Size-Constrained Elliptical Stepped Bonded Repair for Composite Laminates: Geometry-Driven Failure Transitions and Design Optimization

Stepped bonded repair is widely used to restore load-carrying capacity in damaged composite structures, yet conventional circular-patch configurations require repair footprints that are frequently prohibited by spatial and geometric constraints in service environments. This study proposes an elliptical stepped repair strategy in which the patch axes are independently sized to accommodate directional space restrictions while preserving effective load transfer. A parametric three-dimensional finite element framework incorporating a Hashin-based progressive damage model and a cohesive-zone traction–separation law is developed and validated against both in-house lap-joint tests and an independent stepped-repair benchmark from the literature (discrepancy < 10%). Systematic variation in the elliptical geometry reveals that the major axis—oriented along the loading direction—is the dominant geometric parameter controlling strength recovery and failure mode: insufficient major-axis length results in premature adhesive debonding, whereas an appropriately sized major axis shifts failure to parent-laminate fracture and raises the ultimate load by up to 20% relative to a circular repair of equal minor-axis dimension. The minor axis plays a secondary but non-trivial role, and a synergistic optimum is identified at the 40–90 mm (minor–major) configuration. Regarding step partitioning, a four-step arrangement consistently maximizes ultimate load across all tested geometries due to the competition between transition-gradient smoothness and step-edge stress concentration density. Finally, an external woven overlay is shown to both improve and equalize strength across geometrically distinct repairs by suppressing interfacial stress concentration and engaging a global cooperative failure mode. These findings establish design guidelines for elliptical stepped repairs under engineering space constraints.