how to convert creep curve to relaxation curve for viscoelastic material?

[tomyliu]

Dear all
I have obtained the master compliance creep curve of epoxy by experiment,
it can be fitted with prony series using 12 terms.
dose anyone know how to convert it to relaxation curve?
when i using laplace convert, I found it have large error.
are there some other convenient method?

[Jorgen]

It sounds like you already have the Prony series, which means that you can directly calculate the relaxation modulus. There is no need use a Laplace transform even.
If the predicted relaxation behavior is in poor agreement with experimental data then you may need a large time range for the creep data, or perhaps your epoxy material is not linear viscoelastic.

-Jorgen

[tomyliu]

thanks for your reply,Jorgen!
Sorry maybe I have not expressed my idea clearly, I mean that the compilance curve can be fited by 12 term series,
D(t)=D0+SIGMA(j=1 to 12)Dj(1-EXP(-t/Taoj)),

while the modulus
E(t)=E0+SIGMA(i=1 to n)Ei(1-EXP(-t/Raoj)),

however I did not obtain the ralaxation modulus curve, and could not fit it.
somebody says that the Taoj not equal to Raoj, also maybe n is not equal to 12, I am a beginer of viscoelastic, not sure about this.
I want find out the relaxation curve by some methoed, can you help me.

Logt (s) ---- D(t) (1/MPa)
-0.956294079 ---- 0.040421401
-0.721454512 ---- 0.040430359
-0.486565574 ---- 0.04057135
-0.251588238 ---- 0.040572975
-0.016502606 ---- 0.04082148
0.218680006 ---- 0.04088098
0.453909138 ---- 0.041149837
0.68908379 ---- 0.04132727
0.924085872 ---- 0.041531074
1.158844366 ---- 0.04188418
1.393340427 ---- 0.041938841
1.627592347 ---- 0.042527017
1.861648301 ---- 0.0432312
2.095578875 ---- 0.043971939
2.329457369 ---- 0.044727324
2.563293364 ---- 0.045494422
2.797064368 ---- 0.046279086
3.030746083 ---- 0.047087253
3.264313477 ---- 0.04792454
3.497736962 ---- 0.048797085
3.73098652 ---- 0.049710401
3.964018279 ---- 0.050672259
4.196651025 ---- 0.051716891
4.428588646 ---- 0.052891609
4.659436968 ---- 0.054244736
4.888650049 ---- 0.055827161
5.115532178 ---- 0.057686101
5.339148894 ---- 0.059870812
5.558762465 ---- 0.062394187
5.774718993 ---- 0.065187256
5.987792185 ---- 0.068172975
6.198992609 ---- 0.071276101
6.409414032 ---- 0.074426477
6.620238228 ---- 0.077552542
6.832537236 ---- 0.080587499
7.046616684 ---- 0.083508119
7.262048843 ---- 0.086338141
7.478405379 ---- 0.089104208
7.695306897 ---- 0.091831742
7.912353693 ---- 0.094548891
8.129175258 ---- 0.097282114
8.345473113 ---- 0.100052313
8.561249714 ---- 0.102858773
8.77653026 ---- 0.105699226
8.991396791 ---- 0.108567683
9.20588702 ---- 0.111461309
9.420072835 ---- 0.114375107
9.634008268 ---- 0.117305369
9.847767671 ---- 0.120247141
10.06139092 ---- 0.123197778
10.27496202 ---- 0.126151804

[Jorgen]

It is not trivial to go from creep data to a Prony series (stress relaxation data). What FE software do you use?

Also, MCalibration (http://polymerfem.com/content.php?9-MCalibration) may be able to help since it can calibrate a Prony series directly to creep data without the need for a Laplace transform.

-Jorgen

[tomyliu]

thanks Jorgen, I use ABAQUS.
since creep data is more easy to be obtained than relaxation data, also i know abaqus can fit normallized creep data to prony series, but I often get
less terms than 12 with poor fit, i do not know the tricks. so i want convert creep data to prony series by some other methoed.