New method to determine the exact periodic boundary conditions for macro-microscopic homogenization analysis and its application on the prediction of effective elastic constants of periodic materials

Dongmei Luo, Wenxue Wang, Yoshihiro Takao, Koichi Kakimoto

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

A new method is proposed to determine the exact periodic boundary conditions for the macro-microscopic homogenization analysis of materials with periodic micro-structures. A homogeneous integral equation is derived to replace the conventional inhomogeneous integral equation related to the microscopic mechanical behavior in the basic unit cell by introducing a new characteristic function. Based on the new solution method, the computational problem of the characteristic function subject to initial strains and periodic boundary conditions is reduced to a simple displacement boundary value problem without initial strains, which simplifies the computational process. Applications to the predication of effective elastic constants of materials with various two-dimensional and three-dimensional periodic microstructures are presented. The numerical results are compared with empirical results obtained from the Halpin-Tsai equations, Mori-Tanaka method and conventional homogenization calculations, which proves that the present method is valid and efficient for prediction of the effective elastic constants of materials with various periodic microstructures.

Original languageEnglish
Pages (from-to)517-523
Number of pages7
JournalJixie Qiangdu/Journal of Mechanical Strength
Volume28
Issue number4
Publication statusPublished - Aug 2006

Fingerprint

Elastic Constants
Elastic constants
Periodic Boundary Conditions
Homogenization
Macros
Boundary conditions
Microstructure
Integral equations
Prediction
Characteristic Function
Integral Equations
Boundary value problems
Mechanical Behavior
Simplify
Boundary Value Problem
Valid
Numerical Results
Three-dimensional
Unit
Cell

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering

Cite this

@article{1c38ef9878f8432680a4742248b21ceb,
title = "New method to determine the exact periodic boundary conditions for macro-microscopic homogenization analysis and its application on the prediction of effective elastic constants of periodic materials",
abstract = "A new method is proposed to determine the exact periodic boundary conditions for the macro-microscopic homogenization analysis of materials with periodic micro-structures. A homogeneous integral equation is derived to replace the conventional inhomogeneous integral equation related to the microscopic mechanical behavior in the basic unit cell by introducing a new characteristic function. Based on the new solution method, the computational problem of the characteristic function subject to initial strains and periodic boundary conditions is reduced to a simple displacement boundary value problem without initial strains, which simplifies the computational process. Applications to the predication of effective elastic constants of materials with various two-dimensional and three-dimensional periodic microstructures are presented. The numerical results are compared with empirical results obtained from the Halpin-Tsai equations, Mori-Tanaka method and conventional homogenization calculations, which proves that the present method is valid and efficient for prediction of the effective elastic constants of materials with various periodic microstructures.",
author = "Dongmei Luo and Wenxue Wang and Yoshihiro Takao and Koichi Kakimoto",
year = "2006",
month = "8",
language = "English",
volume = "28",
pages = "517--523",
journal = "Jixie Qiangdu/Journal of Mechanical Strength",
issn = "1001-9669",
publisher = "Journal of Mechanical Strength",
number = "4",

}

TY - JOUR

T1 - New method to determine the exact periodic boundary conditions for macro-microscopic homogenization analysis and its application on the prediction of effective elastic constants of periodic materials

AU - Luo, Dongmei

AU - Wang, Wenxue

AU - Takao, Yoshihiro

AU - Kakimoto, Koichi

PY - 2006/8

Y1 - 2006/8

N2 - A new method is proposed to determine the exact periodic boundary conditions for the macro-microscopic homogenization analysis of materials with periodic micro-structures. A homogeneous integral equation is derived to replace the conventional inhomogeneous integral equation related to the microscopic mechanical behavior in the basic unit cell by introducing a new characteristic function. Based on the new solution method, the computational problem of the characteristic function subject to initial strains and periodic boundary conditions is reduced to a simple displacement boundary value problem without initial strains, which simplifies the computational process. Applications to the predication of effective elastic constants of materials with various two-dimensional and three-dimensional periodic microstructures are presented. The numerical results are compared with empirical results obtained from the Halpin-Tsai equations, Mori-Tanaka method and conventional homogenization calculations, which proves that the present method is valid and efficient for prediction of the effective elastic constants of materials with various periodic microstructures.

AB - A new method is proposed to determine the exact periodic boundary conditions for the macro-microscopic homogenization analysis of materials with periodic micro-structures. A homogeneous integral equation is derived to replace the conventional inhomogeneous integral equation related to the microscopic mechanical behavior in the basic unit cell by introducing a new characteristic function. Based on the new solution method, the computational problem of the characteristic function subject to initial strains and periodic boundary conditions is reduced to a simple displacement boundary value problem without initial strains, which simplifies the computational process. Applications to the predication of effective elastic constants of materials with various two-dimensional and three-dimensional periodic microstructures are presented. The numerical results are compared with empirical results obtained from the Halpin-Tsai equations, Mori-Tanaka method and conventional homogenization calculations, which proves that the present method is valid and efficient for prediction of the effective elastic constants of materials with various periodic microstructures.

UR - http://www.scopus.com/inward/record.url?scp=33751555716&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33751555716&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33751555716

VL - 28

SP - 517

EP - 523

JO - Jixie Qiangdu/Journal of Mechanical Strength

JF - Jixie Qiangdu/Journal of Mechanical Strength

SN - 1001-9669

IS - 4

ER -