FLAC3D Theory and Background • Constitutive Models

Isotropic Elastic Model

In this isotropic elastic (or just, elastic, for simplicity) model, strain increments generate stress increments according to the linear and reversible law of Hooke:

(1)Δσij=2G Δϵij+α2 Δϵkk δij

where the Einstein summation convention applies, δij is the Kroenecker delta symbol, and α2 is a material constant related to the bulk modulus, K, and shear modulus, G, as

(2)α2=K23 G

New stress values are then obtained from the relation

(3)σNij=σij+Δσij

Bulk modulus, K, and shear modulus, G, are related to Young’s modulus, E, and Poisson’s ratio, ν, by the following equations:

(4)K=E3(12ν)G=E2(1+ν)

or

(5)E=9KG3K+Gν=3K2G2(3K+G)


elastic Model Properties

Use the following keywords with the zone property (FLAC3D) or block zone property (3DEC) command to set these properties of the elastic (isotropic) model.

isotropic
bulk f

bulk modulus, K

poisson f

Poisson’s ratio, ν

shear f

shear modulus, G

young f

Young’s modulus, E

Notes

  • Only one of the two options is required to define the elasticity: bulk modulus K and shear modulus G, or, Young’s modulus E and Poisson’s ratio ν. When choosing the latter, Young’s modulus E must be assigned in advance of Poisson’s ratio ν.