Damage and fracture of solids
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Fracture mechanics: Computational methods
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A stablized mixed finte element method (mixed-FEM) for modelling shear failure, slip, and stick of crack surfaces, including treatment of intersecting cracks, see Wang et al. (2022, Engineering Fracture Mechanics).
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Linear elastic fracture mechancis (LEFM) combined with the singular-finite element method (singular-FEM), modelling propagation of multiple cracks, see Wang et al. (2024, International Journal of Fracture).
Fracture mechanics: Analytical methods
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The classical complex variable method, develoepd by Muskhelishivili (1977) in his prestigious monograph, applied in the plane fracture mechanics problems, with solutions of stress intensity factors (SIFs) in I-, II-, and mixed I-II modes, see Wang et al. (2019, Theoretical and Applied Fracture Mechanics).
Fracture mechanics: Applications
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Fractue mechanics combined with the cohesive zone model (CZM), proposed by Dugdale (1960) and Barenblatt (1962), and their application in rock engineering, see Wang et al. (2019, Journal of Mountain Science) and Wang et al. (2020, Bulletin of Engineering Geology and the Environment) for slope engineering and underground excavation, respectively.
Advanced methods: peridynamics
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Peridynamics, a theory of reformulation of classical continuum mechanics pioneered by Silling (2000), used for analysing dynamic damage and fragmentation of cracked solids during impact contact, see Wang et al. (2024, Engineering Fracture Mechanics).
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Finite deformation and progressive failure of hyperelastic solid modelled by implicit non-ordinary state-based peridynamics, see Wang and Yin (2024, Computer Methods in Applied Mechanics and Engineering) and Wang and Yin (2025, Computer Methods in Applied Mechanics and Engineering).