Plot summation series | For Loop | Creep Strain

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)

Answer 1

[VBBV]

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]

@VBBV @Akira Agata you both got it right. @VBBV you got it right first.

Answer 2

[Akira Agata]

How about the following?

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)")

[mpz]

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*Do+s*sum(D.*(1-exp(-1*t./ta)), dim);

figure
plot(t, strn)
xlabel("Time [sec]")
ylabel("Strain \epsilon(t)")

@Akira Agata and @VBBV I believe this should solve my problem

[VBBV]

Yes,by adding an offset Do, your code seems to produce what you have shown in the figure.