In this paper, the elastic field in an infinite elastic body containing a polyhedral inclusion with uniform eigenstrains is investigated. Exact solutions are obtained for the stress field in and around a fully general polyhedron, i.e., an arbitrary bounded region of three-dimensional space with a piecewise planner boundary. Numerical results are presented for the stress field and the strain energy for several major polyhedra and the effective stiffness of a composite with regular polyhedral inhomogeneities. It is found that the stresses at the center of a polyhedral inclusion with uniaxial eigenstrain do not coincide with those for a spherical inclusion (Eshelby’s solution) except for dodecahedron and icosahedron which belong to icosidodeca family, i.e., highly symmetrical structure.
Elastic Fields in a Polyhedral Inclusion With Uniform Eigenstrains and Related Problems
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the ASME Applied Mechanics Division, May 13, 1999; final revision, April 14, 2000. Editor: L. T. Wheeler. Discussion on the paper should be addressed to the Editor, Professor Lewis T. Wheeler, Department of Mechanical Engineering, University of Houston, Houston, TX 77204-4792, and will be accepted until four months after final publication of the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Nozaki, H., and Taya, M. (April 14, 2000). "Elastic Fields in a Polyhedral Inclusion With Uniform Eigenstrains and Related Problems ." ASME. J. Appl. Mech. May 2001; 68(3): 441–452. https://doi.org/10.1115/1.1362670
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