A frequency domain Ritz-method-based spectral finite element methodology for the computation of band structure of the pentamode metamaterials

Sushovan Mukherjee; S. Gopalakrishnan

doi:10.1117/12.2219224

16 April 2016 A frequency domain Ritz-method-based spectral finite element methodology for the computation of band structure of the pentamode metamaterials

Sushovan Mukherjee, S. Gopalakrishnan

Author Affiliations +

Proceedings Volume 9802, Nanosensors, Biosensors, and Info-Tech Sensors and Systems 2016; 98020P (2016) https://doi.org/10.1117/12.2219224
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2016, Las Vegas, Nevada, United States

Abstract

The class of fabricated materials known as metamaterials, with its promises for unconventional material properties or characteristics, has opened up a whole new paradigm of possibilities and challenges. The primary enablers have been capabilities at the very low length scale and novel design configurations. Pentamode metamaterials, having fluid like properties, is one such idea to have been realized in recent past. This type of fabricated materials show high bulk modulus but low shear modulus. The fundamental constituent element is a rod like structure tapered down on both ends. Four of such elements meet at any joint, two of which in a plane orthogonal to that of the other two. The dynamics and wave propagation characteristics of such structures have been studied with an aim to obtain band structures formed because of their periodic nature. Here, a methodology has been developed to compute the wave propagation characteristics of such pentamode structures using spectrally formulated finite elements based on frequency domain Ritz method. Bloch theory has also been used to represent the dynamics of an infinite structure through that of a unit cell. The proposed method is computationally more efficient compared to one using conventional finite element. A few variants of pentamodes are also analyzed to arrive at configurations with superior wave propagation characteristics.

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Sushovan Mukherjee and S. Gopalakrishnan "A frequency domain Ritz-method-based spectral finite element methodology for the computation of band structure of the pentamode metamaterials", Proc. SPIE 9802, Nanosensors, Biosensors, and Info-Tech Sensors and Systems 2016, 98020P (16 April 2016); https://doi.org/10.1117/12.2219224

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KEYWORDS

Chemical elements

Metamaterials

Wave propagation

Electroluminescent displays

3D printing

Bismuth

Kinematics

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