Mechanical coupling effects of 2D lattices uncovered by decoupled micropolar elasticity tensor and symmetry operation

TL;DR

This paper systematically uncovers and correlates mechanical coupling effects in 2D lattices with symmetry properties using decoupled micropolar elasticity tensors, providing theoretical insights for designing advanced mechanical metamaterials.

Contribution

It introduces a systematic method to identify and relate mechanical couplings in 2D lattices to symmetry, advancing the theoretical foundation for metamaterial design.

Findings

Identified eight mechanical coupling effects in 2D lattices.

Established correlation between coupling effects and point-group symmetry.

Provided a framework for designing metamaterials with tailored mechanical responses.

Abstract

Mechanical couplings such as axial-shear and axial-bending have great potential in the design of active mechanical metamaterials with directional control of input and output loads in sensors and actuators. However, the current ad hoc design of mechanical coupling without theoretical support of elasticity cannot provide design guidelines for mechanical coupling with lattice geometries. Moreover, the correlation between mechanical coupling effects and geometric symmetry is not yet clearly understood. In this work, we systematically search for all possible mechanical couplings in 2D lattice structures by determining the non-zero diagonal terms in the decomposed micropolar elasticity tensor. We also correlate the mechanical couplings with the point-group symmetry of 2D lattices by applying the symmetry operation to the decomposed micropolar elasticity tensor. The decoupled micropolar constitutive equation uncovers eight coupling effects for 2D lattice structures. The symmetry operation of the decoupled micropolar elasticity tensor reveals the correlation of the mechanical coupling with the point groups. Our findings can strengthen the design of mechanical metamaterials with potential applications in areas including sensors, actuators, soft robots, and active metamaterials for elastic/acoustic wave guidance and thermal management.