Micropolar beam-like structures under large deformation

Abstract

Results from experimental torsion and bending tests show the existence of a size effect, which conventional continuum models are unable to describe. Therefore, the incorporation of the micropolar media into numerical approaches for the analysis of materials with a complex microstructure looks necessary. So far, most studies utilize Cosserat continuum theory with 3D finite solid elements, even though, it covers only few beam elements developed within a linear strain–displacement relationship, and therefore only works in a small deformation regime. In this study, the authors aim to develop a size-dependent 3D continuum beam element based on the absolute nodal coordinate formulation (ANCF) with microstructure inclusions. Comparing analytical solutions within the Cosserat continuum model and models based on the proposed and already existing 3D micropolar solid elements, one can see a good correlation between them, with a faster convergence rate for the developed ANCF beam element. That allows exploiting the developed beam element within the non-linear deformation range, which is usually bypassed because of high computational costs, thus, accounting fully for differences between two media descriptions.