Chirale elastische metamaterialien: grundlegende mechanismen und deren nutzung zur strukturoptimierung

Abstract: Chiral metamaterials can translate purely translational motions into rotations. The strength of this coupling is quantified by the chiral response, which describes the angle by which a straight prismatic rod twists when subjected to a pure tensile or compressive load. The blocking torque describes how much torque is required to prevent the rod from twisting. For continuum mechanical modeling of a chiral response, generalized models such as micropolar continuum theory are needed. In micropolar elasticity, various characteristic lengths exist, allowing size-dependent material properties to be modeled. If the dimension of a sample is much larger than the characteristic length related to chirality, the chiral response vanishes. In this case, it approaches its limit with a characteristic decay inversely proportional to the sample size. In this work, finite element simulations of an idealized lattice structure under tensile load were used to show that the characteristic length can be tailored over orders of magnitude when chiral unit cells are connected via compliant achiral coupling elements. The characteristic length increases as the connecting elements become more compliant. As the characteristic length increases, so does the chiral response. In addition, the influence of geometric nonlinearities and the sensitivity to boundary conditions increase with increasing characteristic length. The design principle derived from the idealized lattice structure has been used to design a chiral metamaterial fabricatable by two-photon stereolithography. Through direct comparison with experiments on lattice structures consisting of more than 10⁵ unit cells, the relationships predicted by the finite element simulations were validated. Lastly, non-periodic chiral structures were considered and it was shown that they can have advantageous properties over periodic structures, especially with respect to the blocking torque.