Modelling of rock materials subjected to dynamic loading using a particle-based numerical manifold method (PNMM)

摘要

A particle-based numerical manifold method (PNMM) is proposed and implemented to simulaterndynamic behavior of rock materials. By introducing the concept of particle presentation into the numericalrnmanifold method (NMM), the PNMM inherits the flexibility in fracturing simulation from the NMM andrngains the ability to simultaneously represent the microstructure and macroscopic behavior of rock. The basicrnidea of PNMM is to represent the microstructure of rock materials with a group of particles and simulate thernmacroscopic behavior of rock masses through polygonal elements. This is carried out by a dual-level discretizationrnsystem. The first discretization is in the manner of the FEM, reducing the infinite degrees of freedomrnof a continuum to the finite degrees of freedom of polygonal elements. Then, each finite element is furtherrndiscretized into a group of particles with varying diameters and material properties. The latter discretizationrndoes not further influence the degrees of freedom of the model, and the behavior of internal particles are obtainedrnfrom the mechanical fields of their governing element. Benefiting from this characteristic, the degreesrnof freedom of the model is separated from the simulation of the microstructure of rock materials. Similar tornthe NMM, a dual-layer-cover system, i.e. the mathematical cover and the physical cover, is adopted in thernPNMM. As the result of such a cover system, interpolation fields are free from the shape of modeling domain,rnso that fractures, especially those with complex geometry, can be naturally represented and conducted. InrnPNMM, microcracks can be induced at the micro-level between particles, based on the Mohr-Coulomb with arntensile cut-off criterion. And the coalescence of microcracks is to simulate the initiation and propagation ofrnfractures on macroscopic level. A modified Johnson-Holmquist-Beissel (JHB) material model is incorporatedrninto the PNMM to simulate the behavior of rock materials at high strain rates and pressures. In the originalrnJHB model, a damage model with an analytical failure strain represents the material from an intact state to arnfailed state. The modifications to the JHB model are carried out by associating the damage coefficient withrnthe number of microcracks. Numerical simulations show a good agreement with experimental results concerningrnthe same conditions conducted by a split Hopkinson pressure bar and a plate impact facility.