Point Deflection in Topological Interlocking Plates

The bending of topological interlocking (TI) plates under point loading is not smooth; it is accompanied by developing lines of localization commensurate with the symmetry of the interlocking assembly. Furthermore, the developed stage of deflection is characterized by post-peak softening. This paper proposes a new concept that explains these experimentally observed phenomena. A new model considers that due to the absence of bonding between the blocks, they assume independent rotational degrees of freedom; this is missed in the traditional modeling of TI structures. The bending resistance of TI beams relies on the elasticity of the peripheral constraint (frame or post-tensioning cables) resisting the additional loading caused by the relative rotation of blocks—a phenomenon called elbowing. This is independent of the particulars of the shape of interlocking blocks, which makes it possible to model the deflection of the TI beams as the deflection of fragmented beams consisting of parallelepiped blocks with restricted out-of-beam relative displacements. The model demonstrates that the bending of TI beams produces the experimentally observed point deflection, which is considerably different from that of conventional beams. This is a consequence of independent block rotation and elbowing. It is shown that the other consequence of block rotation with elbowing is the force–deflection relationship exhibiting a post-peak softening (apparent negative stiffness). Based on the point deflection model, it is demonstrated that oscillations of TI blocks involve a unidirectional damping with discontinuous velocity dependence. This paper develops a model of such damping. The results are important for designing flexible topological interlocking structures with energy absorption.