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In the Self-Contact Problem in Nonlinear Elasticity

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Abstract

In this paper, we consider the minimization problem of 3-dimensional nonlinear hyperelastic bodies moving in \({\mathbb {R}}^{3}\), which enables frictionless self-contact and forbids self-intersection. For this, we define a new class of admissible deformations based on a natural homotopy constraint. We study strictly orientation-preserving Sobolev maps in this new class and their global invertibility properties from a topological point of view. In this fashion, we prove that, under suitable hypotheses, such maps are actually homeomorphisms. Applying this result to the mixed displacement-traction problem, the existence of homeomorphic minimizers is shown for nonlinear stored energy functions with suitable properties

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Authors and Affiliations

  1. Laboratoire LIABM, Département de Mathémathiques, Faculté des Sciences, Université Mohammed Premier, Oujda, Morocco

    Anass Nifa & Bouchta Bouali

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  1. Anass Nifa
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  2. Bouchta Bouali
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Communicated by A. Braides.

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Nifa, A., Bouali, B. In the Self-Contact Problem in Nonlinear Elasticity. Arch Rational Mech Anal 243, 1433–1448 (2022). https://doi.org/10.1007/s00205-021-01752-2

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