Plugin object types

The XFEM plugin publishes two objects type depending on the nature of the problem (Mechanical or Hydromechanical) and so references to the plugin name while creating a physics object don't need to include a type name.

objects type	Mechanical problems	hydromechanical problems
PlaneStrain	Yes	No
HydroMechanic	No	Yes

State variables

The XFEM plugin requires the model to contain the following state variables for mechanical or hydromechanical problems:

State variables	Mechanical problems	hydromechanical problems
u	Yes	Yes
a	Yes	Yes
P	No	Yes
Pa	No	Yes
Pf	No	Yes

Example:

StateVar{id = 'u', description = 'Displacements in the X and Y directions',         unit = 'm'}
StateVar{id = 'a', description = 'Enriched displacement in the X and Y directions', unit = 'm'}
StateVar{id = 'P', description = 'Pore pressure degree-of-freedom',                 unit = 'kPa'}
StateVar{id = 'Pa',description = 'Enriched pore pressure degree-of-freedom',        unit = 'kPa'}
StateVar{id = 'Pf',description = 'Fracture pressure degree-of-freedom',             unit = 'kPa'}

Material types

The XFEM plugin uses the concept of a metrial type since it features multiple constitutive laws. The Mechanical and Hydromechanical material behavior are fully described by the material properties below.

Material properties

The following material properties are supported (required) by the XFEM plugin:

Property	Description	Type	Def. Unit	Mechanical problems	hydromechanical problems
E	Elasticity modulus	Scalar	kPa	Yes	Yes
nu	Poisson ratio	Scalar	–	Yes	Yes
K	Hydraulic permeability (1)	Scalar or matrix	m/s	No	Yes
gw	Specific weight of water	Scalar	kN/m3	No	Yes
Pht	Porosity	Scalar	–	No	Yes
SPMax	Maximum principal stress	Scalar	kPa	Yes	Yes
Gap	Initial gap opening	Scalar	m	Yes	Yes
Ufw	Dynamic fluid viscosity	Scalar	kPa*s	No	Yes
Lkt	Leakoff at top	Scalar	m/(kPa*s)	No	Yes
Lkb	Leakoff at bottom	Scalar	m/(kPa*s)	No	Yes
elastic	Mechanical XFEM material type	String	–	Yes	No
poroElastic	Hydromechanical XFEM material type	String	–	No	Yes

(1) The hydraulic conductivity tensor is a 'dxd' matrix, where 'd' is either 2 or 3 depending on the model dimension. It can be replaced by a vector or a scalar instead. If a vector with size 'd' is given, the tensor matrix is formed with the vector values in its diagonal, with other elements set to 0. For a scalar value, the matrix will be isotropic with the given value at the diagonal.

Material properties are normally read from a property set. If a property is not found at the mesh property sets, it will also be searched in the mesh list of cell attributes. This second option is handy if one wants to create individual materials for each cell (working with a stochastic distribution for a material property, for example).

If, for any reason, the model contains compatible material properties with names other than the expected values above, a renaming table can be included in the set of physics attributes to perform the required name translations.

Example:

PropertySet
{
  id          = 'MatProp',
  typeName    = 'GemaPropertySet',
  description = 'Material properties',
  properties  = {
    {id = 'E',   description = 'Elasticity modulus',                  unit = 'kPa'},
    {id = 'nu',  description = 'Poisson ratio',                       unit = ''},
        {id = 'K',  description = 'Hydraulic permeability',               unit = 'm/s'},
        {id = 'gw',  description = 'Specific weight of water',            unit = 'kN/m3'},
    {id = 'Pht',  description = 'Porosity',                           unit = ''},
        {id = 'SPMax', description = 'Maximum principal stress',          unit = 'kPa'},
        {id = 'Gap', description = 'Initial gap opening',                 unit = 'm'},
        {id = 'Ufw', description = 'Dynamic fluid viscosity',             unit = 'kPa*s'},
    {id = 'Lkt', description = 'Leakoff at top',                      unit = 'm/(kPa*s)'},
        {id = 'Lkb', description = 'Leakoff at bottom',                   unit = 'm/(kPa*s)'},
        {id = 'material',  description = 'Mechanical XFEM material type', constMap = constants.Xfem.materialModels},
  },
  values = {
    {E = 14.4e+6, nu = 0.2,  K = 9.8e-7, gw = 9.81, Pht = 0.2, SPMax= 1e3,
     Gap = 0.002, Ufw = 1e-6, Lkt = 1e-19, Lkb = 1e-19,  material = 'poroElastic'},
  }
}

