ProductsAbaqus/StandardAbaqus/CAE Defining pore fluid flow propertiesThe fluid constitutive response comprises:
The flow patterns of the pore fluid in the element are shown in Figure 1. Figure 1. Flow within cohesive elements.
The fluid is assumed to be incompressible, and the formulation is based on a statement of flow continuity that considers tangential and normal flow and the rate of opening of the cohesive element. Specifying the fluid flow propertiesYou can assign tangential and normal flow properties separately. Tangential flowBy 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 fluidIn the case of a Newtonian fluid the volume flow rate density vector is given by the expression $$\mathbf{q}d={k}_{t}\nabla p,$$ where ${k}_{t}$ is the tangential permeability (the resistance to the fluid flow), $\nabla p$ is the pressure gradient along the cohesive element, and $d$ is the gap opening. In Abaqus the gap opening, $d$, is defined as $$d={t}_{curr}{t}_{orig}+{g}_{init},$$ where ${t}_{curr}$ and ${t}_{orig}$ are the current and original cohesive element geometrical thicknesses, respectively; and ${g}_{init}$ 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: $${k}_{t}=\frac{{d}^{3}}{12\mu},$$ where $\mu $ is the fluid viscosity and $d$ is the gap opening. You can also specify an upper limit on the value of ${k}_{t}$. 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: OtherPore FluidGap Flow: Type: Newtonian: Toggle on Maximum Permeability and enter the value of ${k}_{\mathrm{max}}$ Power law fluidIn the case of a power law fluid the constitutive relation is defined as $$\tau =K{\dot{\gamma}}^{\alpha},$$ where $\tau $ is the shear stress, $\dot{\gamma}$ is the shear strain rate, $K$ is the fluid consistency, and $\alpha $ is the power law coefficient. Abaqus defines the tangential volume flow rate density as $$\mathbf{q}d=\left(\frac{2\alpha}{1+2\alpha}\right){\left(\frac{1}{K}\right)}^{\frac{1}{\alpha}}{\left(\frac{d}{2}\right)}^{\frac{1+2\alpha}{\alpha}}{\parallel \nabla p\parallel}^{\frac{1\alpha}{\alpha}}\nabla p,$$ where $d$ is the gap opening. Input File Usage GAP FLOW, TYPE=POWER LAW Abaqus/CAE Usage Property module: material editor: OtherPore FluidGap Flow: Type: Power law Normal flow across gap surfacesYou can permit normal flow by defining a fluid leakoff coefficient for the pore fluid material. This coefficient defines a pressureflow 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 2. Figure 2. Leakoff coefficient interpretation as a permeable layer.
The normal flow is defined as $${q}_{t}={c}_{t}\left({p}_{i}{p}_{t}\right)$$ and $${q}_{b}={c}_{b}\left({p}_{i}{p}_{b}\right),$$ where ${q}_{t}$ and ${q}_{b}$ are the flow rates into the top and bottom surfaces, respectively; ${p}_{i}$ is the midface pressure; and ${p}_{t}$ and ${p}_{b}$ are the pore pressures on the top and bottom surfaces, respectively. Input File Usage Abaqus/CAE Usage Property module: material editor: OtherPore FluidFluid Leakoff: Type: Coefficients Defining leakoff coefficients as a function of temperature and field variablesYou 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: OtherPore FluidFluid Leakoff: Type: Coefficients: Toggle on Use temperaturedependent data and select the number of field variables. Defining leakoff coefficients in a user subroutineUser 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 solutiondependent state variables. Input File Usage FLUID LEAKOFF, USER Abaqus/CAE Usage Property module: material editor: OtherPore FluidFluid Leakoff: Type: User Tangential and normal flow combinationsTable 1 shows the permitted combinations of tangential and normal flow and the effects of each combination.
Initially open elementsWhen 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 solutionThe 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). Additional considerationsYour use of cohesive element fluid properties and your property values can impact your solution in some cases. Large coefficient valuesYou 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 simulationsDefinition 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. OutputThe following output variables are available when flow is enabled in pore pressure cohesive elements:
