Vol. 3, No. 9, 2008

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ISSN: 1559-3959
Reconsidering the boundary conditions for a dynamic, transient mode I crack problem

Tanya L. Leise, Jay R. Walton and Yuliya Gorb

Vol. 3 (2008), No. 9, 1797–1807
Abstract

A careful examination of a dynamic mode I crack problem leads to the conclusion that the commonly used boundary conditions do not always hold in the case of an applied crack face loading, so that a modification is required to satisfy the equations. In particular, a transient compressive stress wave travels along the crack faces, moving outward from the loading region on the crack face. This does not occur in the quasistatic or steady state problems, and is a special feature of the transient dynamic problem that is important during the time interval immediately following the application of crack face loading. We demonstrate why the usual boundary conditions lead to a prediction of crack face interpenetration, and then examine how to modify the boundary condition for a semi-infinite crack with a cohesive zone. Numerical simulations illustrate the resulting approach.

Keywords
transient fracture analysis, opening mode crack, boundary conditions, Dirichlet-to-Neumann map
Milestones
Received: 4 September 2008
Revised: 18 November 2008
Accepted: 20 November 2008
Published: 1 November 2008
Authors
Tanya L. Leise
Amherst College
Department of Mathematics and Computer Science
Amherst, MA 01002
United States
Jay R. Walton
Texas A & M University
Department of Mathematics
College Station, TX 77843-3368
United States
Yuliya Gorb
Texas A & M University
Department of Mathematics
College Station, TX 77843-3368
United States