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Numerical studies of loss of ellipticity near singularities in an elastic material

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Abstract

Numerical solutions of anti-plane shear crack problems and screw dislocation problems are presented for materials in which the equilibrium equation varies in type locally from elliptic to hyperbolic as a result of deformation. These results show the emergence of surfaces of discontinuity in the displacement field in some materials. In other materials they show a chaotic mixture of elliptic phases at intermediate distances from the singularity. A statistical analysis applied to the numerical solutions demonstrates the role of elastic stability in the mechanics of these deformations.

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Author notes

  1. S. A. Silling

    Present address: Division of Engineering, Brown University, 02912, Providence, RI, USA

Authors and Affiliations

  1. Division of Engineering and Applied Science, California Institute of Technology, 91125, Pasadena, CA, USA

    S. A. Silling

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Silling, S.A. Numerical studies of loss of ellipticity near singularities in an elastic material. J Elasticity 19, 213–239 (1988). https://doi.org/10.1007/BF00045617

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  • DOI: https://doi.org/10.1007/BF00045617

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