Hi Minh,

On 25.5.2018 16:03, Minh Nguyen wrote:

Hi Cimrman,

You are right; your excellent answer fits to my question. You can see the attachment file for my restate problem. I am solving the 2 scale problem where I homogenize the heterogeneity in microstructure at each Gauss quadrature point. The method in 2 scale is Finite Element Method for 2 BVPs.

I have run the nonlinear_hyperelastic_mM.py and it takes a bit long time to get results and I believe that this is in 2-scale solutions even though to be honest I do not fully understand the code and its sub classes, sub functions. However, I might doubt if the method you used to solve is FE^2 formerly addressed by F. Feyel [1] as I remember because I aim to this method. Could you give me a description or references for the problem in nonlinear_hyperelastic_mM.py ?

The nonlinear homogenization problem implemented in SfePy is briefly explained in the attached articles.

Second, I do not understand the sentence you said "because as the large deformation proceeds, a micro-RVE in each quadrature point deforms differently and the initial global periodicity is lost". Why the initial global periodicity is lost? If it is lost how to establish the BVP in microstructure?

The microscopic responses (correctors or corrector functions) computed at the microlevel (within the RVE) are periodic, so the BVP is solved with the periodic boundary conditions, see the attached articles.

As I understand you are saying in the context of large deformation in which the weak form is established under the current configuration, not initial configuration as usual. Is it right?

Thank you for your kind support,

Best regards, Minh Nguyen

[1] https://www.sciencedirect.com/science/article/pii/S0045782503003487

On Thu, May 24, 2018 at 11:28 AM, Robert Cimrman <cimrman3@ntc.zcu.cz <mailto:cimrman3@ntc.zcu.cz>> wrote:

Hi Minh,

On 05/23/2018 05:30 PM, Minh Nguyen wrote:

    Dear,

    Recently I have used SfePy for the computational homogenization
    and I found
    that SfePy has offered the homogenization component. Thanks for
    that.
    However, this feature is only for microscopic structure that
    means the
    simulation is for an RVE (Representative Volume Elements) with the
    deformation gradient or strain in the context of solid mechanics
    as the
    input to set boundary conditions for microscopic structure.

    In my work, I simulate a structure made of the inhomogeneous
    materials.
    This means that at each Gauss points in computing of stiffness
    matrix we
    compute the average stress and effective moduli by simulating the
    microscopic RVE (this feature is already available in SfePy).
    However, In
    SfePy we set up a material object with its parameters at the
    beginning and
    call or setup a *terms *file.

    Do you know the solution or the way using terms feature to
    compute the
    homogenization in macro scale?


Solving a (different) micro-level problem in each macro-level
quadrature point is possible (if that's what you ask for). For
example, the large deformation homogenization [1] uses this feature,
because as the large deformation proceeds, a micro-RVE in each
quadrature point deforms differently and the initial global
periodicity is lost.

If you refine your question, maybe we (especially Vladimir) can
provide more answers.

Cheers,
r.

[1]
http://sfepy.org/doc-devel/examples/homogenization/nonlinear_hyperelastic_mM.html
<http://sfepy.org/doc-devel/examples/homogenization/nonlinear_hyperelastic_mM.html>
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Regards, Vladimir