Adaptive periodical representative volume element for simulating periodical postbuckling behavior

Abstract

SUMMARYFinite 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.

Nonlinear mechanics of non-dilute viscoelastic layered composites

“…With this choice, the buckling wavelength predicted by ABAQUS, L cr | F EM , was a discrete value that was equal to or directly adjacent to the expected value for L cr | th . A more elegant approach would have been to use Bloch wave analysis for a unit cell of height H (where H can take any value) [8,2] or the adaptive representative volume element recently proposed by Ton et al [37]. However, since the main goal of these buckling simulations was to validate the buckling theory and to select appropriate volume fractions for non-dilute composites, the approach described above is sufficient.…”