Classification of rotational zero modes in 2D micropolar solids

Abstract

Zero modes, which are deformations that cost zero energy, underlie many exotic behaviors in elastic metamaterials. While classical linear Cauchy elasticity explains many of these modes, those linked to the rotations of metamaterial inner components often lie beyond its scope. Micropolar elasticity, which incorporates translation and rotation degrees of freedom, provides a framework for capturing these rotational modes. Herein, we present the first complete symmetry-based classification of zero modes in two-dimensional micropolar solids, with an emphasis on rotation-related modes. Guided by this classification, we construct threefold rotationally symmetric micropolar metamaterials and realize typical rotational micropolar zero modes. We further show that these metamaterials exhibit wave phenomena forbidden in Cauchy continua, including the emergence of three bulk waves in the long-wavelength limit and associated triple refraction, chiral acoustic modes, as well as strong wave anisotropy. All intriguing properties are quantitatively captured by micropolar continuum descriptions, whereas the classical Cauchy continuum theory fails to predict these behaviors, even at a qualitative level. Our results establish a general framework for engineering rotation-based zero modes, opening avenues for designing metamaterials with novel wave properties.

6 figures

References in corpus (28)

• Topological Boundary Modes in Isostatic Lattices
• Acoustic cloaking theory
• On the feasibility of pentamode mechanical metamaterials
• Odd elasticity
• Achieving control of in-plane elastic waves
• Observation of Roton Mode Population in a Dipolar Quantum Gas
• Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices
• Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices
• Acoustic metafluids
• Topological Phase Transition in Mechanical Honeycomb Lattice
• Broadband solid cloak for underwater acoustics
• Mechanical Weyl Modes in Topological Maxwell Lattices
• Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots
• An asymmetric elastic metamaterial model for elastic wave cloaking
• Quasi isotropic underwater acoustic carpet cloak based on latticed pentamode metafuid
• Soft modes and elasticity of nearly isostatic lattices: randomness and dissipation
• Chirality-induced Phonon Dispersion in a Noncentrosymmetric Micropolar Crystal
• Polar metamaterials: A new outlook on resonance for cloaking applications
• Design of an underwater acoustic bend by pentamode metafluid
• The dispersion relation of Landau elementary excitations and the thermodynamic properties of superfluid ${}^4$He
• Extreme Spatial Dispersion in Nonlocally-Resonant Elastic Metamaterials
• Microtwist elasticity: A continuum approach to zero modes and topological polarization in Kagome lattices
• Mapping of Elastic Properties of Twisting Metamaterials onto Micropolar Continuum using Static Calculations
• Mechanical coupling effects of 2D lattices uncovered by decoupled micropolar elasticity tensor and symmetry operation
• Mechanical couplings of 3D lattice materials discovered by micropolar elasticity and geometric symmetry
• Rayleigh surface waves of extremal elastic materials
• Electronic rotons and Wigner crystallites in a two-dimensional dipole liquid
• Classifying topological floppy modes in the continuum