Physics attributes

When defining a XFEM plugin Physics object, the following fields are available for usage during the definition:

Attribute	Description	Type	Required	Def. Value
id	The physics name.	String	Yes	-
id	Example: id = 'myPhysicsName'
typeName	Physics plugin name. Should be equal to 'Xfem.HydroMechanic'.	String	Yes	-
typeName	Required value: typeName = 'Xfem.HydroMechanic'
type	Type of physics object. Should be equal to 'fem'.	String	Yes	-
type	Required value: type= 'fem'
ruleSet	Integration rule set selected for simulation elements.	String	No	Empty
ruleSet	Example: ruleSet = 1

mesh	The mesh name.	String	Yes	-
mesh	Example: mesh = 'myMeshName'
boundaryConditions	Table filled with the names of the boundary conditions associated with this physics.	String table	Yes	-
boundaryConditions	Example: boundaryConditions = {'myBc1', 'myBc2', 'myBc3'}

Like other Fem physics, stateVar, property and attribute renaming fields are supported. Likewise, restricting the physics application domain to a set of cell groups, setting the desired integration rule and unit system remapping are also available. Those common optional fields are detailed at the gemaFemProcessCommonFemPhysicsOptions page.

Example for mechanical problems:

PhysicalMethod {
  id       = 'XfemMechanic',
  typeName = 'Xfem.PlaneStrain',
  type     = 'fem',
  mesh = 'mesh',
  ruleSet = 1,
  boundaryConditions = {'bc2'},
  materials = {'elastic'},
}

Example for hydromechanical problems:

PhysicalMethod {
  id       = 'HMCoupledXfem',
  typeName = 'Xfem.HydroMechanic',
  type     = 'fem',
  mesh     = 'mesh',
  ruleSet  = 1, 
  boundaryConditions = {'bc1','bc2','bc4','bc5','bc6'},
  materials = {'poroElastic'},
}

Boundary conditions

The XFEM plugin physics supports both Dirichlet and Neumann conditions. The injection process is applied to the model by defining a fluid flow rate as a boudary condition. Injection Flow Rate definition m3/s, negative signal means that flow is entering into the model

Example:

BoundaryCondition {
  id   = 'bc5',
  type = 'node fracture flow',
  mesh = 'mesh',
  properties  = {
    {id = 'qfw',  description = 'concentrated fracture flow'},
    
  },
  nodeValues = {
--    {node,      qw }    
      {1   ,  -0.0001},     -- this node will be changed to a crack node in solution file : ProcessScript() 
  }
}

Here this condition is defined in a standard mesh node (model file), then in the solution file is changed to the crack mouth node or injection point. This is done because initially no crack nodes are defined in the mesh, they only appear after the preprocessing (crack geometrical treatment) when crack nodes are added to the mesh

Example:

local bc = modelData:boundaryCondition('bc5') -- Just defininig a parameter name bc to used it below to define the injection point in a ghost(crack) node

bc:setNode(1, setMeshGhostFlag(2)) -- Changing node 1 in bc5 (model file) by the Second ghost node of each crack to inject fluid

Solver Options

The XFEM plugin has several options used to solve the equation system for mechanical or hydromechanical problems.

Solver type	Mechanical problems	hydromechanical problems
static linear	Yes	No
transient nonlinear	No	Yes

The static linear solver has some strategies for incrementalization and iterations in order to facilitate convergence.

