Combination of discrete element and finite element methods for dynamic analysis of geomechanics problems

Abstract The paper presents combination of discrete element method (DEM) and finite element method (FEM) for dynamic analysis of geomechanics problems. Combined models can employ spherical (or cylindrical in 2D) rigid elements and finite elements in the discretization of different parts of the system. The FEM is a suitable tool to model soil/rock materials while the FEM in many cases can be a better choice to model other parts of the system considered. A typical example can be an idealization of rock cutting with a tool discretized with finite elements and rock or soil samples modelled with discrete elements. The FEM presented in the paper allows large elasto-plastic deformations in the solid regions. Such problems require the use of stabilized FEM to deal with the incompressibility constraint in order to eliminate the volumetric locking defect, especially when using triangular and tetrahedra elements with equal order interpolation for the displacement and the pressure variables. In the paper a stabilization based on the finite calculus (FIC) approach is used. Both theoretical algorithms of DEM and stabilized FEM are implemented in an explicit dynamic code. The paper presents some details of both formulations. A combined numerical algorithm is described finally. Selected numerical results illustrate the possibilities and performance of discrete/finite element analysis in geomechanics problems.

[1]  Dale S. Preece,et al.  Simulation of blasting induced rock motion using spherical element models , 1992 .

[2]  Eugenio Oñate,et al.  Derivation of stabilized equations for numerical solution of advective-diffusive transport and fluid flow problems , 1998 .

[3]  Richard P. Jensen,et al.  Discrete Element Methods: Numerical Modeling of Discontinua , 2002 .

[4]  T. Hughes,et al.  The Galerkin/least-squares method for advective-diffusive equations , 1988 .

[5]  Ramon Codina,et al.  Stabilized finite element method for the transient Navier–Stokes equations based on a pressure gradient projection , 2000 .

[6]  Robert L. Taylor,et al.  The patch test for mixed formulations , 1986 .

[7]  Miguel Cervera,et al.  A stabilized formulation for incompressible plasticity using linear triangles and tetrahedra , 2004 .

[8]  Oubay Hassan,et al.  An averaged nodal deformation gradient linear tetrahedral element for large strain explicit dynamic applications , 2001 .

[9]  J. Archard.  Contact and Rubbing of Flat Surfaces , 1953 .

[10]  Eugenio Oñate,et al.  A general procedure for deriving stabilized space–time finite element methods for advective–diffusive problems , 1999 .

[11]  Nenad Bićanić,et al.  Discrete Element Methods , 2004 .

[12]  C. A. Saracibar,et al.  A stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations , 2002 .

[13]  I. Babuska.  The finite element method with Lagrangian multipliers , 1973 .

[14]  Eugenio Oñate,et al.  COMPUTATION OF THE STABILIZATION PARAMETER FOR THE FINITE ELEMENT SOLUTION OF ADVECTIVE-DIFFUSIVE PROBLEMS , 1997 .

[15]  J. Bonet,et al.  Stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications , 2001 .

[16]  Eugenio Oñate,et al.  A finite element method for fluid-structure interaction with surface waves using a finite calculus formulation , 2001 .

[17]  Eugenio Oñate,et al.  A finite point method for incompressible flow problems , 2000 .

[18]  Eugenio Oñate,et al.  A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation , 2000 .

[19]  E. Onate,et al.  An Unstructured Finite Element Solver for Ship Hydrodynamics Problems , 2003 .

[20]  J. Z. Zhu,et al.  The finite element method , 1977 .

[21]  J. Williams,et al.  Discrete element simulation and the contact problem , 1999 .

[22]  E. Rabinowicz,et al.  Friction and Wear of Materials , 1966 .

[23]  P. Cundall,et al.  A discrete numerical model for granular assemblies , 1979 .

[24]  O. Zienkiewicz,et al.  The finite element patch test revisited a computer test for convergence, validation and error estimates , 1997 .

[25]  R. Codina.  Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods , 2000 .

[26]  O. C. Zienkiewicz,et al.  Triangles and tetrahedra in explicit dynamic codes for solids , 1998 .

[27]  Charles S. Campbell,et al.  RAPID GRANULAR FLOWS , 1990 .

[28]  F. Brezzi.  On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers , 1974 .

[29]  J. Argyris.  An excursion into large rotations , 1982 .

[30]  P. A. Cundall,et al.  FORMULATION OF A THREE-DIMENSIONAL DISTINCT ELEMENT MODEL - PART I. A SCHEME TO DETECT AND REPRESENT CONTACTS IN A SYSTEM COMPOSED OF MANY POLYHEDRAL BLOCKS , 1988 .