Multiscale method with model reduction

Julien Yvonnet's picture

Model reduction based on Propper Orthogonal decomposition is widely used in Computational mechanics to reduce the number of degrees of freedom in systems. In the attached papers, we introduced a POD-based model reduction in a multiscale framework to significantly reduce the computations.


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[12] R3M.pdf1.75 MB
[17] R3M thermique.pdf727.22 KB
vinh phu nguyen's picture

Very interesting work

Hi Julien,

I am working on homogenization-based multiscale modelling of failure in the spirit of the FE2 method. It is extremely computationally demanding particularly without parallel computers.

I therefore seek for advanced methods to reduce the computational cost and it seems that model reduction might be a good choice. I do not understand your paper fully, but I think model reduction was applied to the micro models. Is this right? Could you tell me to what extent this is independent of the model used at the microscale? For example can it be applied for a continuum damage model at the microscale?

 Looking forward to hear from you. 

Merci beaucoup.

 


Julien Yvonnet's picture

Dear  Vinh

Dear  Vinh Phu,

 

You
are right, in the proposed approach the model reduction is applied to
the local scale. You first need to construct a reduced basis that can
describe your microscale model for different possible loadings
prescribed by the macroscale. In our cases the problems were
history-independent. To my opinion the proposed framework needs to be
extended to be applied to damage model. Model reduction of problems with internal variables has been recently proposed in 

Hyper-reduction of mechanical models involving internal variables

Ryckelynck D, International journal for Numerical Methods in Engineering, 77(1): 75-89 (2009). 

 Maybe there is a hint here to combine multiscale and model reduction for your problems ?

Best regards,

Julien


vinh phu nguyen's picture

Hi Julien,  Thanks for

Hi Julien,

 Thanks for mentioning the paper.

 Phu