Homogenization in macroscopic and microscopic
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?
Thanks and Best Regards, Minh Nguyen
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) microlevel problem in each macrolevel 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 microRVE 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/docdevel/examples/homogenization/nonlinear_hyperelastic_mM...
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 2scale 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 ?
Second, I do not understand the sentence you said "because as the large deformation proceeds, a microRVE 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? 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 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) microlevel problem in each macrolevel 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 microRVE 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/docdevel/examples/homogenization/nonlinear _hyperelastic_mM.html _______________________________________________ SfePy mailing list sfepy@python.org https://mail.python.org/mm3/mailman3/lists/sfepy.python.org/
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 2scale 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 microRVE 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) microlevel problem in each macrolevel 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 microRVE 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/docdevel/examples/homogenization/nonlinear_hyperelastic_mM.html <http://sfepy.org/docdevel/examples/homogenization/nonlinear_hyperelastic_mM.html> _______________________________________________ SfePy mailing list sfepy@python.org <mailto:sfepy@python.org> https://mail.python.org/mm3/mailman3/lists/sfepy.python.org/ <https://mail.python.org/mm3/mailman3/lists/sfepy.python.org/>
SfePy mailing list sfepy@python.org https://mail.python.org/mm3/mailman3/lists/sfepy.python.org/
Regards, Vladimir
participants (3)

Minh Nguyen

Robert Cimrman

Vladimír Lukeš