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A three-dimensional inverse problem for inhomogeneities in elastic solids

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Abstract

The Newtonian potential is used to solve an inverse problem in which we seek the shape of an inhomogeneity in an infinite elastic matrix under uniform applied stresses at infinity such that certain stress components are uniform on the boundary of the inhomogeneity. It is shown that ellipsoids furnish the solution of this inverse problem. Exact and general expressions for the stress and displacement are given explicitly for points in the elastic matrix outside the inhomogeneity. The solution of the corresponding plane deformation problem is found as a limiting case. Several applications are presented, and results from the literature are confirmed as special cases.

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Author notes

  1. Bahir H. Eldiwany

    Present address: Kalsi Engineering, Inc., 77478, Sugarland, TX, USA

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Houston-University Park, 77004, Houston, TX, USA

    Bahir H. Eldiwany & Lewis T. Wheeler

Authors
  1. Bahir H. Eldiwany
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  2. Lewis T. Wheeler
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Eldiwany, B.H., Wheeler, L.T. A three-dimensional inverse problem for inhomogeneities in elastic solids. J Elasticity 16, 201–211 (1986). https://doi.org/10.1007/BF00043586

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  • DOI: https://doi.org/10.1007/BF00043586

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