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An Inverse Method to Get Further Analytical Solutions for a Class of Metamaterials Aimed to Validate Numerical Integrations

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Mathematical Modelling in Solid Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 69))

Abstract

We consider an isotropic second gradient elastic two-dimensional solid. Besides, we relax the isotropic hypothesis and consider a D4 orthotropic material. The reason for this last choice is that such anisotropy is the most general for pantographic structures, which exhibit attracting mechanical properties. In this paper we analyze the role of the external body double force \(m^{ext}\) on the partial differential equations and we subsequently revisit some analytical solutions that have been considered in the literature for identification purposes. The revisited analytical solutions will be employed as well for identification purposes in a further contribution.

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Authors and Affiliations

  1. Faculty of Engineering, International Telematic University Uninettuno, C.so Vittorio Emanuele II, 39, 00186, Rome, Italy

    Luca Placidi

  2. Dipartimento di Ingegneria Meccanica e Aerospaziale, Universitá di Roma La Sapienza, Via Eudossiana 18, 00184, Rome, Italy

    Emilio Barchiesi

  3. Laboratory of Science for Environmental Engineering, Université de La Rochelle, La Rochelle, France

    Antonio Battista

Authors
  1. Luca Placidi
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  2. Emilio Barchiesi
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  3. Antonio Battista
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Correspondence to Luca Placidi .

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Editors and Affiliations

  1. Università di Roma "La Sapienza" , Roma, Italy

    Francesco dell'Isola

  2. Université de Perpignan Via Domitia, LAboratoire de Mathématiques et PhySique Université de Perpignan Via Domitia, Perpignan, France

    Mircea Sofonea

  3. Dept Mechanical Engineering, UC Berkeley Dept Mechanical Engineering, Berkeley, California, USA

    David Steigmann

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Placidi, L., Barchiesi, E., Battista, A. (2017). An Inverse Method to Get Further Analytical Solutions for a Class of Metamaterials Aimed to Validate Numerical Integrations. In: dell'Isola, F., Sofonea, M., Steigmann, D. (eds) Mathematical Modelling in Solid Mechanics. Advanced Structured Materials, vol 69. Springer, Singapore. https://doi.org/10.1007/978-981-10-3764-1_13

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