A phase-field ductile fracture model with a variable regularization length parameter

In the last decade, one of the gradient damage models called “phase-field fracture model” has been receiving attention. The model for brittle fractures has acquired great success, but that for ductile fractures is still under development. In this context, we propose a novel phase-field model with a variable regularization length parameter that is defined as an increasing function of the measure of the plastic strain. Since the regularization length parameter l representing the width of a diffuse crack is known to determine the damaged region around the crack, it has been modified so as to increase depending on the amount of plastic deformation. Thanks to this variable regularization length parameter l^∗, the phase-field parameter d is calculated in consideration of the damage due to plastic deformation. The conventional elasto-plastic model with J₂ theory in plasticity is employed and couple to our proposed phase-field model. Several numerical examples are conducted to demonstrate the capability of our proposed model and validate the introduction of l^∗ in comparison with the experimental result.