Size effects in lattice structures and a comparison to micropolar elasticity

Abstract

This work models periodic thin walled cellular materials using either a discrete beam element lattice model or nominally equivalent micropolar elastic model. When the material properties of cellular materials are tested, small samples may have different apparent material properties than large samples. This difference is known in the literature as a size effect. The predictions of size effects from discrete and micropolar simulations are examined. Although the literature explains size effects arising from the effects simulated in the micropolar model, the micropolar model typically under predicts the stiffness due to size effects seen in the lattice model by an order of magnitude. The lattice size effects are examined for patterns and the size effect patterns found can be explained by the shape of the free edges, and by the specifics of how material is distributed within the material domain. These are causes for size effects that are not captured in the micropolar model.