Abstract
The recently developed weakly nonlinear theory of dynamic fracture predicts corrections to the standard asymptotic linear elastic displacement gradients, where is measured from the tip of a tensile crack. We show that the singularity does not automatically conform with the notion of autonomy (autonomy means that any crack tip nonlinear solution is uniquely determined by the surrounding linear elastic fields) and that it does not automatically satisfy the resultant Newton’s equation in the crack parallel direction. We show that these two properties are interrelated and that by requiring that the resultant Newton’s equation is satisfied, autonomy of the singular solution is retained. We further show that the resultant linear momentum carried by the singular fields vanishes identically. Our results, which reveal the physical and mathematical nature of the solution, are in favorable agreement with recent near-tip measurements.
- Received 13 May 2010
DOI:https://doi.org/10.1103/PhysRevE.82.015101
©2010 American Physical Society