Microscopic derivation for energy equation based on lattice dynamics

Yoshihiro Yasui, Kazuyuki Shizawa, Kunihiro Takahashi

Research output: Contribution to journalArticlepeer-review


In the previous report, a method is proposed to obtain the definitions for internal forces of continua, and then the balance equations for mass, force and moment are formulated using microscopic quantities. In the present paper, heat flux and internal energy are formulated and the energy equation is derived on the basis of lattice dynamics. In order to derive a definition of heat flux, a kinematical quantity of an atom is divided into macroscopic and thermal motion, and heat flux is defined using the thermal motion. Internal energy is defined as kinematical energy and potential energy of atoms in the mesodomain. These definitions of heat flux and internal energy are useful in obtaining macroscopic quantities from numerical solutions calculated by the molecular dynamics. The energy equation which includes heat flux and internal energy is expressed in terms of microscopic quantities.

Original languageEnglish
Pages (from-to)2116-2121
Number of pages6
JournalNippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A
Issue number601
Publication statusPublished - 1996 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering


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