Deformation mode in 3-point flexure on pantographic block

Abstract

Pantographic blocks are metamaterials made of a finite number of parallel pantographic sheets interconnected by cylindrical pivots. In this paper, a pantographic block subjected to 3-point flexure, where the prescribed displacements are parallel to the pantographic plane, shows essentially monoclastic deformation (i.e., one of the principal curvatures of the top surface is found to be negligible wrt. the other one). Pantographic blocks are modeled herein with a second gradient 3-dimensional continuum model that is valid at the length scale of pantographic cells. This reduced order model allows for predictive numerical simulations whose computational burden is relatively small. Second gradient effects (i.e., higher-order terms contributing to the strain energy) are limited to the second derivatives along the fibers of their transverse displacements. Digital Volume Correlation (DVC) techniques are employed to measure deformed shapes of pantographic blocks. A model-driven initialization procedure of DVC is followed to quantify the shape of such pantographic blocks in large displacements and strains.