# Plot summation series | For Loop | Creep Strain

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mpz on 10 Apr 2022
Commented: VBBV on 10 Apr 2022
Hi,
Need some assistance in plotting the below equation. I don't know why it is not coming out right. Below is my code and the plot below shows the expected results. Appreciate any feedback.
See picture at the bottom for equation to plot (strain vs time)
t=0:10000 (in seconds)
sigma0=100 MPa
D0= 360e-6 MPA^-1
D1=11.05e-6 MPa^-1; tr1=10 s;
D2=12.27e-6 MPa^-1; tr2=100 s;
D3=17.35e-6 MPa^-1; tr3=1000 s;
D4=21.63e-6 MPa^-1; tr4=10000 s;
D5=13.13e-6 MPa^-1; tr5=100000 s;
D6=41.78e-6 MPa^-1; tr6=1000000 s;
r in the summation series goes from r=1 to r=6 representing the D1,D2,D3,D4,D5,D6 clear all;clc
%% Linear Creep Example
s=100; % constant tensile stress, (MPa)
t=linspace(0,10000,11); % duration of applied stress on specimen (seconds)
D=[11.05e-6 12.27e-6 17.35e-6 21.63e-6 13.13e-6 41.78e-6]; % Prony series coefficients, (MPA^-1)
ta=[10 100 1000 10000 100000 1000000]; % seconds
% D1=11.05e-6;ta1=10;
% D2=12.27e-6;ta2=100;
% D3=17.35e-6;ta3=1000;
% D4=21.63e-6;ta4=10000;
% D5=13.13e-6;ta5=100000;
% D6=41.78e-6;ta6=1000000;
% strn=s*(D(1)*(1-exp(-t(1)/ta(1))) + D(2)*(1-exp(-t(1)/ta(2))) + D(3)*(1-exp(-t(1)/ta(3)))...
% + D(4)*(1-exp(-t(1)/ta(4))) + D(5)*(1-exp(-t(1)/ta(5))) + D(6)*(1-exp(-t(1)/ta(6))));
strn=zeros(1,11);
for i=1:11
for n=1:6
strn(i)=s*(D(n)*(1-exp(-t(i)/ta(n))));
end
end
plot(t,strn)

VBBV on 10 Apr 2022
Edited: VBBV on 10 Apr 2022
clear all;clc
%% Linear Creep Example
s=100; % constant tensile stress, (MPa)
t=linspace(0,10000,11); % duration of applied stress on specimen (seconds)
D=[11.05e-6 12.27e-6 17.35e-6 21.63e-6 13.13e-6 41.78e-6]; % Prony series coefficients, (MPA^-1)
ta=[10 100 1000 10000 100000 1000000]; % seconds
% D1=11.05e-6;ta1=10;
% D2=12.27e-6;ta2=100;
% D3=17.35e-6;ta3=1000;
% D4=21.63e-6;ta4=10000;
% D5=13.13e-6;ta5=100000;
% D6=41.78e-6;ta6=1000000;
% strn=s*(D(1)*(1-exp(-t(1)/ta(1))) + D(2)*(1-exp(-t(1)/ta(2))) + D(3)*(1-exp(-t(1)/ta(3)))...
% + D(4)*(1-exp(-t(1)/ta(4))) + D(5)*(1-exp(-t(1)/ta(5))) + D(6)*(1-exp(-t(1)/ta(6))));
strn=zeros(1,11);
for i=1:11
for n=1:6
strn(n,i)=(D(n)*(1-exp(-t(i)/ta(n)))); % multiply the s outside the summation
end
Strn(i) = s*sum(strn(:,i)); % multiply with s here
end
plot(t,Strn) Multiply with s outside of the summation.
mpz on 10 Apr 2022
@VBBV @Akira Agata you both got it right. @VBBV you got it right first.

Akira Agata on 10 Apr 2022
s = 100; % constant tensile stress, (MPa)
t = linspace(0, 10000)'; % duration of applied stress on specimen (seconds)
D = [11.05e-6 12.27e-6 17.35e-6 21.63e-6 13.13e-6 41.78e-6]; % Prony series coefficients, (MPA^-1)
ta = [10 100 1000 10000 100000 1000000]; % seconds
dim = 2;
strn = s*sum(D.*(1-exp(-1*t./ta)), dim);
figure
plot(t, strn)
xlabel("Time [sec]")
ylabel("Strain \epsilon(t)") ##### 2 CommentsShowHide 1 older comment
VBBV on 10 Apr 2022
Yes,by adding an offset Do, your code seems to produce what you have shown in the figure.

R2021b

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