Surface-based cohesive modeling of Mode I delamination in vascular self-healing composites: finite element analysis and multi-objective optimization

Abstract This study presents a macromechanical finite element model based on a surface-based cohesive approach to predict and optimize the Mode I delamination behavior of vascular self-healing polymer composites. A two-dimensional Double Cantilever Beam (DCB) model incorporating bilinear traction–separation laws was developed in ABAQUS and validated against experimental results, with a maximum deviation of 4.444% in Mode I fracture toughness (Gi) A comprehensive parametric study evaluated the effects of Hollow Glass Fiber Outer Diameter (HGFO), Distance between Hollow Glass Fibers (DHGF), Resin-Rich Cohesive Strength (RCS), Resin-Rich Cohesive Energy (RCE), Interfacial Cohesive Strength (IFCS), and Interfacial Cohesive Energy (IFCE) on maximum load (Pm) and Gi. Results showed that increasing HGFO from 0 to 680 μm enhanced Gi from 510 to 805 J m −1 and Pm from 21 to 29 N, while increasing RCE from 53 to 153 J m −1 improved Gi from 725 to 822 J m −1 and Pm from 18 to 29 N. In contrast, higher IFCS increased Pm but reduced Gi, whereas higher IFCE improved both properties. A multi-objective optimization using the Box–Behnken Design (BBD) identified optimal parameters, HGFO = 674.85 μm, DHGF = 3 mm, RCS = 70 MPa, RCE = 145.93 J m −1 , IFCS = 61.62 MPa, IFCE = 128 J m −1 , yielding predicted maxima of Pm = 36.02 N and Gi = 995.15 J m −1 . Finite element simulation with these parameters achieved Pm = 39.01 N and Gi = 960.01 J m −1 , with differences below 8%, demonstrating the reliability of the proposed modeling and optimization framework for enhancing vascular self-healing composites.