In this work, a recently proposed high-cycle fatigue cohesive zone model, which covers crack initiation and propagation with limited input parameters, is embedded in a robust and efficient numerical framework for simulating progressive failure in composite laminates under fatigue loading. The fatigue cohesive zone model is enhanced with an implicit time integration scheme of the fatigue damage variable which allows for larger cycle increments and more efficient analyses. The method is combined with an adaptive strategy for determining the cycle increment based on global convergence rates. Moreover, a consistent material tangent stiffness matrix has been derived by fully linearizing the underlying mixed-mode quasi-static model and the fatigue damage update. The enhanced fatigue cohesive zone model is used to describe matrix cracking and delamination in laminates. In order to allow for matrix cracks to initiate at arbitrary locations and to avoid complex and costly mesh generation, the phantom node version of the eXtended finite element method (XFEM) is employed. For the insertion of new crack segments, an XFEM fatigue crack insertion criterion is presented, which is consistent with the fatigue cohesive zone formulation. It is shown with numerical examples that the improved fatigue damage update enhances the accuracy, efficiency and robustness of the numerical simulations significantly. The numerical framework is applied to the simulation of progressive fatigue failure in an open-hole [±45]-laminate. It is demonstrated that the numerical model is capable of accurately and efficiently simulating the complete failure process from distributed damage to localized failure.

A common choice for multiscale modeling of the mechanical response of composites is to use periodic boundary conditions (PBCs) on square and cubical representative volume elements (RVEs). However, when strain localization occurs in the micromodel, these PBCs are unable to reproduce the transverse isotropy of composite materials with a random microstructure. Existing remedies to alleviate this issue have been proposed in literature by either rotating or shifting the periodicity constraints. However, this results in a mismatch of the microstructure on opposing edges which may prevent cracks to cross the boundary and consequently limit the supported localization angles. Furthermore, in absence of a strategy that ensures a single localization band to arise in a fracturing RVE, it is difficult to formulate a generic expression for the length scale parameter that is used to regulate the energy dissipation, which plays an important role in obtaining RVE-size objective results. As an alternative to square (or cubical) RVEs, circular (or spherical) RVEs have been proposed in literature since they provide a response which is independent of the orientation due to shape of the RVE. However, it is shown in this work that the existing formulation with straightforward application of PBCs on a circular RVE fails to predict the correct softening behavior, due to over-constraining when cracks reach the boundary. Therefore, a new formulation of PBCs on a circular RVE is proposed, which allows for a single fully developed localization band under arbitrary angle. The performance of the new formulation is tested with a series of simulations where macroscopic strains are imposed under varying orientations. It is demonstrated that the circular RVE with the new formulation of PBCs successfully predicts a transversely isotropic response with full softening without the issue of mismatching microstructure as with previously developed remedies for the square RVE. In addition, it is shown that the length scale parameter is well-defined and independent of the orientation of the circular RVE.