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Adaptive periodical representative volume element for simulating periodical postbuckling behavior

Bin Liu's picture

Finite element method (FEM) with fixed representative volume element (RVE) encounters some difficulties in simulating the periodical postbuckling behaviors of infinite long beam or infinite large film on soft substrate under compression, because the wavelength and pattern of buckling are not known before simulation and will change with the increase of compression strain. In this paper, an adaptive periodical RVE is constructed in a mapping space to avoid remeshing in the real space, and the mapping coefficients, that is, the dimension and shape of RVE in real space, are treated as variables in average energy density minimization to obtain correct postbuckling configurations. The validness and efficiency of the proposed algorithm have been demonstrated by our numerical examples. The paper can be found at



Dear Prof. Liu,

Thanks for sharing the nice work.  This adaptive method provides a deep insight into our previous buckling analysis of stiff thin films on a soft elastomer.  With ease on the choice of representative volume element and significantly reduced computational time, I believe this method applies to a broader application in the area of buckling/post-buckling.  Excellent "proof-of-concept" examples were given in the paper.  However, I was just wondering whether it is easy to incorporate the codes with the commercial software, such as ABAQUS.


Dear Dr. Cheng,

 Thanks for the nice comments. To answer your question, the approach that combines classical finite element method with general minimization algorithm can be incorporated with Abaqus quite easily, by using script such as Python to automize the procedure. Abaqus can be treated as a calculation subroutine, at call whenever needed.

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