A mixed augmented Lagrangian‐extended finite element method for modelling elastic–plastic fatigue crack growth with unilateral contact

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A generalized finite element method with global-local enrichment functions for confined plasticity problems (2012, methodology): “Enrichment functions for nonlinear fracture analysis based on the Hutchinson-Rice-Rosengren (HRR) elastic-plastic fields were proposed by several researchers [13, 22, 23, 30].”
A contact algorithm for frictional crack propagation with the extended finite element method (2008, methodology): “The latter class of methods are often called the extended FE methods [22–39].”
Stabilized low-order finite elements for frictional contact with the extended finite element method (2010, background): “A challenging aspect of the problem is the enforcement of the contact condition, whether it be in the context of classical nonlinear contact mechanics in which element sides are aligned to the contact faces [26,36,37,39,40,42,49,50], or in the framework of the assumed enhanced strain or extended FEm”