I calculated the relaxation time and it is on the order of 10^-8 s ... I am having a hard time understanding the PHYSICAL meaning of relaxation time. Are we saying the crust relaxes in << 1 second? Because I can't see how that would even be worth considering on the timescales we are interested...
Is strain always recoverable in a viscoelastic solid?
For instance, I thought in the single-branch Maxwell model, there was unrecoverable strain ... or am I wrong?
And then if you use a two branch Maxwell model (one spring, one spring + dashpot), all strain must be recoverable, correct?
If someone were to ask you to define the difference, what would you said? (to justify modeling a material one way or the other)
In an elasto-plastic solid you see permanent deformation after the yield strength is breached as a function of ... stress, right? (in the von Mises regime).
If the...
Many rocks of the composition I'm interested in have undergone stress-strain testing in laboratory conditions that show plastic behaviors under the high confining pressure we see in the Earth's crust ... and for confining pressures up to nearly 100 MPa the behavior is nearly ideally plastic ...
Consider a magma chamber in the Earth's crust ... models show that 1-2 km surrounding this chamber are heated above the brittle-ductile transition zone.
Let's say that you know the yield strength of the crust in general (not heated) is 15 MPa ... and after that, rocks under heavy confining...
So, I was introduced tangentially to plastic deformation and hardening functions. I see we have three basic function ... and the linear and kinematic seem to be the most common defaults ... I see it is a measure of the strain of a material under stress.
But how would you know which version to...
Ok, I've built a numerical model to show the cooling of hot magma sills entered into the crust over time. The results show that the volume of the "hot" zone when the emplacement of a constant volume of hot sills is all done will vary as a matter of two things: the overall rate at which the magma...
Imagine you inject a 16km high stack of magma in the Earth's crust continuously over X years and then analyze the size and shape of the final "hot zone" as your "result" ... let's say you want to quantify the volume of crust at a temperature (T) greater than 1000 Kelvin (K). In case 1, that...
Well, the only analytical comparisons I've made is for cooling of a single sill ... I'm not sure how I'd implement a simple analytical solution to capture the dynamic situation of a deceleration of the cooling rate with the increased surrounding temperature as well as the different dull heights...
I apologize - when I say "40, 400m-high sills" that means there are 40 total sills, each of them 400 meters thick and emplaced at some rate (from 0.0005 to 0.04 meters per year).
I'll also look into moving the post.
I know there must be some kind of "sweet spot" where the repose time between sill-injections and the heat retention of the magma intercept to create a more robust hot zone, but I don't have a pinpoint on exactly why and how to articulate it.
I am modeling the injection of hot magma sills into the Earth's crust at varying rates (and varying sill heights for each rate).
For instance, for a total of 16 km of magma ...
1a-n. 40, 400m high sills emplaced at rate of 5e-3 ma-1, 5e-4 ma-1, 1e-2 ma-1, , 2e-2 ma-1, 3e-2 ma-1, and 4e-2...