An adaptive mixed-dimensional phase-field method for beam fracture

Simulating fracture in beams with high accuracy and efficiency remains a challenge within the phase-field modeling framework due to the dimensionally-reduced kinematics. Traditional approaches usually consider cracks to be constant over the thickness. However, when load cases involve stretching and bending, such an approach often fails to adequately capture fracture behaviors. This paper proposes an adaptive mixed-dimensional method for phase-field modeling of fracture in beams that incorporates the following features: firstly, the computational domain of the beam is automatically decomposed into ‘critical’ and ‘safe’ regions according to the evolving phase-field damage variable; secondly, the local critical region where crack propagation occurs is modeled as a 2D solid, whereas the remaining safe region is represented by a simplified 1D beam model. The solid and beam models are coupled at the shared interfaces using multipoint constraint methods. By combining a 1D beam description for the majority of the structure with a 2D solid representation of the local fracture zone, the resulting model has the advantage of reducing computational cost, while still being able to accurately capture the evolution of cracks through the thickness of beams. Several numerical examples ranging from standalone beams to lattice structures test and validate the applicability of the approach.