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 \(j\ =\ 1,\ N\ \)
\(\mathbb{K}\ [i,\ j]\ =\ 0\ \)