Interaction and multiscale mechanics

  • 제3권1호
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  • Pages.1-22
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  • 2010
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  • 1976-0426(pISSN)
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  • 2092-6200(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

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

  • 투고 : 2009.12.01
  • 심사 : 2010.02.19
  • 발행 : 2010.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

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.

키워드

참고문헌

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  2. A method of multiscale modelling considered as a way leading to unified mechanics of materials vol.226, pp.5, 2015, https://doi.org/10.1007/s00707-014-1261-7
  3. Problems Associated with Transferring of Engineering to Small Scale - Towards Theoretical Nanotechnology vol.130, pp.6, 2016, https://doi.org/10.12693/APhysPolA.130.1295
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  5. Multiscale modeling of the anisotropic shock response of β-HMX molecular polycrystals vol.4, pp.2, 2010, https://doi.org/10.12989/imm.2011.4.2.139