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Tractable Models of Solid Mechanics pp 167–236Cite as

Infinite Discrete Systems

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Part of the book series: Foundations of Engineering Mechanics ((FOUNDATIONS))

Abstract

Discrete systems comprising an infinite number of particles are rather challenging for a formulation of tractable models. The simplifications related to a low number of the degrees of freedom or normal modes cannot normally be implemented directly. Transition to a continuum and to a description in terms of partial differential equations may be involved and normally requires a number of assumptions; each of them should be carefully checked. In particular, for different regimes of motion of the discrete system one can obtain rather different continuous approximations. On the other side, such systems are extremely important both in mechanics (for modeling arrays of structural elements etc.) and in physics. For the study of the relationship between macroscopic properties and the microscopic structure in classical physics, the models of this sort are the best possible.

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Authors and Affiliations

  1. Russian Academy of Sciences, Inst. Chemical Physics, Kosygina St. 4, 119991, Moscow, Russia

    Prof. Leonid I. Manevitch

  2. Fac. Mechanical Engineering, Technion Israel Institute of Technology, 32000, Haifa, Israel

    Prof. Oleg V. Gendelman

Authors
  1. Prof. Leonid I. Manevitch
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  2. Prof. Oleg V. Gendelman
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Manevitch, L.I., Gendelman, O.V. (2011). Infinite Discrete Systems. In: Tractable Models of Solid Mechanics. Foundations of Engineering Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15372-3_3

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  • DOI: https://doi.org/10.1007/978-3-642-15372-3_3

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