Analysis of a transversely isotropic rod containing a single cylindrical inclusion with axisymmetric eigenstrains Z. Zhong a, * , Q.P. Sun b a Solid Mechanics Key Laboratory of MOE, Department of Engineering Mechanics and Technology, Tongji University, Shanghai 200092, China b Department of Mechanical Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR, China Received 16 January 2002; received in revised form 7 August 2002 Abstract This paper studies a transversely isotropic rod containing a single cylindrical inclusion with axisymmetric eigen- strains. The analytical elastic solution is obtained for the displacements, stresses and elastic strain energy of the rod. The effects of microstructural parameters and its evolution on the elastic stress and strain fields as well as the strain energy of the rod are quantitatively demonstrated through examples. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Transversely isotropic rod; Cylindrical inclusion; Axisymmetric eigenstrain 1. Introduction Experimental observations on tensile test of NiTi polycrystalline shape memory alloy wires and strips have shown that the deformation in the superelastic region is realized by the reversible propagation of single band and multi-bands during the forward and reverse transformations (Leo et al., 1993; Lin et al., 1994; Shaw and Kyriakides, 1995, 1997). These phenomena motivated the study of a new type of inclusion- matrix system: an infinite circular cylindrical rod containing a single inclusion with uniform axisymmetric eigenstrains (Zhong et al., 2000). This kind of inclusion problem is different from the traditional Eshelby- type inclusion problems (Eshelby, 1957; Mura, 1987; among others) in that the inclusion is not fully bounded by the matrix. The solution of such a new inclusion problem has been employed to predict the force–displacement relationship in the uniaxial tensile loading of the SMA wire specimen under isothermal or very slow loading rate cases (Sun and Zhong, 2000). In our previous paper (Zhong et al., 2000), the assumption of isotropy was made for the elastic properties of the rod, while in the present paper we considered a more general case of transversely isotropic rod International Journal of Solids and Structures 39 (2002) 5753–5765 www.elsevier.com/locate/ijsolstr * Corresponding author. Tel.: +86-21-65982483. E-mail address: zhongk@online.sh.cn (Z. Zhong). 0020-7683/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0020-7683(02)00459-6