FLAC3D Modeling • Introduction

Comparison with Other Methods

How does FLAC3D compare to the more common method of using finite elements for numerical modeling? Both methods translate a set of differential equations into matrix equations for each element, relating forces at nodes to displacements at nodes. Although FLAC3D’s equations are derived by the finite volume method, the resulting element matrices for an elastic material are identical to those of the finite element method (for constant-strain tetrahedra). However, FLAC3D differs in the following respects:

1. The “mixed discretization” scheme (Marti and Cundall 1982) is used for accurate modeling of plastic collapse loads and plastic flow. This scheme is believed to be physically more justifiable than the “reduced integration” scheme commonly used with finite elements.
2. The full dynamic equations of motion are used, even when modeling systems that are essentially static. This enables FLAC3D to follow physically unstable processes without numerical distress. The approach to provide a time-static solution is discussed in the definition for static solution.
3. An “explicit” solution scheme is used (in contrast to the more usual implicit methods). Explicit schemes can follow arbitrary nonlinearity in stress/strain laws in almost the same computer time as linear laws, whereas implicit solutions can take significantly longer to solve nonlinear problems. Furthermore, it is not necessary to store any matrices, which means: 1) a large number of elements may be modeled with a modest memory requirement; and 2) a large-strain simulation is hardly more time-consuming than a small-strain run, because there is no stiffness matrix to be updated.
4. FLAC3D is robust in the sense that it can handle any constitutive model with no adjustment to the solution algorithm; many finite element codes need different solution techniques for different constitutive models.
5. FLAC3D uses an incremental formulation in almost all areas. This means that displacements are not directly related to stresses and can be changed at any time, and that material properties can change without affecting the current stress state.

These differences are mainly in FLAC3D’s favor, but there are two disadvantages:

1. Linear simulations run more slowly with FLAC3D than with equivalent finite element programs. FLAC3D is most effective when applied to nonlinear or large-strain problems, or to situations in which physical instability may occur.
2. The solution time with FLAC3D is determined by the ratio of the longest natural period to the shortest natural period in the system being modeled. This point is discussed in more detail in the section on Formulation of a 3D Explicit Finite Difference Model, but certain problems are very inefficient to model (e.g., beams, represented by solid elements rather than structural elements, or problems that contain large disparities in elastic moduli or element sizes).

Reference

Marti, J., and P. A. Cundall. “Mixed Discretization Procedure for Accurate Solution of Plasticity Problems,” Int. J. Num. Methods and Anal. Methods in Geomech., 6, 129-139 (1982).