A hybrid phase-field isogeometric analysis to crack propagation in porous functionally graded structures

Porosities exist as pores of different sizes within a structure to fabricate lightweight materials and the sintering process. The porous structure gives a lower loading capacity than the perfect design. Crack propagation is also a complicated behavior in this structure. The hybrid phase-field approach is suitable to provide an effective computational tool to model the crack propagation of functionally graded materials with porosity effects. We show the influence of porosity on both the critical force and crack path of the FGM structure. In the framework of isogeometric analysis (IGA), a local refinement multi-patch algorithm based on the Virtual Uncommon-Knot-Inserted Master-Slave (VUKIMS) technique allows us to reduce the computational cost of the phase-field model significantly. The study revealed that cubic NURBS elements with the effective element size of half length-scale parameter could be used to achieve the desired accuracy while maintaining a reasonable computational cost.