Structural Modeling of Nonlinear Localized Strain Waves in Generalized Continua

  • Vladimir I. ErofeevEmail author
  • Anna V. Leontyeva
  • Alexey O. Malkhanov
  • Igor S. Pavlov
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 120)


The basic principles of structural modeling for the construction of mathematical models of microstructured media (generalized continua) are given. Here, microstructure means not the smallness of absolute values, but the smallness of some medium scale with respect to other scales, and the particles are considered to be non-deformable and homogeneous, without their own internal structure, presenting realistic materials. A nonlinear dynamically consistent model of a gradient-elastic medium has been elaborated by the method of structural modeling and using the continualization method involving nonlocality of coupling between the displacements of the lattice sites and the obtained continuum. The formation of spatially localized nonlinear strain waves in such media has been investigated.


Structural modeling Gradient theory Nonlinear strain waves 


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The research was carried out under the financial support of the Russian Foundation for Basic Research (projects NN 18-29-10073-mk and 19-08-00965-a).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Vladimir I. Erofeev
    • 1
    Email author
  • Anna V. Leontyeva
    • 1
  • Alexey O. Malkhanov
    • 2
  • Igor S. Pavlov
    • 1
  1. 1.Mechanical Engineering Research Institute of Russian Academy of Sciences, Research Institute for MechanicsNizhny Novgorod Lobachevsky State UniversityNizhny NovgorodRussia
  2. 2.Mechanical Engineering Research Institute of Russian Academy of SciencesNizhny NovgorodRussia

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