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mvanzulli merged 17 commits into from
Feb 4, 2023
Merged

Add Uniaxial compression into docs #600

mvanzulli merged 17 commits into from
Feb 4, 2023

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@mvanzulli mvanzulli commented Feb 3, 2023 •
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Closes #599
Deploy: docs

Just a detail: PR number = 600 💯 🚀 🤓

@mvanzulli mvanzulli requested a review from jorgepz February 3, 2023 23:36
@mvanzulli mvanzulli marked this pull request as ready for review February 3, 2023 23:36
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mvanzulli commented Feb 3, 2023 •
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I have solved the problem considering different neo-Hookean models but I couldn't find the one who gives me the cosserat stress tensor implemented in ONSAS. I have tried with:

$$\Psi(\mathbf{C}) = \frac{\mu}{2} (I_1 - 3) - \mu \ln(J) + \frac{\lambda}{2} \ln(J)^2,$$

and

$$\Psi(\mathbf{C}) = \frac{\mu}{2} (I_1 - 3 - 2\ln(J))$$

Here are some useful identities that I have used:

$$\mathbf{S} = 2 \frac{\partial \Psi }{ \partial \mathbf{C} }$$ $$\frac{\partial tr(\mathbf{C})}{\partial \mathbf{C}} = \mathbf{I}\\$$$$ $$\frac{\partial det(\mathbf{C})}{\partial \mathbf{C}} = det( \mathbf{C} ) \mathbf{C}^{-T}$$

Ohh I think I found it:

$$\Psi(\mathbf{C}) = \frac{\mu}{2}(I_1 -3) + 1/D (J -1)^2$$

then Cosserat is:

$$\mathbf{S} = 2 \frac{\partial \Psi }{\partial \mathbf{C}} = \mu (I_{3,3}) + \frac{2}{D}(J-1) J C^{-T}$$

but in ONSAS we have:

S       = shear * ( eye(3) - invC ) + bulk * ( J * (J-1)* invC) ;

with $K(bulk) = D/2$
@jorgepz ?

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jorgepz commented Feb 4, 2023 •
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Excellent! You found the strain energy function, it is the isotropic term in Equation 2 in this paper.

To obtain the cosserat derivative it could be useful to see that

$$det(C) = J^2$$

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mvanzulli and others added 10 commits February 4, 2023 11:36
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Update examples/uniaxialCompression/uniaxialCompression.m
bf1bc3e 
Co-authored-by: Jorge Pérez Zerpa <42485529+jorgepz@users.noreply.github.com>
@mvanzulli @jorgepz
Update examples/uniaxialCompression/uniaxialCompression.m
b4f1670 
Co-authored-by: Jorge Pérez Zerpa <42485529+jorgepz@users.noreply.github.com>
@mvanzulli @jorgepz
Update examples/uniaxialCompression/uniaxialCompression.m
949b785 
Co-authored-by: Jorge Pérez Zerpa <42485529+jorgepz@users.noreply.github.com>
@mvanzulli @jorgepz
Update examples/uniaxialCompression/uniaxialCompression.m
123fb45 
Co-authored-by: Jorge Pérez Zerpa <42485529+jorgepz@users.noreply.github.com>
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Update examples/uniaxialCompression/uniaxialCompression.m
5d98444 
Co-authored-by: Jorge Pérez Zerpa <42485529+jorgepz@users.noreply.github.com>
uniaxial compression msh (#599)
0c52402
uniaxial compression plot (#599)
27f06ae
uniaxial compression plot deploy (#599)
81ae14a
uniaxial compression plot deploy(#599)
a3dadbf
fixed uniaxial compression plot (#599)
85e62dd
@mvanzulli mvanzulli merged commit eb98e6f into master Feb 4, 2023
@mvanzulli mvanzulli deleted the mvanzulli/UniaxialCompression branch February 4, 2023 15:53
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Add uniaxial compression into docs

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