Skip to main content

Disciplines

Automotive
Business IT + Informatics
Construction + Real Estate
Electrical Engineering + Electronics
Energy + Sustainability
Insurance + Risk
Finance + Banking
Management + Leadership
Marketing + Sales
Mechanical Engineering + Materials

Events

DE
EN

Books

Journals

Start single access now

Request access for companies

EXTENDED SEARCH
Log in
Top

Hint

Swipe to navigate through the chapters of this book

Published in:
Theoretical Basis of the Structural Modeling Method Read chapter Read first chapter

2021 | OriginalPaper | Chapter

6. A Cubic Lattice of Spherical Particles

Authors : Vladimir I. Erofeev, Igor S. Pavlov

Published in: Structural Modeling of Metamaterials

Publisher: Springer International Publishing

Login to get access

Abstract

In the previous chapters, two-dimensional models of microstructured media were discussed, and the particles of which have three degrees of freedom. This chapter is devoted to the elaboration of a three-dimensional model of a crystalline medium consisting of spherical particles with six degrees of freedom. Such a medium is structurally similar to a fullerite crystal with a simple cubic lattice (see Sect. 1.​2). The main objectives of this chapter are to obtain dynamic equations of a crystalline medium consisting of spherical particles by the method of structural modeling and to establish the relationships between the coefficients of these equations and the microstructure parameters of the material at issue.

To get access to this content you need the following product:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt 90 Tage mit der neuen Mini-Lizenz testen!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe



 


Jetzt 90 Tage mit der neuen Mini-Lizenz testen!

inform now
previous chapter Nonlinear Models of Microstructured Media
next chapter Propagation and Interaction of Nonlinear Waves in Generalized Continua
Literature
1.
Pavlov, I.S., Potapov, A.I.: Two-dimensional model of a granular medium. Mech. Solids 42(2), 250–259 (2007) CrossRef
2.
Pavlov, I.S., Potapov, A.I., Maugin, G.A.: A 2D granular medium with rotating particles. Int. J. Solids Struct. 43(20), 6194–6207 (2006) CrossRef
3.
Kuznetsova, E.L., Tarlakovskii, D.V., Fedotenkov, G.V.: Propagation of unsteady waves in an elastic layer. Mech. Solids 46(5), 779–787 (2011) CrossRef
4.
Erofeev, V.I., Pavlov, I.S., Leontiev, N.V. A mathematical model for investigation of nonlinear wave processes in a 2D granular medium consisting of spherical particles. Compos. Mech. Comput. Appl. Int. J. 4`3), 239–255 (2013)
5.
6.
Suiker, A.S.J., Metrikine, A.V., de Borst, R. Comparison of wave propagation characteristics of the cosserat continuum model and corresponding discrete lattice models. Int. J. Solids Struct. 38, 1563–1583 (2001)
7.
Potapov, A.I., Pavlov, I.S., Lisina, S.A.: Acoustic identification of nanocrystalline media. J. Sound Vib. 322(3), 564–580 (2009) CrossRef
8.
Sadovskii, V.M.: Thermodynamically consistent equations of the couple stress elasticity. Dal’nevost. Mat. Zh. 16(2), 209–222 (2016). (in Russian)
9.
Berglund, K. Structural models of micropolar media. In: Brulin, O., Hsieh, R.K.T. (eds.) Mechanics of Micropolar Media, pp. 35–86. World Scientific, Singapore (1982)
Metadata
Title
A Cubic Lattice of Spherical Particles
Authors
Vladimir I. Erofeev
Igor S. Pavlov
Copyright Year
2021
Book
Structural Modeling of Metamaterials

Print ISBN: 978-3-030-60329-8

Electronic ISBN: 978-3-030-60330-4

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-3-030-60330-4_6

Premium Partners

in-adhesives MKVS Ecoclean Hellmich GmbH Krahn Ceramics
    Image Credits