Phase field fracture in elasto-plastic solids: Understanding failure in shells

• Multi-layer phase-field model for fracture in shell structures. • Stress-state-based fracture strain used at each integration layer. • Model validation via bending on hollow tube and compression of Gyroid TPMS. • Captured variation of stress states and fracture variation through shell thickness. The failure of thin-walled elastoplastic structures remains a critical challenge in material and structural engineering. This study adopts a phase field fracture modelling approach to investigate the underlying failure mechanisms in realistic energy-absorbing shell structures, capturing both fracture initiation and propagation in the presence of plastic deformation. A stress-state dependent fracture criterion is incorporated to better model the underlying mechanisms governing failure in complex loading conditions. In a three-point bending test of a square tube with a rectangular cut-out, the proposed shell phase field model accurately reproduced the experimentally observed deformation stages. The numerical results revealed that the damage predominantly developed along the inner top edge and at the cut-out corner area of the tube, the regions of concentrated plastic strains and high stress triaxiality. A compression test simulation of a triply periodic minimum surface (TPMS) −Gyroid lattice further demonstrated similar distributions of plastic strain across both inner and outer surfaces. However, significant differences in damage evolution were observed across the shell thickness, attributable to the varying stress states and fracture strains. These findings underscore the critical importance of incorporating the stress-state-dependent fracture criteria in the shell phase field framework for accurately predicting the failure behaviour of thin-walled elastoplastic structures subjected to coupled plastic-fracture processes.