  Similar to Poisson's effect, mechanical coupling is a directional indirect
response by a directional input loading. With the advance in manufacturing
techniques of 3D complex geometry, architected materials with unit cells of
finite volume rather than a point yield more degrees of freedom and foster
exotic mechanical couplings such as axial-shear, axial-rotation, axial-bending,
and axial-twisting. However, most structural materials have been built by the
ad hoc design of mechanical couplings without theoretical support of
elasticity, which does not provide general guidelines for mechanical couplings.
Moreover, no comprehensive study of all the mechanical couplings of 3D lattices
with symmetry operations has been undertaken. Therefore, we construct the
decoupled micropolar elasticity tensor of 3D lattices to identify individual
mechanical couplings correlated with the point groups. The decoupled micropolar
elasticity tensors, classified with 32 point groups, provide 15 mechanical
couplings for 3D lattices. Our findings help provide solid theoretical
guidelines for the mechanical couplings of 3D structural materials with
potential applications in various areas, including active metamaterials,
sensors, actuators, elastic waveguides, and acoustics.
