I think that this could be explained. - If we perform the integration of the constitutive equation, we can do it ... somehow like a recipe. ... But, if we are about to let DeltaTau --> 0, we have to care about the values of the functions:
For the first term, we know that any sigma is a constant...
Uh ... that was it.
Now I got the solution ... unfortunately I am not sure, whether I really understood the background of this procedure (the 'why' to integrate the constitutive equation) as well as the things, I mentionned in the following:
The constitutive equation is:
\sigma +...
So you mean, i should solve (with z = dε/dt):
\sigma_0 = (\eta_1+\eta_2)\cdot z + \frac{E_1+E_2}{E_1\cdot E_2}\cdot \eta_1\cdot\eta_2 \dot z
for z?! Why?
I can't really follow ... I've already solved the whole constitutive equation (seperately for the homogeneous and for the particular part)...
That might be true ... yes.
Mhhm ... seems that I have to think over the whole procedure again ... But: there's one question remaining and maybe you have a hint for me. It's this "ominous" point "5.c." in this script I mentionned above. There it says (concerning the model which consists of two...
... I see.
But, ... do you think that there exist an analytical solution for the problem? (Even if there are later on some stress-changes when there's a more complex creep-test performed?)
(Some weeks ago I tried it to solve the whole ODE by Laplace Transform; unfortunately this wasn't very...
Hello Chet,
thanks a lot for your reply.
[unfortunately] I have to solve it (for each time-step) in the exact form (I just can move to numerical methods, if there's no way round) ...
this evening, I found an interesting script with some examples for rheological models in solid mechanics...
Hello guys,
actually I'am working on a model to describe the creep-behaviour of a concrete specimen. This model is based on a 'generalized maxwell-chain'. I attached a picture, where you can see it:
The acting load is the tension \sigma, while E_0 and E_1 are the stiffnesses of the...