Adaptive periodical representative volume element for simulating periodical postbuckling behavior

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.