Submitted to 1 DOI: 10.1002/adma.201302949 Phononic crystal with adaptive connectivity By Andrea Bergamini* 1 , Tommaso Delpero 1 , Luca De Simoni, Luigi Di Lillo, Massimo Ruzzene and Paolo Ermanni T. Delpero, L. De Simoni, L. Di Lillo, Prof. P. Ermanni Centre of Structure Technologies, ETH Swiss Federal Institute of Technology Zürich, 8092 (Switzerland) [*] Dr. A. Bergamini Swiss Federal Laboratories for Materials Science and Technology, EMPA Dübendorf , 8600 (Switzerland) E-mail: andrea.bergamini@empa.ch Prof. M. Ruzzene School of Aerospace Engineering, Georgia Institute of Technology Atlanta, GA 30332 (USA) Keywords: Phononic crystal, adaptive connectivity, mechanical metamaterial The properties of metamaterials result rather from the chosen geometric arrangement of the unit cells than from the bulk behavior of the materials they are composed. [1, 2] While in a mathematical sense, the connectivity between elements of a lattice is plainly defined by its topology, [3, 4] in a physical context it implies the ability of neighbors to interact with one another. In this communication, we introduce a first implementation of a metamaterial with variable mechanical connectivity, whose effective properties can be tuned by exploiting a transducive material. In the phononic crystal described by Wu, [5] the periodic distribution of masses connected to the continuous substrate is responsible for the generation of Bragg-type bandgaps. Here we show that by interposing variable stiffness links between the substrate and the masses, we can adaptively control the connectivity between the elements of the phononic crystal and therefore its band structure. The concept of adaptive augmentation of the unit cell of a metamaterial is demonstrated in the mechanical domain and is expected to be applicable also to other physical domains. Following their electromagnetic counterparts, mechanical metamaterials [6] have recently received increased attention due to the unusual properties that they can exhibit. Their dynamic features result from the tailoring of acoustic waves scattering events coupled, in some instances, with internally resonating units. [7-9] Atypical dispersion properties, such as negative group velocity, [10] stop bands [11] and acoustic cloaking [12-14] have been reported for suitably designed materials. With respect to the quasi-static mechanical properties, negative Poissons ratio, [15, 16] stiffer than diamond materials, [17] extreme damping in composite materials with negative stiffness inclusions, [18] as well as materials with out-of-the-ordinary ratios of bulk to shear modulus known as meta-fluids have been reported. [19] These peculiar properties stem from specific geometrical connectivity patterns between the structural elements (that can be viewed as artificial 'atoms' [1] ). A very limited number of these unusual behaviors, such as 1 A. Bergamini and T. Delpero contributed equally to this work.