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Analytical Solutions of 2-dimensional Second Gradient Linear Elasticity for Continua with Cubic-D4 Microstructure

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New Achievements in Continuum Mechanics and Thermodynamics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 108))

Abstract

We consider in this paper analytical solutions for some remarkable cases and for a linear anisotropic D4 second gradient elastic model. The purpose is that of constitutive parameter identification. In general, analytical solutions are considered less important than in the past due to fast numerical tools and to the fact that they are generally very difficult to achieve. However, they still play very important roles such as for numerical comparison and for dealing with pathological mechanical systems.

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Acknowledgements

Authors thank the Laboratoire International Associé Coss&Vita for the support via “Fédération Francilienne de Mécanique, CNRS FR2609”. Giuseppe Rosi has been supported by the CNRS through the PEPS program “HipImpact”.

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Authors and Affiliations

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

    Luca Placidi

  2. Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Université Paris-Est, 61 av du Général de Gaulle, 94010, Créteil Cedex, France

    Giuseppe Rosi

  3. Dipartimento di Ingegneria Strutturale e Geotecnica, Università degli Studi di Roma “La Sapienza”, Via Eudossiana 18, 00184, Rome, Italy

    Emilio Barchiesi

Authors
  1. Luca Placidi
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  2. Giuseppe Rosi
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  3. Emilio Barchiesi
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Corresponding author

Correspondence to Luca Placidi .

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Editors and Affiliations

  1. Institute of Mechanics, Technische Universität Berlin, Berlin, Germany

    Bilen Emek Abali

  2. Institut für Mechanik, Otto-von-Guericke-University Magdeburg, Magdeburg, Germany

    Holm Altenbach

  3. Dipartimento di Ingegneria Strutturale e Geotecnica, Università degli Studi di Roma “La Sapienza”, Roma, Italy

    Francesco dell'Isola

  4. Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Gdansk, Poland

    Victor A. Eremeyev

  5. Fakultät Maschinenbau, Esslingen University of Applied Sciences, Esslingen, Germany

    Andreas Öchsner

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Placidi, L., Rosi, G., Barchiesi, E. (2019). Analytical Solutions of 2-dimensional Second Gradient Linear Elasticity for Continua with Cubic-D4 Microstructure. In: Abali, B., Altenbach, H., dell'Isola, F., Eremeyev, V., Öchsner, A. (eds) New Achievements in Continuum Mechanics and Thermodynamics. Advanced Structured Materials, vol 108. Springer, Cham. https://doi.org/10.1007/978-3-030-13307-8_26

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  • DOI: https://doi.org/10.1007/978-3-030-13307-8_26

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