June 03, 2024, 08:55:37 AM
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Topic: Maxwell model of viscoelastic behaviour - Derivation of governing equation  (Read 5652 times)

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Offline mark_d89

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Hi everyone,

i'm a 3rd year undergraduate chemical engineering student from Scotland, and i am wondering if anyone could help me with the following past paper question in my plastics engineering class. The question is based on the maxwell model of viscoelastic behaviour. Apologies if i have posted in the wrong section.

"In a tensile test on a plastic the material is subjected to a constant strain rate of 10^-5/s. The material may have it's behaviour modelled by a maxwell element with elastic constant 20GN/m^2 and viscous constant 1000 GNs/m^2.
(a) Starting from the governing equation for a maxwell element, derive the following expression for the stress in the material at any instant.    stress=n2*strain*[1-exp(-G1*t/n2)]"
...

I have derived the governing equation down to the point,  stress(t)=stress0*exp(-G1*t/n2) , but have not been able to get it to resemble the equation shown in the question. I'll attach a picture of the question for more clarity.

Any help is much appreciated, Thanks

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