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UBC Theses and Dissertations

Modeling of dynamic fracture problems using AL finite element formulation Abdelgalil, Abdelgader I.


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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