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| The recent progress in peridynamics and its numerical simulation in rock |
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Abstract The complex problem concerning the initiation and propagation of the crack in brittle materials is one of the most significant challenges in solid mechanics. As a common phenomenon, material failure may occur in the form of generation and growth of discontinuities such as cracks in engineering structures, resulting in great economic losses or even loss of life. At present, various numerical methods based on classical continuum mechanics are employed to model crack growth and material failure. However, the crack nucleation and singular crack-tip stress can hardly be solved due to the incapability of currently available continuum mechanics-based numerical methods to handle the discontinuous problems. Peridynmics (PD) is a nonlocal formulation based on integro-differential governing operators instead of the spatial derivative terms. The peridynamic theory is suited for modeling the non-continuity structural domains without any special treatment and can well describe the mechanical behaviors from continuity to non-continuity. In this paper, the current situation and the developing trend of peridynamics in material model and failure problems of rock and other materials are reviewed through introducing the theoretical basis of peridynamics. Numerical simulations of rock materials subjected to uniaxial tension, uniaxial compression, conventional triaxial compression and true triaxial compression are performed, respectively. The irregularity fracture of the rock slab with a circular hole under uniaxial tension loading condition is then analyzed by using the band-based peridynamics. Moreover, the uniaxial, conventional triaxial and true triaxial numerical tests under three-dimensional conditions are investigated based on state-based peridynamics. Subsequently, the fracture process of rock mass at the Mine-by tunnel in Canada is simulated. The present numerical results indicate that the peridynamic theory can be commendably applied in the non-continuity mechanical behaviors of rock. Finally, some current problems of peridyanmics in the rock fracture simulation and some worthy issues in further are discussed.
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Received: 07 January 2019
Published: 28 August 2019
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2019, Vol. 40 
