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 |
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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 |
All Science Journal Classification (ASJC) codes
- Mechanical Engineering