Computational study of a homogenized nonlinear generalization of Timoshenko beam proposed by Turco et al

Mechanical metamaterials are most often assemblies of stocky beam elements connected through rigid connections, hinges, or flexural joints. The description of these materials through classical beam theories is challenging because of the wide variety of complex phenomena observed in the severe deformation regime mechanical metamaterials must undergo and because most classical beam theories can only be applied to elements with sufficiently high slenderness. In the spirit of Hencky, Turco et al. (2020) has recently formulated an intrinsically discrete nonlinear elastic model suitable for the design of mechanical metamaterials. The objective of this contribution was to present a numerical study of the nonlinear generalization of the Timoshenko beam that results from the asymptotic homogenization of the discrete model introduced by Turco et al. The present numerical study took into account several loading cases and elucidated the sensitivity of the homogenized continuum with respect to axial, bending, and shear stiffness parameters, as well as to load imperfections, in terms of mechanical behavior, including buckling onset and post-critical behavior. It was found that the predictions obtained with the homogenized model in the large deformation regime matched excellently with those of the discrete model proposed by Turco et al.