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Analysis of Velocity Singularity in Dynamic Cohesive Fracture

Morgan Hawker and Robert Haber, Department of Theoretical & Applied Mechanics

Velocity follows inverse rootVelocity follows inverse root

Analysis shows the velocity follows classic inverse root of r form. Zoom image

Animation of shock hitting crack

Detail of shock hitting crack; transition to singular response at initiation. Color is strain energy density; height is velocity magnitude.


Dynamic fracture along interfaces describes certain forms of material failure as well as the mechanics of earthquakes at much larger length scales. We study numerically the dynamics of fracture using a cohesive damage model. We discovered unexpected singular velocity response at cohesive crack tips; we seek a deeper understanding of this phenomenon.


We embed a cohesive failure model within an elastodynamic spacetime discontinuous Galerkin (SDG) model. Adaptive analysis techniques guarantee very high-resolution solutions. Post-simulation analysis reveals singular response with the same form as in classical, non-cohesive fracture, possibly with non-singular core.


The discovery of the crack-tip velocity singularity suggests a fundamental rethinking of the physics of dynamic fracture that can lead to improved understanding and prediction of materials failure under dynamic loads and of geological fractures along fault lines in earthquakes.

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