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Interaction and Multiscale Mechanics
  Volume 3, Number 1, March 2010, pages 1-22
open access

Collection of dynamical systems with dimensional reduction as a multiscale method of modelling for mechanics of materials
Jaroslaw Kaczmarek

    In this paper one introduces a method of multiscale modelling called collection of dynamical systems with dimensional reduction. The method is suggested to be an appropriate approach to theoretical modelling of phenomena in mechanics of materials having in mind especially dynamics of processes. Within this method one formalizes scale of averaging of processes during modelling. To this end a collection of dynamical systems is distinguished within an elementary dynamical system. One introduces a dimensional reduction procedure which is designed to be a method of transition between various scales. In order to consider continuum models as obtained by means of the dimensional reduction one introduces continuum with finite-dimensional fields. Owing to geometrical elements associated with the elementary dynamical system we can formalize scale of averaging within continuum mechanics approach. In general presented here approach is viewed as a continuation of the rational mechanics.
Key Words
    mechanics of materials; multiscale modelling.
Jaroslaw Kaczmarek: Institute of Fluid-Flow Machinery, Polish Academy of Sciences, 80-952 Gdansk, ul. J.Fiszera 14, Poland

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