A Lagrangian integration point finite element method for large deformation modeling of viscoelastic geomaterials

We review the methods available for large deformation simulations of geomaterials before presenting a Lagrangian integration point finite element method designed specifically to tackle this problem. In our Ellipsis code, the problem domain is represented by an Eulerian mesh and an embedded set of Lagrangian integration points or particles. Unknown variables are computed at the mesh nodes and the Lagrangian particles carry history variables during the deformation process. This method is ideally suited to model fluid-like behavior of continuum solids which are frequently encountered in geological contexts. We present benchmark examples taken from the geomechanics area.

[1]  P. Smolarkiewicz,et al.  The multidimensional positive definite advection transport algorithm: further development and applications , 1986 .

[2]  Jean Braun,et al.  A numerical method for solving partial differential equations on highly irregular evolving grids , 1995, Nature.

[3]  Antonio Huerta,et al.  Viscous flow with large free surface motion , 1988 .

[4]  Manfred Koch,et al.  A benchmark comparison for mantle convection codes , 1989 .

[5]  James Dorman,et al.  World seismicity maps compiled from ESSA, Coast and Geodetic Survey, epicenter data, 1961-1967 , 1969, Bulletin of the Seismological Society of America.

[6]  Louis Moresi,et al.  The Interplay of Material and Geometric Instabilities in Large Deformations of Viscous Rock , 2002 .

[7]  T. Belytschko,et al.  Element‐free Galerkin methods , 1994 .

[8]  Alison Ord,et al.  A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements , 1999 .

[9]  Louis Moresi,et al.  Inversion in geology by interactive evolutionary computation , 2001, 2001 IEEE International Conference on Systems, Man and Cybernetics. e-Systems and e-Man for Cybernetics in Cyberspace (Cat.No.01CH37236).

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

[11]  Yehuda Ben-Zion,et al.  Characterization of Fault Zones , 2003 .

[12]  Richard H. Gallagher,et al.  Finite elements in fluids , 1975 .

[13]  David M. Rubin,et al.  Identification of the gal4 suppressor Sug1 as a subunit of the yeast 26S proteasome , 1996, Nature.

[14]  J. Cahouet,et al.  Some fast 3D finite element solvers for the generalized Stokes problem , 1988 .

[15]  N. Ribe,et al.  Observations of flexure and the geological evolution of the Pacific Ocean basin , 1980, Nature.

[16]  Howard L. Schreyer,et al.  Axisymmetric form of the material point method with applications to upsetting and Taylor impact problems , 1996 .

[17]  R. L. Sani,et al.  Advection-dominated flows, with emphasis on the consequences of mass lumping. [Galerkin finite-element method] , 1976 .

[18]  Guirong Liu,et al.  A point interpolation method for two-dimensional solids , 2001 .

[19]  Louis Moresi,et al.  Mantle convection with a brittle lithosphere: thoughts on the global tectonic styles of the Earth and Venus , 1998 .

[20]  P. M. De Zeeuw,et al.  Matrix-dependent prolongations and restrictions in a blackbox multigrid solver , 1990 .

[21]  Louis Moresi,et al.  Numerical investigation of 2D convection with extremely large viscosity variations , 1995 .

[22]  J. Monaghan Smoothed particle hydrodynamics , 2005 .

[23]  Jean Braun,et al.  Dynamical Lagrangian Remeshing (DLR): A new algorithm for solving large strain deformation problems and its application to fault-propagation folding , 1994 .

[24]  D. C. Drucker,et al.  Mechanics of Incremental Deformation , 1965 .

[25]  D. Sulsky,et al.  A particle method for history-dependent materials , 1993 .