Unveiling new mechanical couplings in 3D lattices: axial-bending and the role of symmetry breaking

Abstract Mechanical couplings with symmetry breaking enable novel applications in robotic metamaterials and directional mechanical signal guidance. While previous studies of three-dimensional (3D) mechanical couplings have focused primarily on axial-twist designs, we extend this limitation by characterizing 3D axial-bending (AB) coupling and its relationship to non-centrosymmetry and chirality. By incorporating mirror and inversion symmetry breaking, we identify AB coupling effects of non-centrosymmetric lattices with both achiral and chiral geometries. Applying an extended 3D micropolar homogenization method, we systematically quantify anisotropic physical properties and mechanical couplings as functions of curvature and handedness, integrating point group symmetry with micropolar constitutive mechanics of curved cubic lattices. Our investigation, supported by experiments and finite-element (FE) simulations, reveals that chirality weakly correlates with both AB and axial-twisting (AT) couplings. We employ Neumann's principle to both design and characterize the anisotropic behaviour of these structures, enabling the development of multimodal mechanical couplings. This work presents a robust framework for understanding mechanical couplings related to symmetry breaking and spatial anisotropy in metamaterial design, drawing an analogy to crystal physics and crystal chemistry.