Size effects in hexagonal and Re-entrant metamaterial beams under bending

This paper investigates the effects of boundary conditions, cell topology, relative density, and functionally graded pattern on the size effects of metamaterial beams with a hexagonal unit cell subjected to concentrated transverse bending loads. Beams with clamped and simply supported end conditions were studied. Two hexagonal unit cell topologies (regular hexagonal and re-entrant geometries) and two functionally graded approaches (transversally functionally graded and axially functionally graded patterns) are adopted to create various metamaterial beams with different configurations. Numerical finite element analysis (FEA) simulations and the Euler-Bernoulli (EB) beam model were used to estimate the bending responses of the different metamaterial beams.

The results indicate that metamaterial beams with hexagonal unit cells exhibit stiffness-softening size effects under bending. This means that the smaller the difference between the unit cell size and the overall beam size, the larger the apparent deflection of the beam. This size-dependent behaviour of the hexagonal metamaterial beam is well captured by a nonlocal strain-gradient model. The cell topology and functionally graded patterns displayed limited impact on the size effects, while the relative density significantly influenced the size effects. Metamaterial beams with high relative density exhibit weaker size effects than their low relative density counterparts.