Equivalent thermo-mechanical parameters for perfect crystals

  • V. A. Kuzkin
  • A. M. Krivtsov
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 27)


Thermo-elastic behavior of perfect single crystal is considered. The crystal is represented as a set of interacting particles (atoms). The approach for determination of equivalent continuum values for the discrete system is proposed. Averaging of equations of particles’ motion and long wave approximation are used in order to make link between the discrete system and equivalent continuum. Basic balance equations for equivalent continuum are derived from microscopic equations. Macroscopic values such as Piola and Cauchy stress tensors and heat flux are represented via microscopic parameters. Connection between the heat flux and temperature is discussed. Equation of state in Mie-Gruneisen form connecting Cauchy stress tensor with deformation gradient and thermal energy is obtained from microscopic considerations.


Discrete System Spatial Average Cauchy Stress Perfect Crystal Energy Balance Equation 
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© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Institute for Problems in Mechanical Engineering RASSt. PetersburgRussia

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