Compact closed-form micromechanical expressions for the effective uncoupled and coupled linear properties of layered composites

Abstract

This work aims mainly to derive closed-form expressions for the effective properties of layered composites when linear uncoupled and coupled phenomena, such as conduction, elasticity, thermoelectricity and piezomagnetoelectricity, are concerned. In addition, properties may be graded in the direction normal to the layer plane. The remarkable feature of the obtained results is that they are expressed in a unified and very compact way for all uncoupled and coupled linear mechanical and physical phenomena. Our results include as special ones all the relevant results reported up to now in the literature. The key to obtaining our general compact coordinate-free results resides in extending Hill’s interfacial relations for a perfect elastic interface to the setting of an arbitrary finite number of uncoupled and coupled linear phenomena. The effects of the presence of stiffeners and softeners on the effective properties of layered composites are also investigated. In particular, four limiting cases for piezoelectricity are studied in detail. As illustrations, the general results are applied to several coupled phenomena and to functionally graded layered composites.

Keywords:

• layered structures
• perfect interface
• micromechanical model
• effective properties

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11202173]; the Fundamental Research Funds for the Central Universities [grant number B14020183]; the Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering Institute of Rock and Soil Mechanics, Chinese Academy of Sciences [grant number Z013009].