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Within the XFEM often near linear dependencies between the standard degrees of freedom and enriched degrees of freedom and also among enriched degrees of freedom occur. During the last years, several remedies to that problem have been presented. Here, an extension of the regularization technique described in [1] to finite deformation problems and inelastic material behaviour as well as to multifield problems is proposed.

Throughout the last 60 years, nickel (Ni) based superalloys have been the standard high-temperature material used in mobile and stationary gas turbines. The ever increasing temperatures necessitate further improvements of those alloys, foremost, enhancing their creep-resistance. Creep denotes a macroscopic, permanent change of shape which, amongst other effects, stems from thermally and mechanically induced dislocation movement. The key microstructural feature of most modern alloys is a uniform distribution of particles of the L12-ordered γ phase which are embedded into the nickel-based matrix. Most importantly, these particles are impenetrable to matrix-dislocations. This leads to numerous dislocation effects encountered in such microstructured alloys. A wealth of different material modeling-approaches exists in the literature which try to capture creep behavior. Due to the multiscaled nature of the physical problem, most crystal plasticity approaches are phenomenological and, thus, rely on many parameters. Finding suitable constitutive equations that capture experimental results becomes a challenge. A large deformation crystal plasticity framework has been set up which allows for an efficient comparison of different material formulations. This has been achieved by the use of AceGEN. The analytically generated tangent-subroutine is linked into a FEAP polycrystal plasticity model and thus, global quadratic convergence is reached. In future work, a variety of flow rules, dislocation density based (cross-) hardening formulae and parameters can be studied in a unified way [6].Modeling of nickel-based superalloys is still an open challenge in crystal plasticity. The overall goal is a constitutive formalism that captures the mechanical response to temperature, loading state and chemically reactive environments. Numerous deformation mechanisms have been discovered in experimental works which strongly depend on the mechanical and thermic loading [1,2]. The complexity mainly stems from two slightly different phases existing in these alloys. The nickel-rich FCCmatrix is clustered with particles ( Fig. 3) of the L 12 long-range ordered crystal-structure. All corner atoms of the nickel FCC unit-cell are replaced by aluminum (Al) or titanium (Ti) atoms (Fig. 1). Fig. 1: Unit cell of the γ -phase Fig. 2: APB in the wake of dislocations within γ -phase Fig. 3: In-lense scanning electron microscope image showing precipitates of γ -phaseA matrix-dislocation a/2<110>(111) would leave behind an Anti-Phase-Boundary (APB) in its wake [3] when shearing a γ particle (Fig. 2 upper). Amongst other effects, dislocations pile up at the interface between matrix and precipitates during the first stages of creep. The dislocations react and form ribbons which are able to enter the γ particles because the APB is confined to in between the dislocations (Fig. 2 lower). Therefore, matrix dislocations have to first pile up and then react in order to shear the γ -particles. As the stacking fault energy rises with temperature dislocation movement is...

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