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This work presents a new adaptive approach for the numerical simulation of aphase-field model for fractures in nearly incompressible solids. In order tocope with locking effects, we use a recently proposed mixed form where we havea hydro-static pressure as additional unknown besides the displacement fieldand the phase-field variable. To fulfill the fracture irreversibilityconstraint, we consider a formulation as a variational inequality in thephase-field variable. For adaptive mesh refinement, we use a recently developedresidual-type a posteriori error estimator for the phase-field variationalinequality which is efficient and reliable, and robust with respect to thephase-field regularization parameter. The proposed model and the adaptiveerror-based refinement strategy are demonstrated by means of numerical testsderived from the L-shaped panel test, originally developed for concrete. Here,the Poisson's ratio is changed from the standard setting towards theincompressible limit $\nu \to 0.5$.

Adaptive Numerical Simulation of a Phase-field Fracture Model in Mixed Form tested on an L-shaped Specimen with High Poisson Ratios