Numerical solution of dynamic stresses induced by moving cracks

Jacob Aboudi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Elastodynamic problems involving mixed boundary conditions are considered. In these problems uniform and non-uniform extension of semi-infinite cracks under anti-plane and in-plane loadings are treated. The equations of motion are transformed to a coordinate system in which the moving tip of the crack appears always at the origin of the coordinates, and then a finite difference approximation is developed. The proposed numerical scheme is explicit and of a four-level type so that the displacements in the region can be computed whenever their values are known at the three previous time steps throughout the region. A stability analysis of the difference scheme is given, and stability criteria are presented which involve the material parameters as well as the velocity and acceleration of the propagating crack. The reliability of the proposed numerical process is examined in several situations in which some analytical results are known and good agreement is obtained. It is also shown that the dynamic stress intensity factors can be extracted from the numerical solution.

Original languageEnglish
Pages (from-to)301-316
Number of pages16
JournalComputer Methods in Applied Mechanics and Engineering
Issue number3
StatePublished - 1976


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