Zone
Orientation of Nodes and Faces within a Zone
A zone is a closed geometric domain, with nodes at the vertices and faces forming the boundary of the zone (surfaces in 3D or edges in 2D).
Zones in 3D
The relative orientation of the nodes and faces is shown in the figure below for the basic zone types: brick, wedge, pyramid, degenerate brick and tetrahedron (see zone create
for full list). Each face has vertices; these vertices are also identified in the figure. Several FLAC and FISH commands (e.g., zone attach
) refer to this orientation.
Zones in 2D
The relative orientation of the nodes and faces is shown in the figure below for the basic zone types: quadrilateral and triangle (see zone create2d
for full list). Each face (represented by an edge in 2D) has two connected vertices; these vertices are also identified in the figure. Several FLAC and FISH commands (e.g., zone attach
) refer to this orientation.
Condition Measure of Zones
A zone condition number is a measure of how badly deformed a zone is. Several basic measures are included, and the condition number is taken as their minimum to characterize the worst case. The range of a zone condition number is between 0 and 1. The larger the zone number is, the better the zone geometry is. For detailed information about how zone condition number is calculated, refer to zone geometrytest
.
Zone Field Data Names
In FLAC, the FISH zone field data functions allow the user to make queries about the values of a model variable at arbitrary locations in space. This includes zonebased information as well as gridpointbased information. The FISH functions in this section are statebased. Some of them set the particular data type (and the methods and properties used to get that data), while others retrieve the data once these values have been set.
By default, queries operate as quickly as possible for individual calls. If many (hundreds or more) points of data are to be queried, you can initialize the system to optimize multiple calls. This makes it unnecessary to calculate data more than once in a given zone or gridpoint. As an example, here is a FISH fragment that queries for the gridpointbased value \(x\)displacement at a single location in space:
zone.field.name = 'displacementx'
local result = zone.field.get(vector(3.5,4.3,6.7)) ; for FLAC3D
local result = zone.field.get(vector(3.5,6.7)) ; for FLAC2D
Here is a FISH fragment that performs many queries on a line in space, on the zonebased values of horizontal stress:
array dataset(100)
zone.field.name = 'stressxx'
zone.field.method.name = ’poly’ ; Use polynomial fit extrapolation
zone.field.init
loop ii (1,100)
local xp = 5.0 + float(ii)/10.0
dataset(ii) = zone.field.get(3.5,4.3,xp) ; for FLAC3D
end_loop
zone.field.reset
The available zone field data names are described in the table below. Note that these are the same values available under zone history
, for example.
Zone Field Data Names
Name 
Description 

