We propose a Virtual Element Method (VEM) framework that couples linear cohesive elements with lowest-order virtual elements to simulate the interplay between matrix cracking and interfacial delamination in composite structures. The matrix domain is discretized using virtual elements based on a phase-field brittle fracture model, enabling accurate representation of crack kinking, curving, and branching. Interfaces are discretized using cohesive elements derived from a potential-based cohesive zone model to capture mixed-mode separation. This coupled discretization handles rapid mesh transitions along interfaces and allows inclusions to be modeled as single polygonal elements with a large number of edges, offering significant meshing flexibility. We validate the framework through numerical examples encompassing mixed-mode interfacial debonding, matrix cracking, crack penetration and deflection at interfaces, and crack kinking from interfaces, comparing results against existing numerical and experimental data. Additionally, we demonstrate a hybrid strategy where the virtual elements are used to discretize inclusions while the finite elements are used to discretize a 3D-printed hyperelastic matrix domain. This hybrid discretization is then employed to simulate multiple crack nucleation and crack coalescence in a 3D-printed hyperelastic composite undergoing finite deformation before brittle fracture. The VEM framework is implemented in the commercial finite element software ABAQUS (Standard) via user-defined elements, making advanced virtual element capabilities accessible within an industry-standard platform. This approach thus provides a robust and flexible tool for simulating brittle fracture in composites with complex damage mechanisms.
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