Strength, stability, and interlocking efficacy in topologically interlocked materials based on tetrahedra and octahedra

Topologically Interlocked Materials (TIMs) are segmented systems composed of stiff blocks that interact through sliding, rotation, and jamming at contact interfaces. While TIMs improve toughness, this often comes at the expense of strength. Although recent experiments demonstrate the potential to overcome this trade-off, clear guidelines for achieving stiffness and strength in TIMs are still needed. In this study, we study the mechanical response of tetrahedral and octahedral TIM panels under out-of-plane loading using finite element models (FEM). We introduced two kinematic descriptors: Collective slippage and collective rotation, both of which capture inter-block deformation and show strong dependence on interfacial friction. To quantify the interlocking efficacy, we propose a new metric called the participation ratio, which is based on the strain energy distribution across blocks. This ratio was found to be 1.5 times higher in octahedral TIMs than in tetrahedral ones, indicating more effective load sharing among blocks. Contact force maps and stress trajectories revealed that the octahedral TIMs had a more interconnected force network, whereas the tetrahedra showed directional load channels. A key difference lies in the static stability: Octahedra can maintain equilibrium even in the absence of friction and thus are intrinsically stable TIMs, whereas tetrahedra require friction to achieve static equilibrium. We also proposed a strength-to-tensile stress ratio to capture the mechanical potential of TIMs independent of the base material properties, in which octahedra outperformed tetrahedra by 5.6 times. Overall, the greater number of contact surfaces and hexagonal base tessellation of octahedral TIMs confer superior interlocking efficacy, leading to enhanced stiffness, strength, and toughness.