Dynamic crack propagation analysis using Eulerian-Lagrangian kinematic descriptions

A dynamic version of the Eulerian-Lagrangian kinematic description (ELD) (Koh and Haber (1986 a) is applied to the analysis of elastodynamic fracture problems. The ELD formulation leads to moving finite element procedures which adjust the mesh to changes in the structural geometry due to crack extension. The use of quarter-point isoparametric finite elements with the dynamic ELD ensures correct modeling of the singular forms in both the strain field and the material velocity field. A two-level mapping is used to describe the Eulerian mesh motion based on the crack-tip motion. This greatly reduces, or eliminates, the need to remesh and interpolate field variables to the new node locations, as is required in transient analyses based on Lagrangian models. Stress intensity factors are computed from numerical evaluations of either the actual dynamic energy release rate for running cracks or the instantaneous virtual energy release rate for stationary cracks. Numerical examples indicate that the ELD accurately models geometric changes due to crack growth and their effect on material motion. Three-dimensional color computer visualization techniques are used to interpret the transient field solutions.