Vibrant times for mechanical metamaterials
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Vibrant times for mechanical metamaterials Johan Christensen, DTU Fotonik, Department of Photonics Engineering, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark Muamer Kadic and Martin Wegener, Institute of Applied Physics, Karlsruhe Institute of Technology (KIT), D-76128 Karlsruhe, Germany Oliver Kraft, Institute for Applied Materials, Karlsruhe Institute of Technology (KIT), D-76128 Karlsruhe, Germany Martin Wegener, Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), D-76021 Karlsruhe, Germany Address all correspondence to Johan Christensen at [email protected] (Received 15 May 2015; accepted 22 June 2015)
Abstract Metamaterials are man-made designer matter that obtains its unusual effective properties by structure rather than chemistry. Building upon the success of electromagnetic and acoustic metamaterials, researchers working on mechanical metamaterials strive at obtaining extraordinary or extreme elasticity tensors and mass-density tensors to thereby mold static stress fields or the flow of longitudinal/transverse elastic vibrations in unprecedented ways. In this prospective paper, we focus on recent advances and remaining challenges in this emerging field. Examples are ultralight-weight, negative mass density, negative modulus, pentamode, anisotropic mass density, Origami, nonlinear, bistable, and reprogrammable mechanical metamaterials.
Introduction Stone Age, Copper Age, Bronze Age, Iron Age: We name the eras of mankind after mechanical materials. Is the Metamaterial Age next? Physicists, material scientists, and engineers alike are already working at going beyond (“meta”) what nature has given to us. Significant recent advances in threedimensional printing on the micro- and macro-scale help them to succeed. The goal is to rationally design and realize tailored artificial media with mechanical characteristics distinct from their constituents to achieve, e.g., effectively stronger, tougher, or lighter materials. In some cases, one can even go beyond what seemed to be fundamental restrictions. As usual, the mechanics of solid bodies deals with deformations and motions resulting from external forces via Newton’s law. For sufficiently small deviations from equilibrium, Hooke’s law can be applied. For the paradigm of an elastic Hooke’s spring, it simply states that force and extension are proportional. When considering general mechanical materials under arbitrary compression, stretching, and shearing, Hooke’s law translates into rank-two tensors for stress and strain, which are connected via the rank-four elasticity tensor (Box 1). Mechanical waves in an isotropic material are an illustrative example. Generally, they can have one longitudinal polarization (like for acoustic sound waves in a gas or fluid) and two orthogonal transverse polarizations (like usually for electromagnetic waves). These three polarizations make elastodynamics even richer than acoustics and electromagnetism. It is hard to say when the first mechanical metamaterial was conceived. However,
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