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 language | English |
|---|---|
| Pages (from-to) | 517-523 |
| Number of pages | 7 |
| Journal | Jixie Qiangdu/Journal of Mechanical Strength |
| Volume | 28 |
| Issue number | 4 |
| Publication status | Published - Aug 2006 |
Fingerprint
All Science Journal Classification (ASJC) codes
- Mechanical Engineering
Cite this
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. / Luo, Dongmei; Wang, Wenxue; Takao, Yoshihiro; Kakimoto, Koichi.
In: Jixie Qiangdu/Journal of Mechanical Strength, Vol. 28, No. 4, 08.2006, p. 517-523.Research output: Contribution to journal › Article
}
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 -