  This paper presents an algorithm for the efficient simulation of ductile
crack propagation through heterogeneous structures, as e.g. metallic
microstructures, which are given as voxel data. These kinds of simulations are
required for e.g., the numerical investigation of wear mechanisms at small
length scales, which is still a challenging task in engineering. The basic idea
of the proposed algorithm is to combine the advantages of the Finite Cell
Method allowing for a convenient integration of heterogeneous finite element
problems with the eigenerosion approach to still enable the mesh-independent
simulation of crack propagation. The major component is to switch from finite
subcells to finite elements wherever the crack progresses, thereby
automatically adaptively refining at the crack tip by managing the newly
appearing nodes as hanging nodes. Technically relevant problems of crack
propagation at the microscale are mostly linked with sub-critical crack growth
where the crack moves fast and stepwise with subsequent load cycles. Therefore,
inertia may become important which is why dynamics are taken into account by
spreading the mass of the eroded elements to the nodes to avoid a loss in mass
resulting from the erosion procedure. Furthermore, a certain treatment for the
finite cell decomposition is considered in order to ensure efficiency and
accuracy. The numerical framework as well as the voxel decomposition techniques
are analyzed in detail in different three-dimensional numerical examples to
show the performance of the proposed approach.
