An efficient and robust staggered algorithm applied to the quasi-static description of brittle fracture by a phase-field approach

The phase field method has been widely adopted in brittle fracture analysis for its ability to handle complex crack topology. This paper presents a novel efficient and robust phase field algorithm for quasi-static brittle fracture analysis. This algorithm overcomes two major issues that affect significantly the numerical cost of the method: the treatment of discontinuous crack propagation and the inequality constraint associated with the irreversibility of the damage evolution. To handle discontinuous crack propagation, a semi-implicit scheme, which combines the usual explicit and implicit schemes, is proposed. Different from explicit schemes that require small time steps and purely implicit schemes that lose immediately efficiency when encountering discontinuous propagation, the proposed method can alleviate the steps constraint while keeping a good robustness with discontinuous cracking. Concerning the irreversibility constraint, this work proposes a practical and easy-to-implement method. It is shown that this method is extremely efficient and robust without any supplementary numerical coefficient. The efficiency of the method is demonstrated by means of representative numerical examples.