[GeomechanicsApplication] Add documentation for compression cap#14348
[GeomechanicsApplication] Add documentation for compression cap#14348mnabideltares wants to merge 4 commits intomasterfrom
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WPK4FEM
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WPK4FEM
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Hi Mohamed,
Please find my comments.
Wijtze Pieter
| ```math | ||
| A = 1 + b_1 a_2^2 | ||
| ``` | ||
| ```math | ||
| B = -2 b_1 a_2 c_2 | ||
| ``` | ||
| ```math | ||
| C = b_1 c_2^2 - c_1 | ||
| ``` | ||
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| ```math | ||
| b_1 = 1 / X^2 | ||
| ``` | ||
| ```math | ||
| c_1 = p_c^2 | ||
| ``` | ||
| ```math | ||
| a_2 = \frac{6 \sin{\phi}}{3 - \sin{\phi}} | ||
| ``` | ||
| ```math | ||
| c_2 = \frac{6 c \cos{\phi}}{3 - \sin{\phi}} | ||
| ``` |
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The many intermediate variable definitions are more a programming aid than making it more readable for me.
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I tried to show how the second order polynomian equation was derived, to be able to follow the process if it will be necessary in the future. So, I tried to include the intermediate process. What do you think about it?
| We define the following vectors, | ||
| ```math | ||
| \Delta \sigma = \left[\sigma_1 - \sigma_2 \; , \; \sigma_2 - \sigma_3 \; , \; \sigma_3 - \sigma_1 \right]^T | ||
| ``` | ||
| ```math | ||
| \Delta \sigma^{cor} = \left[\sigma_1^{cor} - \sigma_2^{cor} \; , \; \sigma_2^{cor} - \sigma_3^{cor} \; , \; \sigma_3^{cor} - \sigma_1^{cor} \right]^T | ||
| ``` |
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Naming these differences "Delta" is confusing for me. In return mapping the Delta sigma is usually a stress increment.
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What do you suggest for naming?
| ``` | ||
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| ### Return mapping from cap corner zone | ||
| The cap compression zone is the rigion where the trial principal stresses are, |
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| The cap compression zone is the rigion where the trial principal stresses are, | |
| The cap compression zone is the region where the trial (p, q) stress invariants are demarcated by the following two lines, |
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I still find "rigion" on that line.
| Subsituting the stresses with the mapped stresses, we get the following relations. | ||
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| ```math | ||
| A = \frac{\Delta \sigma^{cor} \cdot \Delta \sigma^{cor}}{2 X^2} + \frac{1}{9} \left( \sum_{i=1}^3{\sigma_i^{cor}} \right)^2 |
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Then \sum sigma_i / 3 looks like p^{cor}, but that would lead to a confusing mix of principal stresses and p,q stress invariants.
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\sigma^{cor} is defined beforehand, in line 265.
However, if you think it is still confusing, what do you suggest?
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📝 Description
The formulations for the compression cap and its intersection with Coulomb yield surface, and return mappping need to be documented.
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