### Abstract

In previous papers, microscopic expression of stress and balance equations for a solid which has a simple lattice were described with the microscopic values in the mesodomain without an assumption of a constrained gradient. In this paper, the solid is remodeled as an assembly of atoms which are arranged randomly. Microscopic expressions of stress, higher-order stress and heat flux are newly discussed expressing the equilibrium conditions for the tetrahedral element in the mesodomain. Stress is represented as an area averaged values with microscopic quantities such as interatomic potential, body force, inertia force and fabric vectors related to the configuration of atoms in the mesodomain. Balance laws of momentum and moments of momentum are derived on the basis of the equations of the motion of atoms. The energy equation is described with the averaged values over the domain dividing the velocity of an atom into the macroscopic motion and thermal motions.

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

Pages (from-to) | 1694-1700 |

Number of pages | 7 |

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

Volume | 63 |

Issue number | 612 |

Publication status | Published - 1997 Aug |

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*(612), 1694-1700.

**Generalized expression of macroscopic stress and balance equations of micromorphic continuum based on lattice dynamics.** / Nakane, Motoki; 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. 612, pp. 1694-1700.

}

TY - JOUR

T1 - Generalized expression of macroscopic stress and balance equations of micromorphic continuum based on lattice dynamics

AU - Nakane, Motoki

AU - Shizawa, Kazuyuki

AU - Takahashi, Kunihiro

PY - 1997/8

Y1 - 1997/8

N2 - In previous papers, microscopic expression of stress and balance equations for a solid which has a simple lattice were described with the microscopic values in the mesodomain without an assumption of a constrained gradient. In this paper, the solid is remodeled as an assembly of atoms which are arranged randomly. Microscopic expressions of stress, higher-order stress and heat flux are newly discussed expressing the equilibrium conditions for the tetrahedral element in the mesodomain. Stress is represented as an area averaged values with microscopic quantities such as interatomic potential, body force, inertia force and fabric vectors related to the configuration of atoms in the mesodomain. Balance laws of momentum and moments of momentum are derived on the basis of the equations of the motion of atoms. The energy equation is described with the averaged values over the domain dividing the velocity of an atom into the macroscopic motion and thermal motions.

AB - In previous papers, microscopic expression of stress and balance equations for a solid which has a simple lattice were described with the microscopic values in the mesodomain without an assumption of a constrained gradient. In this paper, the solid is remodeled as an assembly of atoms which are arranged randomly. Microscopic expressions of stress, higher-order stress and heat flux are newly discussed expressing the equilibrium conditions for the tetrahedral element in the mesodomain. Stress is represented as an area averaged values with microscopic quantities such as interatomic potential, body force, inertia force and fabric vectors related to the configuration of atoms in the mesodomain. Balance laws of momentum and moments of momentum are derived on the basis of the equations of the motion of atoms. The energy equation is described with the averaged values over the domain dividing the velocity of an atom into the macroscopic motion and thermal motions.

UR - http://www.scopus.com/inward/record.url?scp=0031209531&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031209531&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031209531

VL - 63

SP - 1694

EP - 1700

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 - 612

ER -