Circular inclusions in anti-plane strain couple stress elasticity |
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| Affiliation: | 1. Institute of Applied Mechanics of Russian Academy of Sciences, Moscow, Russia;2. Moscow Aviation Institute, Moscow, Russia;1. Department of Mechanical Engineering, University of Chile, Santiago 8370448, Chile;2. Institute for Computational Engineering, Faculty of Science, Technology and Communication, University of Luxembourg, Luxembourg;3. Department of Civil and Environmental Engineering, University of Waterloo, ON, Canada;4. Cardiff University, Institute of Mechanics and Advanced Materials, School of Engineering, College of Physical Sciences and Engineering, UK;5. University of Western Australia, Intelligent Systems for Medicine Laboratory, School of Mechanical and Chemical Engineering, Australia |
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| Abstract: | The solution for a circular inclusion with a prescribed anti-plane eigenstrain is derived. It is shown that the components of the Eshelby tensor within the inclusion, corresponding to a uniform eigenstrain, can be either uniform or non-uniform, depending on the imposed interface conditions. The stress amplification factors due to circular void or rigid inclusion in an infinite medium under remote anti-plane shear stress are calculated. The failure of the couple stress elasticity to reproduce the classical elasticity solution in the limit of vanishingly small characteristic length is indicated for a particular type of boundary conditions. The solution for a circular inhomogeneity in an infinitely extended matrix subjected to remote shear stress is then derived. The effects of the imposed interface conditions, the shear stress and couple stress discontinuities, and the relationship between the inhomogeneity and its equivalent eigenstrain inclusion problem are discussed. |
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