Increment strategies	ID
load_control_increment	0
cylindrical_arc_length_increment	1
spherical_arc_length_increment	2
external_work_increment	3
displacement_control_increment	4
dissipated_energy_increment	5
combined_arc_dissipated_energy_increment	6

Iteration strategies	ID
load_control	0
linear_arc_length	1
cylindrical_arc_length	2
spherical_arc_length	3
minimal_norm	4
orthogonal_residue	5
displacement_control	6
dissipated_energy	7
combined_arc_dissipated_energy	8

The static linear solver has two options for the Newton-Raphson method.

Newton Raphson Mode	ID
Modified	0
Full	1

Example for mechanical problems:

solverOptions = { 
  type                      = 'static linear',
  tolerance                     = {mechanic = 1e-5},  --Tolerance for convergence
  stepsMax                                      = 1,                  -- Total step of analysis
  loadPredictorIncrement        = 1,                  -- Load increment for each step 
  loadMaxIncrement                      = 1,                  -- Maximum step increment
  loadMax                                       = 4,                  -- Maximum Load of analysis
  minDissipatedEnergy       = 5.0e-5,             -- Minimum magnitude of dissipated energy (only when Dissipated Energy strategy is used)
  initialEnergyIncrement    = 0.00005,            -- Initial Energy Increment (only when Dissipated Energy strategy is used)
  incrementsStrategy            = 4,                  -- ID of the Increment strategy to be used
  iterationsStrategy            = 5,                  -- ID of the Iteration strategy to be used
  newtonRaphsonMode         = 0,                  -- ID of the Newton-Raphson mode 
  attemptsMax               = 20,                 -- Maximum number of attempts
  loadAdjustStep            = 0,                  -- Maximum limit value to adjust the step load
  convergenceCriterion      = 1                   -- convergence by Load =0 or by displacement =1
}

Example for hydromechanical problems:

solverOptions = { 
  type = 'transient nonlinear',            -- Type of solver to be used
  timeMax            = 200,                -- Total time of analysis
  timeInitIncrement  = 1,                  -- Initial time increment
  timeMinIncrement   = 1,                  -- Minimum time increment
  timeMaxIncrement   = 5.0,                -- Maximum time increment
  iterationsMax      = 5000,               -- Maximum number of iterations
  eulerTheta         = 1.0,                -- Solver parameter              
  tolerance          = {mechanic = 1e-4, hydraulic = 1e-4} -- tolerances for convergence criteria
}

XFEM Options

The XFEM plugin has some specific options to treat fracture propagation.

Example:

xfemOptions={
  propagationCriteria       = 'MaxPS',        -- Maximum principal stress criterium for crack propagation
  evaluationZone            = 'nonLocalQuad', --create a quadrilateral region at the crack tip to compute the average maximum principal stress of the gauss points which are inside this region
  weightFunction            = 'uniform',      -- every gauss point inside the quadrilateral region used for MaxPS has the same weight value eventhough a point is nearer than other to the crack tip 
  geometricTol              = 1e-6,           -- Geometric tolerance to determine which gauss points are considered for Maximum principal stress calculation
  geoStatic                 = 0,              -- zero when no geoStatic step is performed
}

Derived results

Besides calculating Displacement and porepressure values, the XFEM plugin can also recover stress and strain values on Gauss points. Additionaly, fracture pressures are calculated on fracture nodes.

If, for any reason, the model contains compatible node and/or Gauss attributes with names other than 'q', a renaming table can be included in the set of physics attributes to perform the required name translations.

Supported elements

The XFEM plugin supports 2D elements. Supported elements are:

quad4
tri3

Unit system

E = 'kPa'

nu = –

K = 'm/s'

gw = 'kN/m3'

Pht = –

SPMax = 'kPa'

Gap = 'm'

Ufw = 'kPa*s'

Lkt = 'm/(kPa*s)'

Lkb = 'm/(kPa*s)'