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On the impossibility of arbitrary deformations in nonlinear elasticity

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Abstract

We employ partly Sobolev classes to obtain a necessary condition for mappings of \(W^{1,p}\)-class to be deformations of nonlinearly elastic bodies that can be induced by \(L^{q}\)-forces, \(1\le p,\,q <\infty \). This condition is useful for studying continuous deformations of non-homogeneous materials and for obtaining stable numerical methods for nonlinear elasticity.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, The George Washington University, Washington, DC, 20052, USA

    Arzhang Angoshtari

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  1. Arzhang Angoshtari
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Correspondence to Arzhang Angoshtari.

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Angoshtari, A. On the impossibility of arbitrary deformations in nonlinear elasticity. Z. Angew. Math. Phys. 69, 1 (2018). https://doi.org/10.1007/s00033-017-0895-4

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  • DOI: https://doi.org/10.1007/s00033-017-0895-4

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