Length Scale Insensitive Phase-Field Fracture Methodology for Brittle and Ductile Materials

We present length scale insensitive phase-field fracture models for brittle and ductile fracture to address the deficiencies of widely implemented models which over-estimate crack dissipation. An approach is proposed to attain a regularization length scale insensitive mechanical response, which considers a continuous approximation of a crack boundary with a function of infinite support. This is in contrast to previous approaches to attain a length scale insensitive response which exploited approximations of the crack boundary with functions of finite support. The choice of these functions with finite support creates implementational challenges which are avoided in the presented quasi-brittle and ductile fracture models with infinite support of the phase-field. The capability of these models is demonstrated in several benchmarks with attention given to the sensitivity of the structural response with respect to the choice of regularization length scale. The models are validated against a three-point bending test on a concrete specimen and an in-plane shear test on a steel specimen.