Archive of Applied Mechanics

, Volume 89, Issue 12, pp 2545–2562 | Cite as

Conventional and star-shaped auxetic materials for the creation of band gaps

  • Panagiotis I. Koutsianitis
  • Georgios K. Tairidis
  • Georgios A. Drosopoulos
  • Georgios E. StavroulakisEmail author


A band gap region, or simply a band gap, is a range of frequencies where vibrations of certain frequency ranges are isolated. In the present paper, such ranges are sought through the study of different cases for the shape of the unit cells of a lattice, i.e., of an assembly of classical structural elements, such as beams and plates. A lattice with a specific, special designed microstructure is considered in the present investigation. Each particular cell of the examined lattice is studied as a classical composite material consisting of a matrix and the reinforcing core (e.g., matrix-fiber composite), and it is discretized by using two-dimensional plane stress finite elements. The form of the core of the unit cells can be of several shapes, e.g., quadratic, circular, and star. Some of these shapes provide the whole lattice with auxetic behavior, with negative Poisson’s ratio at the homogenized properties. The shape and the microstructure of the lattice is optimized in order to achieve isolation of the desired frequencies. A first attempt on the optimization of star-shaped microstructures is also presented. The optimization is carried out using powerful global optimization methods, such as the genetic algorithms. Results indicate that band gaps may appear in both conventional and auxetic microstructures. Moreover, the appearance and the size of the band gaps depend on the selected microstructure.


Auxetic material Band gaps Optimization Vibration 



The research work was supported by the Hellenic Foundation for Research and Innovation (HFRI) and the General Secretariat for Research and Technology (GSRT), under the HFRI PhD Fellowship Grant (GA. no. 34254).


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Production Engineering and Management, Institute of Computational Mechanics and OptimizationTechnical University of CreteChaniaGreece
  2. 2.Discipline of Civil Engineering, Structural Engineering and Computational Mechanics GroupUniversity of KwaZulu-NatalDurbanSouth Africa

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