On the mechanical behavior of elastic crenelated beams

Abstract This paper derives the one-dimensional equivalent continuous model for elastic crenelated beams composed of the periodic repetition of orthogonally connected Euler–Bernoulli beams. The effective behavior is obtained through an asymptotic homogenization of periodic discrete media conducted at leading order. The resulting homogenized model is shown to be formally identical to a classical Euler–Bernoulli beam, with explicit analytical expressions for the effective extensional and bending stiffnesses in terms of the geometric and mechanical properties of the elementary beams. Despite the intrinsic chirality of the crenel microstructure, the equivalent one-dimensional continuum exhibits no extension-bending coupling at the macroscopic level. However, the chiral nature of the microstructure persists in the local deformation fields and may significantly influence the global structural response through the application of specific boundary conditions. In particular, when the conditions derived for the 1D effective model are imposed to the local beams of the crenel, the extension and bending deformation modes are coupled. The theoretical predictions are validated by direct numerical simulations on finite crenelated beams, showing very good agreement.