32.5.7 Defining the constitutive response of fluid within the cohesive element gap
Products: Abaqus/Standard Abaqus/CAE
References
Overview
The cohesive element fluid flow model:
is typically used in geotechnical applications, where fluid flow continuity within the gap and through the interface must be maintained;
enables fluid pressure on the cohesive element surface to contribute to its mechanical behavior, which enables the modeling of hydraulically driven fracture;
enables modeling of an additional resistance layer on the surface of the cohesive element; and
can be used only in conjunction with traction-separation behavior.
Defining pore fluid flow properties
The fluid constitutive response comprises:
Tangential flow within the gap, which can be modeled with either a Newtonian or power law model; and
Normal flow across the gap, which can reflect resistance due to caking or fouling effects.
Specifying the fluid flow properties
You can assign tangential and normal flow properties separately.
Tangential flow
By default, there is no tangential flow of pore fluid within the cohesive element. To allow tangential flow, define a gap flow property in conjunction with the pore fluid material definition.
Newtonian fluid
In the case of a Newtonian fluid the volume flow rate density vector is given by the expression
is the tangential permeability (the resistance to the fluid flow), 
is the pressure gradient along the cohesive element, and 
is the gap opening. In Abaqus the gap opening, , is defined as
and 
are the current and original cohesive element geometrical thicknesses, respectively; and 
is the initial gap opening, which has a default value of 0.002. Abaqus defines the tangential permeability, or the resistance to flow, according to Reynold's equation:
is the fluid viscosity and is the gap opening. You can also specify an upper limit on the value of .| Input File Usage: | Use the following option to define the initial gap opening directly: |
*SECTION CONTROLS, INITIAL GAP OPENING Use the following option to define the tangential flow in a Newtonian fluid: *GAP FLOW, TYPE=NEWTONIAN, KMAX |
| Abaqus/CAE Usage: | Initial gap opening is not supported in Abaqus/CAE. |
Property module: material editor: Other |
Power law fluid
In the case of a power law fluid the constitutive relation is defined as
is the shear stress, 
is the shear strain rate, 
is the fluid consistency, and 
is the power law coefficient. Abaqus defines the tangential volume flow rate density as 
is the gap opening.| Input File Usage: | *GAP FLOW, TYPE=POWER LAW |
| Abaqus/CAE Usage: | Property module: material editor: Other |
Normal flow across gap surfaces
You can permit normal flow by defining a fluid leakoff coefficient for the pore fluid material. This coefficient defines a pressure-flow relationship between the cohesive element's middle nodes and their adjacent surface nodes. The fluid leakoff coefficients can be interpreted as the permeability of a finite layer of material on the cohesive element surfaces, as shown in Figure 32.5.7–2.
The normal flow is defined as
and 
are the flow rates into the top and bottom surfaces, respectively; 
is the midface pressure; and 
and 
are the pore pressures on the top and bottom surfaces, respectively.| Input File Usage: | *FLUID LEAKOFF |
| Abaqus/CAE Usage: | Property module: material editor: Other |
Defining leakoff coefficients as a function of temperature and field variables
You can optionally define leakoff coefficients as functions of temperature and field variables.
| Input File Usage: | *FLUID LEAKOFF, DEPENDENCIES |
| Abaqus/CAE Usage: | Property module: material editor: Other |
Defining leakoff coefficients in a user subroutine
User subroutine UFLUIDLEAKOFF can also be used to define more complex leakoff behavior, including the ability to define a time accumulated resistance, or fouling, through the use of solution-dependent state variables.
| Input File Usage: | *FLUID LEAKOFF, USER |
| Abaqus/CAE Usage: | Property module: material editor: Other |
Tangential and normal flow combinations
Table 32.5.7–1 shows the permitted combinations of tangential and normal flow and the effects of each combination.
Table 32.5.7–1 Effects of flow property definition combinations.
| Normal flow is defined | Normal flow is undefined | |
|---|---|---|
| Tangential flow is defined | Tangential and normal flow are modeled. | Tangential flow is modeled. Pore pressure continuity is enforced between facing nodes in the cohesive element only when the element is closed. Otherwise, the surfaces are impermeable in the normal direction. |
| Tangential flow is undefined | Normal flow is modeled. | Tangential flow is not modeled. Pore pressure continuity is always enforced between facing nodes in the cohesive element. |
Initially open elements
When the opening of the cohesive element is driven primarily by entry of fluid into the gap, you will have to define one or more elements as initially open, since tangential flow is possible only in an open element. Identify initially open elements as initial conditions.
| Input File Usage: | *INITIAL CONDITIONS, TYPE=INITIAL GAP |
| Abaqus/CAE Usage: | Initial gap definition is not supported in Abaqus/CAE. |
Use of unsymmetric matrix storage and solution
The pore pressure cohesive element matrices are unsymmetric; therefore, unsymmetric matrix storage and solution may be needed to improve convergence (see “Matrix storage and solution scheme in Abaqus/Standard” in “Defining an analysis,” Section 6.1.2).
Additional considerations
Your use of cohesive element fluid properties and your property values can impact your solution in some cases.
Large coefficient values
You must make sure that the tangential permeability or fluid leakoff coefficients are not excessively large. If either coefficient is many orders of magnitude higher than the permeability in the adjacent continuum elements, matrix conditioning problems may occur, leading to solver singularities and unreliable results.
Use in total pore pressure simulations
Definition of tangential flow properties may result in inaccurate results if the total pore pressure formulation is used and the hydrostatic pressure gradient contributes significantly to the tangential flow in the gap. The total pore pressure formulation is invoked if you apply gravity distributed loads to all elements in the model. The results will be accurate if the hydrostatic pressure gradient (i.e., the gravity vector) is perpendicular to the cohesive element.
Output
The following output variables are available when flow is enabled in pore pressure cohesive elements:
GFVR | Gap fluid volume rate. |
PFOPEN | Fracture opening. |
LEAKVRT | Leak-off flow rate at element top. |
ALEAKVRT | Accumulated leak-off flow volume at element top. |
LEAKVRB | Leak-off flow rate at element bottom. |
ALEAKVRB | Accumulated leak-off flow volume at element bottom. |