Fig. CT specimen tension test. The
crack phase-field contour plot is shown in various stages
6. Conclusion
In this study, the phase-field model for ductile fracture proposed in
Ambati15 has been investigated in more detail, and its
predictions have been compared with literature. The results obtained
from the simulations are in good agreement with the previous
investigations results. In particular, this study showed that the
proposed model can capture the experimentally observed sequence of
elastoplastic deformation and fracture phenomena in purposed specimens.
Moreover, simulation precisely determined the impact of the critical
plastic strain, length scale, and proposed parameters on the
force-displacement response in the presence of the ductile behavior. The
results also showed that not only crack patterns but also
load-displacement curves aspects of the behavior could be accurately
captured.
Appendix
Appendix A: Assembly algorithm for
matrices
An algorithm of the assembly of the global stiffness matrix\(\mathbb{K}\) from contributions of element stiffness matrices k can be
expressed by the following pseudo-code:
\(n\) = number of degrees of freedom per element\(N\) = total number of degrees of freedom in the domain\(E\) = number of elements\(C[E,\ n]\) = connectivity array\(k[n,\ n]\) = element stiffness matrix\(\mathbb{K}[N,\ N]\) = global stiffness matrix
do \(i\ =\ 1,\ N\ \)
do \(j\ =\ 1,\ N\ \)
\(\mathbb{K}\ [i,\ j]\ =\ 0\ \)