Discussion Forum

Hi

have you tried to define the material as anisotropic , in the physics node ?

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Good luck
Ivar

Just select "Equation View", then you can input directly all 36 elements of the elasticity tensor with whatever you want.

Hi Ivar and

Yes, I did. but the anisotropic elasticity matrix still assumes symmetrical tensor. What I need is to define all the elements separately.

for example in my case s12 is not equal to s21.

Thanks

Hi

have you tried to define the material as anisotropic , in the physics node ?

--
Good luck
Ivar

Hi,

A material with unsymmetric stress tensor ("Cosserat elasticity") is rather uncommon, and cannot be modeled using the built-in functionality in COMSOL Multiphysics. All operations assume a symmetric stress tensor.

You can implement it on your own, using either the Physics Builder (as suggesteed by Ivar) or just weak form PDE:s.

There is a paper written about such an implementation:

Jena Jeong and Hamidreza Ramezani: Implementation of the Finite Isotropic Linear Cosserat Models based on the Weak Form. (COMSOL conference 2008)

www.comsol.com/papers/5073/

Regards,
Henrik

Hi,

Actually you can still build on Solid Mechanics. Just do the following:

1. Add one Solid Mechanics and one PDE physics interface.
2. Use the same degree of freedom names in both (u,v,w)
3. Set Young's modulus to zero in Solid Mechanics so that there is no stiffness contribution.

Now you can use all loads and boundary conditions (including the Floquet conditions) from Solid Mechanics. Your PDE interface only needs to implement the material model replacing Linear Elastic.

An alternative is to not add the PDE physics interface at all. Just define all your variables, and add a weak contribution under Solid Mechanics for the internal virtual work. You can also reuse some of the variables like parts of the strain, since they will be defined by the Linear Elastic feature.

Regards,
Henrik

Hi Henrik

many thanks for your comments

On your first approach:

1- COMSOL doesn't allow me to have similar names for dependent variables of two interfaces:

I tried to define the PDE's degrees of freedom (u2,v2,w2) as variables equal to (u,v,w) of (elastic wave interface)

However, I have no idea which one is correct: (u,v,w)=(u2,v2,w2) or (u2,v2,w2)=(u,v,w)??!!

2- should I use the same study for both and couple both? or I need to solve the PDE first?

On your second approach

Didn't 100% understand the approach

Do I need to define the weak forms of the problem from sctratch or just add the extra terms for S21 and S31 in the weak contribution?

Hi Henrik

many thanks for your comments

On your first approach:

1- COMSOL doesn't allow me to have similar names for dependent variables of two interfaces:

I tried to define the PDE's degrees of freedom (u2,v2,w2) as variables equal to (u,v,w) of (elastic wave interface)

However, I have no idea which one is correct: (u,v,w)=(u2,v2,w2) or (u2,v2,w2)=(u,v,w)??!!

2- should I use the same study for both and couple both? or I need to solve the PDE first?

On your second approach

Didn't 100% understand the approach

Do I need to define the weak forms of the problem from sctratch or just add the extra terms for S21 and S31 in the weak contribution?

Hi Alireza,

As it seems that the second approach is the easier, I will focus on that.

1. By setting E=0 in Linear Elastic, you will suppress the whole contribution to the virtual work from the stresses (=the stiffness matrix). The contribution to the mass matrix is still generated, though.

2. All nine components of your stress tensor will need to be defined as variables. So will also 'strain' variable like Cosserat stretch and curvature.

3. Make sure that Show->Advanced Physics Options is selected.

4. At the domain level add More->Weak Contribution.

5. In the Weak expression, fill in the complete virtual work expression for the Cosserat material. The syntax is just as the one you see in equation view under Linear Elastic, i.e. a sum of terms like

my_stress11*test(my_strain11) + ...

6. You can add several Weak contribution features and split the weak contribution into several terms to improve readability. The number of terms in the Cosserat formulation is rather large, since there are the curvature terms as well as the unsymmetric tensors.

It may be possible to keep the Linear Elastic contributions, and only add the 'additional' terms in your own weak expressions, but that will probable be more obscure.

Regards,
Henrik