acceleration 
acceleration magnitude at the gridpoint (only available if 
accelerationx 
\(x\)acceleration at the gridpoint (only available if 
accelerationy 
\(y\)acceleration at the gridpoint (only available if 
accelerationz (3D only) 
\(z\)acceleration at the gridpoint (only available if 
condition 
a measure of how badly deformed a zone is 
density 
the density of the zone 
displacement 
displacement magnitude at the gridpoint 
displacementx 
\(x\)displacement at the gridpoint 
displacementy 
\(y\)displacement at the gridpoint 
displacementz (3D only) 
\(z\)displacement at the gridpoint 
extra 
extra variable value. The extra variable index used will default to 1 and can be changed with the 
factorofsafety 
largest stable factor of safety of a grid point. Calculated during 
porepressure 
pore pressure in zone. By default, this will be the grid point pore pressure but the zone average pore pressure can be specified by using the 
propertyfluid 
a property of the fluid constitutive model of the zone. The property name must be specified using the 
property 
a property of the mechanical constitutive model of the zone. The property name must be specified using the 
propertythermal 
a property of the thermal constitutive model of the zone. The property name must be specified using the 
ratiolocal 
the local unbalanced force ratio at each gridpoint. Like all results, this can be changed to the logarithm of the value by using the 
saturation 
the saturation at the gridpoint (only available if 
strainincrement 
the strain increment tensor of the zone determined by the current displacement field. Use the 
strainrate 
the rate increment tensor of the zone determined by the current velocity field. Use the 
stress 
the stress tensor of the zone determined by the weighted average of the subzone stresses. Use the 
stresseffective 
the effective stress tensor of the zone determined by the weighted average of the subzone stresses minus the zone averaged pore pressure. Use the 
strengthstressratio 
the strengthstress ratio of the zone. Not all constitutive models support this calculation. If unsupported, the value returned will be 10. The value returned is generally held to a maximum of 10. 
temperature 
the temperature at the gridpoints. The 
timestepdynamic 
the local critical dynamic timestep of that particular gridpoint (only available if 
unbalancedforce 
the unbalanced force magnitude at the gridpoint 
unbalancedforcex 
\(x\)unbalanced force at the gridpoint 
unbalancedforcey 
\(y\)unbalanced force at the gridpoint 
unbalancedforcez (3D only) 
\(z\)unbalanced force at the gridpoint 
velocity 
the velocity magnitude at the gridpoint 
velocityx 
\(x\)velocity at the gridpoint 
velocityy 
\(y\)velocity at the gridpoint 
velocityz (3D only) 
\(z\)velocity at the gridpoint 
Zone Field Quantity Names
The field data names above may return a range of quantities. The options are listed in the following table. The definitions of the field data of a tensor (stress, strain increment, or strain rate) can be found in Stress/Strain Invariants.
Quantity Name 
Description 

intermediate principal stress or strain (increment/rate) 

maximum (most positive) value of the principal stress or strain (increment/rate) 

mean value defined as the trace of the tensor divided by three 

minimum (most negative) value of the principal stress or strain (increment/rate) 

norm of stress or strain (increment/rate) 

octahedral stress or strain (increment/rate) 

maximum shear stress or strain (increment/rate) 

distance from the origin to the tensor point in the principal space 

trace of the stress or strain (increment/rate) 

von Mises measure of the stress or strain (increment/rate) 

\(xx\)component of the stress or strain (increment/rate) 

\(xy\)component of the stress or strain (increment/rate) 

\(xz\)component of the stress or strain (increment/rate) 

\(yy\)component of the stress or strain (increment/rate) 

\(yz\)component of the stress or strain (increment/rate) 

\(zz\)component of the stress or strain (increment/rate) 
Below is a simple example for 3D case:
zone.field.name = 'stressxx'
; Use polynomial fit extrapolation
zone.field.method.name = 'poly'
; Return stressxx
global value1 = zone.field.get(10,0,20)
; Reset the stress quantity to 'vonmises'
zone.field.quantity = 'vonmises'
; Return stressvonmises
global value2 = zone.field.get(10,0,20)
or (2D case)
zone.field.name = 'stressxx'
; Use Inv. Distance Weighting approach
zone.field.method.name = 'inversedistanceweighting'
; Return stressxx
global value1 = zone.field.get(10,20)
; Reset the filed name directly to 'stressvonmises'
zone.field.name = 'stressvonmises'
; Return stressvonmises
global value2 = zone.field.get(10,20)
StrengthStress Ratio
The strengthstress ratio (SSR) is calculated in some constitutive models as a local indicator of the current stress state’s proximity to failure. Suppose the current effective minimum and maximum principal stresses are \(\sigma_1\) and \(\sigma_3\). The current Mohr circle is plotted in Figure 3. By keeping \(\sigma_3\) fixed, enlarge the Mohr circle so that it is tangent to the shear failure line; the new minimum effective principal stress is denoted by \(\sigma^{\prime}_1\), and the strengthstress ratio is defined as
It is selfevident that if the stress state is in shear failure, SSR = 1. The upper limit of SSR in FLAC3D is set to 10. If the current stress state is in tension failure, the SSR is set to 0. SSR can be plotted as a zone contour value if it is defined in the constitutive model.
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