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<p>The eXtended Finite Element Method (X-FEM) has proven to be a robust method for
simulating crack propagation, but relatively little work has focused on the important
problem of crack initiation or nucleation. In this work, we examine various options
for nucleating cracks within a cohesive framework and the X-FEM. Attention is confined
to shell problems. We discuss the details of the methods and their strengths and
weaknesses. With the introduction of such nucleation algorithms, the need to model
more complex crack growth topologies also arises. In particular, we examine algorithms
for enabling crack branching, focusing on both the mechanics and element kinematic
considerations. The results of various benchmark problems for the nucleation and
branching algorithms are also presented and discussed.</p>
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