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Optimal rigid inclusion shapes in elastic bodies with cracks

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Abstract

The paper concerns the control of rigid inclusion shapes in elastic bodies with cracks. Cracks are located on the boundary of rigid inclusions and in the bulk. Inequality type boundary conditions are imposed at the crack faces to guarantee mutual non-penetration. Inclusion shapes are considered as control functions. First we provide the problem formulation and analyze the shape sensitivity with respect to geometrical perturbations of the inclusion. Then, based on Griffith criterion, we introduce the cost functional, which measures the shape sensitivity of the problem with respect to the geometry of the inclusion, provided by the energy release rate. We prove existence of optimal shapes for the problem considered.

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Authors and Affiliations

  1. Russian Academy of Sciences, Lavrentyev Institute of Hydrodynamics, 630090, Novosibirsk, Russia

    A. Khludnev

  2. Department of Mathematics, University of Pavia, via Ferrata 1, 27100, Pavia, Italy

    M. Negri

Authors
  1. A. Khludnev
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  2. M. Negri
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Correspondence to A. Khludnev.

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Khludnev, A., Negri, M. Optimal rigid inclusion shapes in elastic bodies with cracks. Z. Angew. Math. Phys. 64, 179–191 (2013). https://doi.org/10.1007/s00033-012-0220-1

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  • DOI: https://doi.org/10.1007/s00033-012-0220-1

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