FLAC3D Theory and Background • Theoretical Background

# Theoretical Background

The theoretical background for FLAC3D is presented in this section.
Much of FLAC3D is a direct extension from the two-dimensional version of FLAC.
Refer to the *FLAC User’s Manual* for further background on the explicit finite volume method,
which is the basis for both FLAC and FLAC3D.

There are, however, distinct differences between the two- and three-dimensional formulations, specifically in the 2D-to-3D extension of the mathematical model that describes the mechanics of the system. This section describes the three-dimensional formulation and its implementation in FLAC3D.

Section Outline

- Formulation of a 3D Explicit Finite Volume Model
- Mathematical Model Description
- Numerical Formulation
- Finite Volume Approximation to Space Derivatives
- Nodal Formulation of the Equations of Motion
- Explicit Finite Difference Approximation to Time Derivatives
- Constitutive Equations in Incremental Form
- Large- and Small-Strain Modes
- Mechanical Timestep Determination for Numerical Stability
- Mechanical Damping

- Grid Discretization in FLAC
- Numerical Implementation
- References

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