Flextegrity simple cubic lattices

Abstract

Flextegrity lattices are spatial grids composed of stiff segments kept in contact by compliant pre-tensioned tendons. The kinematic skeleton is sensible to the orientation of the segments, since their relative rotation produces the straining of the tendons to an amount that depends upon the angle of rotation and the shape of the pitch surfaces of the contact joints: these dictate the constitutive properties of the lattice in response to external actions. Two- and three-dimensional lattices are investigated, in which the contact pitch surfaces, obtained with axial-symmetric toothed conjugate profiles, mimic the kinematics of spheres, centred at the nodes of a simple cubic lattice, in pure rolling motion. The allowed mechanisms are discussed under infinitesimal deformation, to recognize possible eigenstress states in the lattice. The response under finite deformations is worked out for two-dimensional lattices under symmetric and asymmetric loading. The theoretical predictions are compared with experimental results on 3D-printed physical models. Possible extensions are discussed for lattices with segments of varying size, different arrangements and multi-stable contact joints. The flextegrity microstructure can represent a mesoscopic model for homogeneous crystals composed of non-pointwise molecules, but it could actually be manufactured in metamaterials with peculiar properties.