Potential-based cohesive modeling of mixed-mode crack kinking

We present a compact finite-element framework for incipient mixed-mode crack kinking in plane strain, in which the physical crack is augmented by a short, zero-thickness cohesive continuation. A thin auxiliary channel is used only for mesh generation and is collapsed after T6 conversion, so that the analysis is carried out on the physical interface with coincident node pairs. The cohesive law is potential-based, differentiable, and characterized by finite normal and tangential cohesive strengths; the corresponding cohesive potential yields an energetically consistent formulation with a symmetric Hessian tangent and robust Newton convergence. The construction of the interface degrees of freedom, jump operator, line-integration operators, and consistent linearization is detailed explicitly. Two complementary selectors are considered for the kink direction: a global load-based criterion and a local energetic mouth criterion. Numerical studies show rapid convergence of the critical load, stable determination of the kink angle, and close agreement between bulk tractions and cohesive tractions reconstructed from the displacement jumps along almost the entire cohesive leg. The framework is examined deliberately in a near-LEFM regime. In this setting, the predicted kink direction remains close to the classical elastic benchmark, whereas the critical load exhibits a clearer sensitivity to the finite cohesive zone and to the traction–separation law. A calibrated sensitivity study of the auxiliary cohesive-leg length shows that, when the active cohesive zone is kept well contained within the trial segment, the directional prediction depends only weakly on this auxiliary choice. The method is therefore best suited to quasi-static mixed-mode crack kinking in a near-LEFM regime, where it provides a controlled finite-process-zone counterpart to classical elastic predictors.