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In classical Cauchy elasticity, 3D materials exhibit six eigenmodes of deformation. Following the 1995 work of Milton and Cherkaev, extremal elastic materials can be classified by the number of eigenmodes, N, out of these six that are "easy". Using Greek number words, this leads to hexamode (N = 6), pentamode (N = 5), tetramode (N = 4), trimode (N = 3), dimode (N = 2), and monomode (N = 1) materials. While hexamode materials are unstable in all regards, the possibility of pentamode metamaterials ("meta-fluids") has attracted considerable attention throughout the last decade. Here, inspired by the 2021 theoretical work of Wei, Liu, and Hu, microstructured 3D polymer-based tetramode metamaterials are designed and characterized by numerical band-structure calculations, fabricated by laser printing, characterized by ultrasound experiments, and compared to the theoretical ideal. An application in terms of a compact and broadband polarizer for acoustical phonons at ultrasound frequencies is demonstrated.
Groß et al. (Tue,) studied this question.