The paper presents the advancement and applications of the elasto-plastic cellular automaton （EPCA）, a simulator for rock mechanics and rock engineering. The most significant feature of EPCA lies in its ＇down-top＇ way of dealing with nonlinear behaviors of rocks. The theory, the basic idea and associated developments, including the definition of cellular automaton, the heterogeneous material model, constitutive relations, failure criteria, the post-yield softening scheme, the thermo-hydro-mechanical coupling process, are described. The applications are presented to show the ability of EPCA to model the rock failure process, fluid flow, heat transfer, and the coupled thermo-hydro-mechanical （THM） process etc.
Combining the radial point interpolation method （RPIM）, the dual reciprocity method （DRM） and the hybrid boundary node method （HBNM）, a dual reciprocity hybrid radial boundary node method （DHRBNM） is proposed for linear elasticity. Compared to DHBNM, RPIM is exploited to replace the moving least square （MLS） in DHRBNM, and it gets rid of the deficiency of MLS approximation, in which shape functions lack the delta function property, the boundary condition can not be applied easily and directly and it＇s computational expense is high. Besides, different approximate functions are discussed in DRM to get the interpolation property, in which the accuracy and efficiency for different basis functions are compared. Then RPIM is also applied in DRM to replace the conical function interpolation, which can greatly improve the accuracy of the present method. To demonstrate the effectiveness of the present method, DHBNM is applied for comparison, and some numerical examples of 2-D elasticity problems show that the present method is much more effective than DHBNM.
Fei Yan Xiating Feng Hui Zhou 1(State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Science,Wuhan 430071,China)
A method of continuous-discontinuous cellular automaton for modeling the growth and coalescence of multiple cracks in brittle material is presented. The method uses the level set to track arbitrary discontinuities, and calculation grids are independent of the discontinuities and no remeshing are required with the crack growing. Based on Grif- fith fracture theory and Mohr-Coulumb criterion, a mixed fracture criterion for multiple cracks growth in brittle mate- rial is proposed. The method treats the junction and coales- cence of multiple cracks, and junction criterion and coales- cence criterion for brittle material are given, too. Besides, in order to overcome the tracking error in the level set ap- proximation for crack junction and coalescence, a dichotomy searching algorithm is proposed. Introduced the above the- ories into continuous-discontinuous cellular automaton, the present method can be applied to solving multiple crack growth in brittle material, and only cell stiffness is needed and no assembled global stiffness is needed. Some numerical examples are given to shown that the present method is efficient and accurate for crack junction, coalescence and percolation problems.
