A variegated effective elastic modulus in metabeams under periodically distributed loads

Abstract

A class of beam-like lattice structures, or metabeams under static, sinusoidally distributed transverse loads is discussed. Their neutral axis deflects either in-phase, out-of-phase or shows no deflection, depending on the beam design parameters, and also on the spatial frequency of the static load. These outcomes contrast the behavior of continuum beams, deflecting always in-phase with the load, and they are interpreted on the basis of a positive, negative and near-infinite effective Young's modulus of the structured beams in bending. They also represent a collective effect of the behavior of multiple elements in the lattice that cannot be realized from the performance of an isolated unit cell. A long-range periodic order and nonlocality of the lattice interaction is essential for this unusual behaviors, and those are particularly pronounced at higher wavenumbers, when the load wavelength becomes comparable with the range of direct interactions in the lattice. Theoretical discussion and predictions agree well with numerical experiments performed on the basis of commonly accepted models. Practical applications could be found in advanced reinforcing materials for building foundations, deformation mitigation for lightweight structures and bridges, and in smart mechanical systems able to differentiate external stimuli and to respond selectively.