### Abstract

Elastic constants, are usually obtained experimentally, since it has some problems to predict elastic constants of materials analytically from atomistic viewpoint. In the previous papers, the authors proposed a method for expressing internal forces from motions of atoms, and the conservation laws for solids are introduced microscopically. In the present paper, constitutive equations and elastic constants not only for stresses but also for higher-order stresses are derived by dividing the kinematical quantities of atoms into the macroscopic deformation and thermal motion. In the process of derivation, a concept of a hierarchical Reynolds decomposition is introduced. It is an expansion in power series which can be divided into an average value and a deviation in each hierarchy. The hierarchical deviation terms are expressed by characteristic tensors which can be called P-tensors. The P-tensors are the indexes of atomic configurations and are used effectively for the expression of the elastic constants.

Original language | English |
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Pages (from-to) | 7-13 |

Number of pages | 7 |

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

Volume | 66 |

Issue number | 641 |

DOIs | |

Publication status | Published - 2000 Jan 1 |

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### Keywords

- Constitutive equation
- Elastic constant
- Hierarchic Reynolds decomposition
- Lattice dynamics
- Mesodomain
- P-tensor

### ASJC Scopus subject areas

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

### Cite this

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

*66*(641), 7-13. https://doi.org/10.1299/kikaia.66.7