A modified combined active-set Newton method for solving phase-field fracture into the monolithic limit

In this work, we examine a numerical phase-field fracture framework in which the crack irreversibility constraint is treated with primal–dual active set method and linearization used degradation function to enhance stability. The first goal carefully derive from complementarity system our formulation, has been literature numerous studies, but for without its detailed mathematical derivation yet. Based on latter, formulate modified combined active-set Newton approach that significantly reduces computational cost comparison comparable prior algorithms quasi-monolithic settings. For many practical problems, converges fast, needs iterations, three different efficiency improvements are suggested paper. Afterwards, design an iteration order iterate problem monolithic limit. Our new implemented programming pfm-cracks Heister Wick (2020). examples, conduct performance studies investigate enhancements. main emphasis complexity by keeping accuracy of solutions functionals. algorithmic suggestions substantiated help several benchmarks two spatial dimensions. Therein, predictor–corrector adaptivity parallel explored as well.