# Constitutive behavior of elasto-plastic vs visco-elastic?

1. Aug 2, 2015

### PinkGeologist

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 same material is modeled as visco-elastic, does any "yield strength" even apply, or do you see some visco-elastic strain over time (and under some load of course, with intervals of deviatoric stress) and thus capture some "extra" details (I don't think "creep" is important because we are talking about the Maxwell treatment).

I have been combing the web and YouTube for a CLEAR and TOTAL distinction between the two and I only find tidbits.

(if you care, the material we are discussing is Earth's crust, heated in the area of a magma chamber, which applies intervals of "excess pressure" to the crust around it when it is being actively filled with magma from below and expanding as gases exsolve).

2. Aug 2, 2015

### NaOH

I don't have any knowledge in area this but maybe this link will help?
In particular, it mentions that for elastic materials it does not dissipate energy, but visco-elastic materials do.

3. Aug 5, 2015

### caz

It's a question of relaxation times and the timescale of the physics you are interested in. If the crust has enough time to relax then you need a visco model. However, if the relaxation is due to thermal softening due to heat transport, you could probably get away with elastic plastic model with thermal softening. The important thing to realize is that most constitutive models are not universal. They are calibrated for a particular regime.

4. Aug 5, 2015

### PinkGeologist

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 in (The surface over a volcano is lifted by 2-16 cm over a period of 2-3 years while the chamber pressurizes).

I think I may not fully understand what that 10^-8 seconds represents.

5. Aug 6, 2015

### caz

I was poking around the web. According to http://www.annualreviews.org/eprint/awH6WGKdJr9HSHgYATuy/full/10.1146/annurev.earth.36.031207.124326 "The rheology of the upper crust appears well described by linear elastic relations between stress and strain ... at stresses lower than those required to induce brittle fracture of intact rock or frictional sliding of faults. Deformation at higher temperatures and pressures involves both elastic (at short timescales) and viscous behavior."

6. Aug 6, 2015

### caz

BTW, wave propagation models can be problematic for deformation because they need to account for a lot of high frequency stuff over very long distances. For yield surfaces, the strength of intact rock is significantly higher at low pressures than the strength from frictional sliding.