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High-frequency parametric approximation of the Floquet-Bloch spectrum for anti-tetrachiral materials

Bacigalupo, Andrea and Lepidi, Marco High-frequency parametric approximation of the Floquet-Bloch spectrum for anti-tetrachiral materials. International Journal of Solids and Structures, 97/98. pp. 575-592. ISSN 0020-7683 (2016)

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The class of anti-tetrachiral cellular materials is phenomenologically characterized by a strong auxeticity of the elastic macroscopic response. The auxetic behavior is activated by rolling-up deformation mechanisms developed by the material microstructure, composed by a periodic pattern of stiff rings connected by flexible ligaments. A linear beam lattice model is formulated to describe the free dynamic response of the periodic cell, in the absence of a soft matrix. After a static condensation of the passive degrees-of-freedom, a general procedure is applied to analyze the wave propagation in the low-dimensional space of the active degrees-of-freedom. The exact dispersion functions are compared with explicit – although approximate – dispersion relations, obtained from asymptotic perturbation solutions of the eigenproblem governing the Floquet–Bloch theory. A general hierarchical scheme is outlined to formulate and solve the perturbation equations, taking into account the dimension of the perturbation vector. Original recursive formulas are presented to achieve any desired order of asymptotic approximation. For the anti-tetrachiral material, the fourth-order asymptotic solutions are found to approximate the dispersion curves with fine agreement over wide regions of the parameter space. The asymptotic eigensolutions allow an accurate sensitivity analysis of the material spectrum under variation of the key physical parameters, including the cell aspect ratio, the ligament slenderness and the spatial ring density. Finally, the explicit dependence of the dispersion functions on the mechanical parameters may facilitate the custom design of specific spectral properties, such as the wave velocities and band gap amplitudes.

Item Type: Article
Identification Number: 10.1016/j.ijsolstr.2016.06.018
Uncontrolled Keywords: Auxetic materials; Chirality; Wave propagation; Beam lattice model; Asymptotic perturbation methods
Subjects: T Technology > T Technology (General)
Research Area: Computer Science and Applications
Depositing User: Caterina Tangheroni
Date Deposited: 21 Mar 2017 11:56
Last Modified: 21 Mar 2017 11:56
URI: http://eprints.imtlucca.it/id/eprint/3668

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