A time‐based arc‐length like method to remove step size effects during fracture propagation

Abstract

An arc-length like method is presented which alters the size of the time increment when simulating crack propagation problems. By allowing the time increment to change during the time step a constraint can be imposed, which is used to enforce the fracture to propagate a single element length per time step. This removes the effect of the (interface) element size on propagating fractures, and therefore allows smooth fracture propagation during the simulation.The benefits of the scheme are demonstrated for three cases: mode-I crack propagation in a double cantilever beam, a shear fracture including inertial and viscoplastic effects in the surrounding material, and a pressurized fracture inside a poroelastic material. These cases highlight the ability of this scheme to obtain more accurate and nonoscillatory results for the force-displacement relation, to remove numerically induced stepwise fracture propagation, and to allow for arbitrary propagation velocities. An added benefit is that plastic strains surrounding a fracture are no longer affected by the (interface) element size.

Spatial and temporal constraints of the cohesive modeling: A unified criterion for fluid‐driven fracture

“…31,75,76 The time step size must be restrainedly selected to capture the temporal character of the fracture solution. In this regard, to overcome this challenge, Hageman and Borst 77 proposed an arc-length-like method to determine the time step size during fracture propagation. Ren and Younis 78 presented a time-continuation scheme for the XFEM to reduce the computational cost.…”