### Abstract

In the previous papers, the authors proposed the concept of the mesodomain which connects microscopic kinematic quantities and macroscopic mechanical ones using an assumption of constrained gradient. However, stress and higher-order stresses obtained from the discussions are not defined as area averages but only as volume averages. In the present paper, mechanical balance equations in the mesodomains are derived based on the conservation law of an atom without the above assumption. Solids are modeled as spring-particle systems in the mesodomains. The averaged values of microscopic quantities over the domain are associated with the center of mass, and macroscopic mechanical balance equations are obtained using these averaged values. Since this model can be regarded as micromorphic continua, we can express Cauchy stress, volume-averaged stress and higher-order stress with microscopic quantities.

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

Pages (from-to) | 1096-1103 |

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), 1096-1103.

**Mechanical balance equations for micromorphic model considering 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. 1096-1103.

}

TY - JOUR

T1 - Mechanical balance equations for micromorphic model considering lattice dynamics

AU - Nakane, Motoki

AU - Fujinuma, Hiroyuki

AU - Shizawa, Kazuyuki

AU - Takahashi, Kunihiro

PY - 1997/5

Y1 - 1997/5

N2 - In the previous papers, the authors proposed the concept of the mesodomain which connects microscopic kinematic quantities and macroscopic mechanical ones using an assumption of constrained gradient. However, stress and higher-order stresses obtained from the discussions are not defined as area averages but only as volume averages. In the present paper, mechanical balance equations in the mesodomains are derived based on the conservation law of an atom without the above assumption. Solids are modeled as spring-particle systems in the mesodomains. The averaged values of microscopic quantities over the domain are associated with the center of mass, and macroscopic mechanical balance equations are obtained using these averaged values. Since this model can be regarded as micromorphic continua, we can express Cauchy stress, volume-averaged stress and higher-order stress with microscopic quantities.

AB - In the previous papers, the authors proposed the concept of the mesodomain which connects microscopic kinematic quantities and macroscopic mechanical ones using an assumption of constrained gradient. However, stress and higher-order stresses obtained from the discussions are not defined as area averages but only as volume averages. In the present paper, mechanical balance equations in the mesodomains are derived based on the conservation law of an atom without the above assumption. Solids are modeled as spring-particle systems in the mesodomains. The averaged values of microscopic quantities over the domain are associated with the center of mass, and macroscopic mechanical balance equations are obtained using these averaged values. Since this model can be regarded as micromorphic continua, we can express Cauchy stress, volume-averaged stress and higher-order stress with microscopic quantities.

UR - http://www.scopus.com/inward/record.url?scp=0031147487&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031147487&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031147487

VL - 63

SP - 1096

EP - 1103

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 -