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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