A Locally Exact Homogenization Theory for Periodic Microstructures With Isotropic Phases
- 17 July 2008
- journal article
- Published by ASME International in Journal of Applied Mechanics
- Vol. 75 (5), 051010
- https://doi.org/10.1115/1.2913043
Abstract
Elements of the homogenization theory are utilized to develop a new micromechanics approach for unit cells of periodic heterogeneous materials based on locally exact elasticity solutions. The interior inclusion problem is exactly solved by using Fourier series representation of the local displacement field. The exterior unit cell periodic boundary-value problem is tackled by using a new variational principle for this class of nonseparable elasticity problems, which leads to exceptionally fast and well-behaved convergence of the Fourier series coefficients. Closed-form expressions for the homogenized moduli of unidirectionally reinforced heterogeneous materials are obtained in terms of Hill’s strain concentration matrices valid under arbitrary combined loading, which yield homogenized Hooke’s law. Homogenized engineering moduli and local displacement and stress fields of unit cells with offset fibers, which require the use of periodic boundary conditions, are compared to corresponding finite-element results demonstrating excellent correlation.Keywords
This publication has 16 references indexed in Scilit:
- Micro-macromechanical analysis of heterogeneous materials: Macroscopically homogeneous vs periodic microstructuresComposites Science and Technology, 2007
- Finite-volume direct averaging micromechanics of heterogeneous materials with elastic–plastic phasesInternational Journal of Plasticity, 2006
- Loosening of elastic inclusionsInternational Journal of Solids and Structures, 2006
- An embedding method for modeling micromechanical behavior and macroscopic properties of composite materialsInternational Journal of Solids and Structures, 2005
- A Second Look at the Higher-Order Theory for Periodic Multiphase MaterialsJournal of Applied Mechanics, 2005
- A calculation of the elastic constants of a unidirectional fibre-reinforced compositeJournal of Physics D: Applied Physics, 1968
- Mechanical Properties of Fiber Reinforced CompositesJournal of Composite Materials, 1967
- PLANE ELASTOSTATIC ANALYSIS OF AN INFINITE PLATE WITH A DOUBLY PERIODIC ARRAY OF HOLES OR RIGID INCLUSIONSPublished by Elsevier BV ,1967
- Elastic equilibrium of an isotropic plane with a doubly periodic system of inclusionsInternational Applied Mechanics, 1966
- Elastic properties of reinforced solids: Some theoretical principlesJournal of the Mechanics and Physics of Solids, 1963