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On pseudo-plane deformations for the neo-Hookean material

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Abstract

For finite elastic deformations of the incompressible neo-Hookean material the problem of determining exact pseudo-plane deformations is considered. In particular three dimensional deformations are examined which are generated by replacing constants of an assumed known plane deformation with functions of a single space variable. Results are given for replacement of constants arising from translational and rotational invariance and stretchings. Finally two specific deformations are considered which provide new exact solutions for the neo-Hookean material.

Zusammenfassung

Exakte Lösungen für das Problem von pseudo-ebenen finiten Deformationen eines elastischen, inkompressiblen, neo-Hookeschen Materials werden ermittelt und diskutiert. Insbesondere werden dreidimensionale Deformationen studiert, welche durch Ersetzen der Konstanten einer als bekannt vorausgesetzten ebenen Deformation mit Funktionen einer einzigen Raumvariablen erzeugt werden. Resultate für den Ersatz der Konstanten aus Translations- und Rotationsinvarianz sowie aus Dehnungen sind aufgeführt. Schließlich werden zwei spezifische Deformationen betrachtet, welche zu neuen exakten Lösungen für das neo-Hookesche Material führen.

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Authors and Affiliations

  1. Dept. of Mathematics, The University of Wollongong, Wollongong, N. S. W., Australia

    James M. Hill

  2. Dept. of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA

    R. T. Shield

Authors
  1. James M. Hill
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  2. R. T. Shield
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Hill, J.M., Shield, R.T. On pseudo-plane deformations for the neo-Hookean material. Z. angew. Math. Phys. 37, 104–113 (1986). https://doi.org/10.1007/BF00955521

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  • DOI: https://doi.org/10.1007/BF00955521

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