Modeling fracture in brittle materials with inertia effects using the phase field method

Abstract

The phase field method uses a length scale parameter to regularize the discrete crack to a diffuse crack, which removes the numerical tracking of the discontinuities in the displacement. The displacement field is coupled with the phase field and both are solved as a sequentially coupled systems using staggered method. The phase field $\varphi$ varies between zero and unity (i.e., $\varphi =0$ for intact region and $\varphi =1$ for fully broken region), and it is a scalar. In this study, a new way of implementation is done using ABAQUS software to solve for the two fields. User defined element subroutine (UEL) is used to solve for the phase field variable and user defined material subroutine (UMAT) for the displacement field variable. Phase field model can simulate any complex crack paths and branching even without previously defined cracks. Some benchmark examples of quasi-static brittle fracture and dynamic brittle fracture are solved and verified with the existing numerical results. To account for the rate-dependent effect under high-rate loading, micro-inertia is incorporated into the phase-field model for dynamic fracture as proposed in the literature and verified with one example.

Keywords:

• Phase field method
• Abaqus implementation
• brittle fracture
• hybrid formulation
• staggered scheme