Pennsylvania State University
University Park, Pennsylvania, U. S. A.
Recently, cohesive zone models have been applied to the study of dynamically propagating crack linear-elastic media [1-3]. The constitutive behavior of these models is often chosen to be rate dependent and non-linear, thus making the overall problem impossible to solve in closed-form and rather difficult to solve computationally.
Numerical methods such as the Finite Element method (FEM) and Finite Differences (FD) [1,2], although useful, seem to provide solutions that are significantly affected by the space-time discretization they employ. In particular, the \emph{noise} that accompanies said solutions may prevent the accurate detection and/or prediction of oscillatory phenomena that have been observed in dynamic crack growth experiments. For this reason, alternative solution methods have has been sought capable of eliminating and/or reducing the effects due to numerical aberration. In particular, an approach based on complex variables and integral transforms has provided a reformulation of dynamic crack propagation problems in elastic (as well as viscoelastic) media as a system of integral-differential equations [3]. Along with this reformulation, a novel numerical technique for the derivation of approximate solutions has been developed which seem to be essentially free from the \emph{noise} mentioned above. This paper is devoted to the discussion of this numerical technique and its application for the solution of both steady state as well as non steady state mode III crack propagation problems using both linear and non-linear cohesive zone models.
References:
[1] X.-P. Xu and A. Needleman, {\em J. Mech. Phys. Solids} {\bf 42}, 1397 (1994).
[2] B. Yang and K. Ravi-Chandar, {\em J. Mech. Phys. Solids}. {\bf 44}, 1955 (1996).
[3] F. Costanzo and J.R. Walton, {\em Int.\ J. Eng.\ Sci.} {\bf 35}, 1085 (1997).