A circular inhomogeneity with mixed-type imperfect interface under in-plane deformations
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A circular inhomogeneity with mixed-type imperfect interface under in-plane deformations Xu Wang . Peter Schiavone
Received: 9 April 2016 / Accepted: 10 May 2016 Ó Springer Science+Business Media Dordrecht 2016
Abstract We investigate the in-plane deformations of a circular inhomogeneity bonded to an infinite matrix through a mixed-type imperfect interface when the matrix is subjected to remote uniform stresses. The inhomogeneity and the matrix are endowed with separate and distinct Gurtin–Murdoch surface elasticities yet bonded together through a spring-type imperfect interface. This arrangement in which a soft interface (represented by the spring model) is bounded by two stiff interfaces (from the surface elasticities) is referred to as a ‘mixed-type imperfect interface’. A closed-form solution to the corresponding deformation problem is obtained via the use of complex variable methods, in particular, analytic continuation. We show that the introduction of the mixed-type imperfect interface leads to stress distributions in the composite which depend on six size-dependent parameters. In particular, the stress distribution inside the inhomogeneity is shown to be generally non-uniform except when a particular condition (which we identify
X. Wang School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, People’s Republic of China e-mail: [email protected] P. Schiavone (&) Department of Mechanical Engineering, Donadeo Innovation Centre for Engineering, University of Alberta, 10-203, Edmonton, AB T6G 1H9, Canada e-mail: [email protected]
explicitly) is satisfied by the material parameters, in which case the internal (size-dependent) stress distribution is uniform for any uniform remote loading. Finally, our solution is used to study the design of neutral and harmonic elastic inhomogeneities. Keywords Mixed-type imperfect interface In-plane deformation Inhomogeneity Analytic continuation
1 Introduction Problems involving elastic inhomogeneities with imperfect bonding at the inhomogeneity/matrix interface (imperfect interface) have generated much interest in the literature, in particular among theoreticians and practitioners in the field of micromechanics. The imperfections in the interface arise mainly as a result of damage due to, for example, sliding, debonding and micro-cracking of the interfacial material lying between the inhomogeneity and the surrounding matrix. The introduction of the spring-type imperfect interface model (Achenbach and Zhu 1989; Hashin 1991; Gao 1995; Ru and Schiavone 1997; Zhong and Meguid 1997) was introduced in an effort to account for these interface imperfections and their significant effect on the corresponding mechanical fields in both the inhomogeneity and the matrix. The spring-type interface model is based on the assumption that tractions are continuous but displacements are
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discontinuous across the interface. More precisely, jumps in displacement components are propor
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