.81, 11.85];

h=figure(18);
hold on 
plot(d,f,'r','LineWidth',0.5)
plot(x,y,'b','LineWidth',1)
plot(xapp,yapp,'k','LineWidth',1.5)
hold off
xlabel('displacement [in]'); ylabel('force [k]'); grid on;

Answer 1

[Mathieu NOE]

hello Emily

this is how I solved it (blue curve)

hope it helps

%Column 2 Force vs Displacement
clc;clear;close all;
%Transverse Force
h=load('InputForceDisp.txt');
f=h(:,1); %force
d=h(:,2); %displacement
% for i=min(d):max(d)
%     x=linspace(min(d),max(d),length(d));
%     if x<=0
%         y=min(f(i))
%     else 
%         y=max(f(i))
%     end
% end
%Values used to sketch approximate curve
xapp=[-5.484, -4.021, -2.655, -0.6775, -0.1959, 0, 0.1914, 1.582, 1.993, 2.29, 2.526];
yapp=[-27.69, -26.23, -25.17, -21.04, -10.25, 0, 11.88, 16.73, 17.09, 14.81, 11.85];
h=figure(18);
hold on 
plot(d,f,'r','LineWidth',0.5)
% plot(x,y,'b','LineWidth',1)
plot(xapp,yapp,'k','LineWidth',1.5)
xlabel('displacement [in]'); ylabel('force [k]'); grid on;

%% create boudary curve data
shrink_factor = 0.5;
k = boundary(d,f,shrink_factor);
dk = d(k);
fk = f(k);

% upper right segment selection
ind_up = find(dk>min(dk)/2 & [diff(dk); 0]< 0);
dk1 = dk(ind_up);
fk1 = fk(ind_up);
dk2 = linspace(0.2,max(dk1),10);
fk2 = interp1(dk1,fk1,dk2);


% lower left segment selection
ind_low = find(dk<0 & [diff(dk); 0]> 0);
dk3 = dk(ind_low);
fk3 = fk(ind_low);
dk4 = linspace(min(dk3),min(0,max(dk3)),10);
fk4 = interp1(dk3,fk3,dk4);



% join the two segments 
dkk = [dk4 dk2];
fkk = [fk4 fk2];

plot(dkk,fkk,'b','LineWidth',2.5);

hold off

[Felix Bouffard]

This is really helpful ! Quick question, how would you solve it to have the blue curve in the lower left segment to be sitting on the curve at the maximum negative force instead of the maximum negative displacement ?