headerpos: 12198
 
 
 

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
Publisher
Journal Information
» Editorial Board
» Editorial Policy
» Archival Policy
» Article Publication Charges
» Copyright and Licensing Policy
Guidelines for Authors
» For Authors
» Instructions to Authors
» LaTex style files
Guidelines for Reviewers
» For Reviewers
» Review Form
Open Access
List of Issues
» 2019
» 2018
» 2017
» 2016
» 2015
» 2014
» 2013
» 2012
» 2011
» 2010
Vol. 59, Issue 4
Vol. 59, Issue 3
Vol. 59, Issue 2
Vol. 59, Issue 1
» 2009
» 2008
» Back Issues Phys. Math.
» Back Issues Chemistry
» Back issues (full texts)
  in Google. Phys. Math.
» Back issues (full texts)
  in Google. Chemistry
» Back issues (full texts)
  in Google Engineering
» Back issues (full texts)
  in Google Ecology
» Back issues in ETERA Füüsika, Matemaatika jt
Subscription Information
» Prices
Internet Links
Support & Contact
Publisher
» Staff
» Other journals

Models for essentially nonlinear strain waves in materials with internal structure; pp. 87–92

(Full article in PDF format) doi: 10.3176/proc.2010.2.05


Authors

Alexey V. Porubov

Abstract

Phenomenological models of essential nonlinear processes in solids with internal structure are developed so as to obtain nonlinear and dispersive features of the material similar to those described by the structural model. The exact solitary wave solutions of the governing equations are used as a tool for a comparison of two kinds of modelling. It is found that the model containing nonlinearity at the microlevel provides maximum similarity with the structural model.

Keywords

mechanics of solids, nonlinear waves, microstructure, dispersion, exact solution.

References

 1. Maugin , G. A. , Pouget , J. , Drouot , R. , and Collet , B. Nonlinear Electromechanical Couplings. John Wiley & Sons , UK , 1992.

  2. Aero , E. L. Micromechanics of a double continuum in a model of a medium with variable periodic structure. J. Eng. Math. , 2002 , 55 , 81–95.
doi:10.1007/s10665-005-9012-3

  3. Aero , E. L. and Bulygin , A. N. Strongly nonlinear theory of nanostructure formation owing to elastic and nonelastic strains in crystalline solids. Mech. Solids. , 2007 , 42 , 807–822.
doi:10.3103/S0025654407050147

  4. Porubov , A. V. , Aero , E. L. , and Maugin , G. A. Two approaches to study essentially nonlinear and dispersive properties of the internal structure of materials. Phys. Rev. E , 2009 , 79 , 046608.
doi:10.1103/PhysRevE.79.046608

  5. Engelbrecht , J. , Berezovsky , A. , Pastrone , F. , and Braun , M. Waves in microstructured materials and dispersion. Philos. Mag. , 2005 , 85 , 4127–4141.
doi:10.1080/14786430500362769

  6. Khusnutdinova , K. R. Nonlinear waves in a two-row system of particles. Vestnik Moskov. Univ. Ser. I Mat. Mekh.} , 1992 , 2 , 71–76 (in Russian).

  7. Janno , J. and Engelbrecht , J. Solitary waves in nonlinear microstructured materials. J. Phys. A: Math. Gen. , 2005 , 38 , 5159–5172.
doi:10.1088/0305-4470/38/23/006

  8. Dragunov , T. N. , Pavlov , I. S. , and Potapov , A. I. Anharmonic interactions of elastic and orientational waves in one-dimensional crystals. Phys. Solid State , 1997 , 39 , 118–124.
doi:10.1134/1.1129811

  9. Engelbrecht , J. and Pastrone , F. Waves in microstructured solids with strong nonlinearities in microscale. Proc. Estonian Acad. Sci. Phys. Math. , 2003 , 52 , 12–20.

10. Porubov , A. V. and Pastrone , F. Nonlinear bell-shaped and kink-shaped strain waves in microstructured solids. Int. J. Nonlinear Mech. , 2004 , 39 , 1289–1299.
doi:10.1016/j.ijnonlinmec.2003.09.002
 
Back

Current Issue: Vol. 68, Issue 4, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December