Cosserat modelling of an elasto-viscoplastic rectangular lattice

摘要

Metallic foams inherit their attractive lightweight properties directly from the cellular microstructure. However, the characteristic material length scale (the cell size) is often not small compared to macroscopic dimensions, which limits the applicability of classical continuum-type constitutive models. Cosserat theory, however, offers a continuum framework that naturally features a length scale related to rotation gradients. In this paper a homogenization procedure is proposed that enables the derivation of macroscopic constitutive equations based on the underlying microstructural morphology (including the cell size) and material behavior. The procedure is demonstrated for a two-dimensional periodic rectangular lattice of elasto-viscoplastic beams, for which closed-form expressions for the macroscopic response are derived.