Phase-field modelings of fracture investigate the influence of interfacial effects on damage and optimal material distribution in brittle inclusion-matrix structures

This present work uses the phase-field modelings to investigate the influence of interfacial effects on damage and mechanical behavior, as well as the optimal distribution of the inclusion shape within brittle inclusion-matrix structures in various typical cases. These two constituent phases in the structures are assumed to be either isotropic or anisotropic. To achieve these goals, this work will: (i) use the phase-field modelings either considering or neglecting interfacial debonding, and the anisotropic phase-field modeling; (ii) determine and incorporate the strain tensor orthogonal decompositions into each specific phase-field modeling to enhance the accuracy and effectiveness of the simulation methods; (iii) combine the phase-field modelings with the BESO topology optimization algorithm to analyze the influence of interfacial effects on relationship curves and the optimal distribution of the inclusion shape. Through proposed numerical examples, it is demonstrated that the interfacial effects strongly influence crack paths, behavior curves, and optimal material distribution in structures. When considering interfacial effects, cracks are almost unable to penetrate into the inclusion phase. However, when neglecting interfacial effects, cracks propagate into the inclusion phase. This reason makes the structure more difficult to damage than when considering the interfacial effects, as evidenced by greater peak load values in behavior curves and greater total fracture resistance of the material. Especially in the example of inclusion phase optimization, the total fracture resistance value of the case neglecting interfacial effects is more than 107.9% greater than that considering interfacial effects.