The standard finite element implementation of intrinsic cohesive zone models (CZMs) based on thepenalty method exhibits a distinct lack of numerical stability and/or convergence for stiff cohesivelaws. This lack of stability is typically observed in the form of spurious oscillations in the normaland tangential tractions recovered at the cohesive interface. In this paper, we will present a robust,stabilized finite element formulation for CZMs that remedies traction oscillations, thus ensuringstability and convergence for any value of initial cohesive stiffness. A key advantage of the proposedformulation is that it generalizes the Nitsche’s method for modeling cohesive fracture with alarge initial cohesive stiffness, thus enabling the implementation of intrinsic and extrinsic CZMs ina unified and variationally consistent manner. We present several numerical examples to demonstratethe stability, convergence and accuracy of the proposed formulation in two-dimensions. First,we will verify the accuracy using simple patch tests considering uniaxial tension, compression andshear loadings. Second, we will demonstrate the lack of spurious traction oscillations at cohesiveinterfaces of rectangular beams loaded under shear and three-point bending. To demonstrate thestability issues related with the spurious traction oscillation, we consider both isotropic as wellas anisotropic CZMs, wherein the normal and tangential cohesive stiffness values are different.Our numerical results for high stiffness cases clearly show that the proposed formulation yieldsa smooth oscillation-free traction profile and ensures stability, whereas the standard formulationsuffers from instability and/or convergence issues.
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