| Summary: | The problem of dynamic crack propagation is widely addressed in the literature. The few
available analytical solutions are limited to simple and idealized geometries and loading
conditions. On the other hand, major approximations and inconsistent assumptions exist
in published numerical models.
In this thesis, the problem of dynamic crack propagation is modeled using a fully coupled
Arbitrary Lagrangian Eulerian (ALE) formulation. The ALE equilibrium equations are
derived, discretized using isoparametric finite elements and implemented into an ALE
dynamic fracture program (ALEFR), based on an implicit solution scheme.
The advantage of the ALE formulation is that the computational grid (finite element
mesh) may have an arbitrary motion with respect to the domain of the deformed body.
Therefore, the complex nature of the developed boundary condition due to a propagating
crack may now be modeled in a continuous and accurate manner.
The process of creating new surfaces due to crack propagation is modeled by splitting
material points. This allows for a more realistic representation of the actual physical
process. The ALE boundary constraint is enforced on the free boundaries, including the
continuously changing free crack surfaces, using a newly developed technique. The dynamic energy release rate is evaluated through the integration of material properties of Lagrangian grid material points. The developed formulations and techniques are then discretized and implemented into a finite element code. The developed code is tested by modeling dynamic stationary and
propagating fracture problems.
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