Revealing the physical insight of a length-scale parameter in metamaterials by exploiting the variational formulation

  • B. Emek Abali
Original Article


For micro-architectured materials with a substructure, called metamaterials, we can realize a direct numerical simulation in the microscale by using classical mechanics. This method is accurate, however, computationally costly. Instead, a solution of the same problem in the macroscale is possible by means of the generalized mechanics. In this case, no detailed modeling of the substructure is necessary; however, new parameters emerge. A physical interpretation of these metamaterial parameters is challenging leading to a lack of experimental strategies for their determination. In this work, we exploit the variational formulation based on action principles and obtain a direct relation between a parameter used in the kinetic energy and a metamaterial parameter in the case of a viscoelastic model.


Mechanics Metamaterial Length scale parameter Variational formulation Principle of least action 


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Chair of Continuum Mechanics and Constitutive Theory, Institute of MechanicsTechnische Universität BerlinBerlinGermany

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