Global-Local techniques for adaptive phase-field fracture
The modeling of crack formation can be achieved in a convenient way by continuum phase-field approaches to fracture, which are based on the regularization of sharp crack discontinuities. Phase-field modeling of fracture has been attracting considerable attention in recent years due to its capability of capturing complex crack patterns in various problems in solid mechanics. For efficient and robust numerical solution procedures, we develop a multi-scale approach where the characteristic length of the local scale is of the same order as its global counter part. This is accomplished by introducing the so-called Global-Local approach. Hereby a multi-physics problem at fracture is solved on a lower (local) scale, while dealing with a purely linear elastic problem on an upper (global) scale. Besides its feasibility for having two ad-hoc finite element models for the global and local domain, enables computations/couplings with legacy codes for industrial applications in more efficient settings. Another important aspect of this contribution is the development of an adaptive Global-Local approach, where a predictor-corrector scheme is designed in which the local domains are dynamically updated during the computation. To cope with different finite element discretizations at the interface between the two nested scales, a non-matching dual mortar method is formulated. Hence, more regularity is achieved on the interface.