### Abstract

In order to model a solid as an assembly of atoms, the mesodomain concept is effective to relate microscopic quantities of atoms with macroscopic quantities of solids. In previous papers, mechanical balance equations were derived on the basis of the equations of motion of atoms without the assumption of a constrained gradient. In the present paper, microscopic expressions of heat flux and internal energy are discussed, expressing the balance of energy with microscopic quantities in the mesodomains. The energy equation is formulated using averaged values of microscopic quantities over the domain by dividing the velocity of an atom into macroscopic motion and thermal motions. Heat flux is defined as an area-averaged value of thermal motions of atoms. Internal energy is described as the sum of the kinematic and potential energies of atoms in the mesodomain. Moreover, it is indicated from the microscopic expressions that the higher-order couple stress power and the moment of inertia are equivalent to the heat flux and the internal energy, respectively.

Original language | English |
---|---|

Pages (from-to) | 1104-1111 |

Number of pages | 8 |

Journal | Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A |

Volume | 63 |

Issue number | 609 |

Publication status | Published - 1997 May |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mechanical Engineering

### Cite this

*Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A*,

*63*(609), 1104-1111.

**Energy equation of micromorphic continuum model based on lattice dynamics.** / Nakane, Motoki; Fujinuma, Hiroyuki; Shizawa, Kazuyuki; Takahashi, Kunihiro.

Research output: Contribution to journal › Article

*Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A*, vol. 63, no. 609, pp. 1104-1111.

}

TY - JOUR

T1 - Energy equation of micromorphic continuum model based on lattice dynamics

AU - Nakane, Motoki

AU - Fujinuma, Hiroyuki

AU - Shizawa, Kazuyuki

AU - Takahashi, Kunihiro

PY - 1997/5

Y1 - 1997/5

N2 - In order to model a solid as an assembly of atoms, the mesodomain concept is effective to relate microscopic quantities of atoms with macroscopic quantities of solids. In previous papers, mechanical balance equations were derived on the basis of the equations of motion of atoms without the assumption of a constrained gradient. In the present paper, microscopic expressions of heat flux and internal energy are discussed, expressing the balance of energy with microscopic quantities in the mesodomains. The energy equation is formulated using averaged values of microscopic quantities over the domain by dividing the velocity of an atom into macroscopic motion and thermal motions. Heat flux is defined as an area-averaged value of thermal motions of atoms. Internal energy is described as the sum of the kinematic and potential energies of atoms in the mesodomain. Moreover, it is indicated from the microscopic expressions that the higher-order couple stress power and the moment of inertia are equivalent to the heat flux and the internal energy, respectively.

AB - In order to model a solid as an assembly of atoms, the mesodomain concept is effective to relate microscopic quantities of atoms with macroscopic quantities of solids. In previous papers, mechanical balance equations were derived on the basis of the equations of motion of atoms without the assumption of a constrained gradient. In the present paper, microscopic expressions of heat flux and internal energy are discussed, expressing the balance of energy with microscopic quantities in the mesodomains. The energy equation is formulated using averaged values of microscopic quantities over the domain by dividing the velocity of an atom into macroscopic motion and thermal motions. Heat flux is defined as an area-averaged value of thermal motions of atoms. Internal energy is described as the sum of the kinematic and potential energies of atoms in the mesodomain. Moreover, it is indicated from the microscopic expressions that the higher-order couple stress power and the moment of inertia are equivalent to the heat flux and the internal energy, respectively.

UR - http://www.scopus.com/inward/record.url?scp=0031145744&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031145744&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031145744

VL - 63

SP - 1104

EP - 1111

JO - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

JF - Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A

SN - 0387-5008

IS - 609

ER -