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Introduction to Geometrically Nonlinear Continuum Dislocation Theory

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Abstract

This chapter first summarizes the content of the book and discusses key results. Subsequently, a multitude of promising future branches of research is outlined. On the one hand, this concerns possible theoretical extensions of the model and the numerical studies. On the other hand, proper experiments are suggested for the validation of the numerical results. Thereby, the focus is on cubic minerals.

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Notes

  1. 1.

    This requires a solution for the problem with potential (3.44) at \(p>1\).

  2. 2.

    The comparison with dislocation cell forming metals and alloys is, of course, limited due to the differences between metallic and ionic bond and the resulting consequences.

  3. 3.

    The actual realization at low temperatures with optical accessibility of the sample poses a technical challenge.

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Authors and Affiliations

  1. Institute of Mechanics and Thermodynamics, Chemnitz University of Technology, Chemnitz, Germany

    Christian B. Silbermann & Jörn Ihlemann

  2. Bau- und Umweltingenieurwesen, Bochum University of Applied Sciences, Bochum, Germany

    Matthias Baitsch

Authors
  1. Christian B. Silbermann
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  2. Matthias Baitsch
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  3. Jörn Ihlemann
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Correspondence to Christian B. Silbermann .

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Silbermann, C.B., Baitsch, M., Ihlemann, J. (2021). Outlook. In: Introduction to Geometrically Nonlinear Continuum Dislocation Theory. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-030-63696-8_8

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