A micromechanics model for estimating the effective thermoelastic properties of layered media Zuo-Rong Chen a , Shou-Wen Yu a , Xi-Qiao Feng a, *, Meng Lu b a Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China b Centre for Advanced Materials Technology, School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, Sydney NSW 2006, Australia Received 18 May 2001; received in revised form 23 November 2001; accepted 17 December 2001 Abstract A micromechanics model is presented for estimating the effective thermoelastic properties of layered media. The continuity con- dition across a perfectly bonded interface between two dissimilar materials is introduced by decomposing the stress and strain tensors into two orthogonal complementary parts, an interior part and an exterior part that are tangential and normal to the interface, respectively. This model follows from the fact that the exterior part of the stress tensor and the interior part of the strain tensor are each continuous across the perfect interface. Thereby, the interaction between different phases of composites is accounted for. The exact expressions for the effective thermoelastic properties of layered media are derived, and the connections between the present scheme and some conventional micromechanics models are examined. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: A. Layered structures; B. Interface; B. Thermomechanical properties; C. Elastic properties; Micromechanics 1. Introduction Layered media have found increasingly wide applica- tions in modern technology, e.g. film-substrate struc- tures, multi-layered magnetic recording media in computers, ceramic capacitors and actuators. The desired macroscopic coupling between mechanical, ther- mal, electrical and magnetic properties as well as the interlayer coupling behaviors can be achieved by tailor- ing the microstructures and properties of constituents. The estimation of the effective properties of layered media in terms of microstructural parameters and the properties of the constituent phases plays a significant role in the designing and manufacturing process. The problemofcalculationofthethermoelasticproper- ties of composites has been investigated by many authors. Levin [1] established a simple relationship between the effective thermal expansion coefficients and the effective elastic moduli of two-phase materials. Budiansky [2] ana- lyzed the thermal and thermoelastic properties of iso- tropic composites by using the self-consistent method. These investigations are concerned mainly about com- posites consisting of isotropic constituents and with roughly spherical inclusions. Rosen and Hashin [3] extended Levin’s method to two-phase composites hav- ing anisotropic constituents, and derived the bounds on theeffectivethermalexpansioncoefficientsofmultiphase anisotropic composites. Another interesting method is adopted by Laws [4] to derive the exact relationship between the effective expansion coefficients and the effective elastic moduli of binary composites with arbi- trary anisotropic constituents. His results are identical with those of Rosen and Hashin [3]. More general con- nections between the mechanical and thermal responses ofcompositeswereestablishedin[5,6].Morerecently,Li [7] proposed an effective-medium-field micromechanics model for predicting the effective thermoelastic moduli of multi-phase composites. These works concentrate mainly on estimation of the effective thermoelastic properties of composites of the matrix-inclusion type. The objective of the present work is to develop a micromechanical homogenization scheme for estimating the effective thermoelastic properties of layered media based on the continuity conditions of perfectly bonded interfaces. The stress and strain tensors are each decomposed into two orthogonal complementary parts, 0266-3538/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(02)00017-9 Composites Science and Technology 62 (2002) 441–449 www.elsevier.com/locate/compscitech * Corresponding author. Tel.: +86-10-6277-2934; fax: +86-10- 6277 2926. E-mail address: fengxq@mail.tsinghua.edu.cn (X.-Q. Feng).