The ; keyword

The keyword ; is not documented yet

The @APosterioriTimeStepScalingFactor keyword

The keyword @APosterioriTimeStepScalingFactor is not documented yet

The @APrioriTimeStepScalingFactor keyword

The keyword @APrioriTimeStepScalingFactor is not documented yet

The @AdditionalConvergenceChecks keyword

The @AdditionalConvergenceChecks keyword is meant to introduce a code block returning stating if convergence has been reached. More precisely, this code block is meant to modify a boolean variable called converged. This boolean is true if the standard convergence criterion has been reached, false otherwise.

One possible usage of this code block is multi-surfaces plasticity treated by activating or deactivating statuses, as described by Simo and Hughes.

Example

Consider a two surfaces plastic behaviour. We will use an array of booleans called statuses.

@Brick StandardElasticity; // to have computeElasticPrediction

@LocalVariable bool statuses[2];

@Prediction{
  // initial status based of the elastic prediction
  auto sigel = computeElasticPrediction();
  for(unsigned short i=0;i!=2;++i){
    statuses[i] = ...
  }
} // end of @Prediction

@Integrator{
  for(unsigned short i=0;i!=2;++i){
    if(statuses[i]){
      ...
    }
  }
} // end of @Integrator

The @Algorithm keyword

The @Algorithm keyword is used to select a numerical algorithm.

The set of available algorithms depends on the domain specific language. As the time of writing this notice, the following algorithms are available:

Example (Runge-Kutta dsl)

@Algorithm rk54;

Example (Implicit dsl)

@Algorithm NewtonRaphson;

The @Author keyword

The @Author keyword is used to give the name of the person who wrote the mfront file.

All the following words are appended to the author’s name up to a final semicolon.

Note: The name of the person who formulated the material property, behaviour or model shall be given in the description section (see the @Description keyword).

Example

@Author Éric Brunon;

The @AuxiliaryStateVar keyword

The @AuxiliaryStateVar keyword is a deprecated synonymous of @AuxiliaryStateVariable.

The @AuxiliaryStateVariable keyword

The AuxiliaryStateVariable keyword introduces one or several new auxiliary state variables. It is followed by a type name and the name(s) of the variable(s) declared, separated by commas.

Example

// scalar auxiliary state variable
@AuxiliaryStateVariables strain p;
// symmetric tensors auxiliary state variable
@AuxiliaryStateVariables StrainStensor evp,evp2;

The @AxialGrowth keyword

The @AxialGrowth keyword let the user specify a linear stress-free expansion:

This keyword is followed by:

Physical description

The value of the axial growth gives the change in length in the axial direction \(\frac{\Delta\,l_{z}}{l_{z}}\).

The axial growth is assumed to be isochoric, so the change of length in each direction of the plane perpendicular to the axial direction is given by: \[ \frac{\Delta\,l_{\parallel}}{l_{\parallel}}=\frac{1}{\sqrt{1+\frac{\Delta\,l_{z}}{l_{z}}}}-1 \]

Notes

Examples

// axial growth defined by an external model
@AxialGrowth 'M5AxialGrowth.mfront';
// axial growth defined by an external state variable
@ExternalStateVariable real ag;
ag.setGlossaryName("AxialGrowth");
@AxialGrowth ag;

The @Behaviour keyword

The @Behaviour defines the name of the behaviour. The name must be a valid C++ class name.

The following characters are legal as the first character of an identifier, or any subsequent character:

_ a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The following characters are legal as any character in an identifier except the first:

0 1 2 3 4 5 6 7 8 9

Example

@Behaviour Norton;

The @Bounds keyword

The @Bounds keyword let the user define the domain of validity of the law.

The @Bounds keyword is followed by a variable name, the keyword in and an interval. The interval may contain the infinity, represented by the ’*’ character.

Effect

What happens if a variable is found to be out of its bounds depends on the interface used. Most interfaces let the user choose one of three following policies:

Example

@Bounds T in [293.15:873.15];

The @Brick keyword

The @Brick keyword introduces a behaviour brick.

Example

@Brick "StandardElasticity";

The @Coef keyword

The @Coef keyword is a deprecated synonymous of @MaterialProperty.

The @CompareToNumericalJacobian keyword

The @CompareToNumericalJacobian keyword enables or disables the comparison of the user defined jacobian to a numerically computed jacobian. This keyword is followed by a boolean value (true or false).

Jacobians are compared by blocks. Blocks for which the comparison failed are reported on the standard output.

The comparison criterion value can be changed used the @JacobianComparisonCriterion keyword.

Example

@CompareToNumericalJacobian true;

The @ComputeFinalStress keyword

The @ComputeFinalStress keyword introduces a code block meant to compute the stress symmetric tensor after the integration.

The code block is called after the update of the state variables. The auxiliary state variable and the external state variables are not updated yet.

Example

@ComputeFinalStress{
  const SlidingSystems& ss = SlidingSystems::getSlidingSystems();
  // approximation de l'inverse de \(\Delta\,F_p\)
  inv_dFp = Tensor::Id();
  for(unsigned short i=0;i!=12;++i){
    inv_dFp -= dg[i]*ss.mu[i];
  }
  real J_inv_dFp = det(inv_dFp);
  inv_dFp /= CubicRoots::cbrt(J_inv_dFp);
  // Fe en fin de pas de temps
  Fe  = Fe_tr*inv_dFp;
  // Piola-Kirchhoff II
  S = D*eel;
  // Cauchy
  sig = convertSecondPiolaKirchhoffStressToCauchyStress(S,Fe);
}

The @ComputeStiffnessTensor keyword

The ComputeStiffnessTensor keyword is used to define the elastic stiffness tensor based on the elastic material properties given as an array of entries. After this array, a semicolon is expected.

This array is used to automatically used to declare the elastic material properties of the behaviour (see the @ElasticMaterialProperties keyword for details).

An entry can be either a string referring to an external MFront file, a formula or a numerical value.

If an entry refers to an external MFront file or the formula, all the inputs of this material property must be either:

of the behaviour.

Isotropic case

In the isotropic case, two entries are expected in the array, in that order:

Orthotropic case

In the orthotropic case, 9 entries are expected in the array, in that order:

In the orthoropic case, computation of the stiffness tensor rely on the definition of an orthotropic convention. For example, the Pipe orthotropic convention will lead to automatically exchange the second and first axes when computing the stiffness tensor for the plane strain, plane stress and generalised plane strain hypotheses. See the OrthotropicBehaviour keyword for details.

Tensors computed

In an implicit scheme, this keyword leads to the definition and the automatic computation of the tensors D and D_tdt which respectively refer to the stiffness tensor at \(t+\theta\,dt\) and \(t+dt\).

In an explicit scheme, this keyword leads to the definition of the stiffness tensor which is automatically updated if this tensor evolves during the time step.

Example

@ComputeStiffnessTensor{7.8e+4,2.64233e+5,3.32e+5,
    0.13,0.24,0.18,
    4.8e+4,1.16418e+5,7.8e+4};

The @ComputeStress keyword

The @ComputeStress keyword introduces a code block meant to compute the stress symmetric tensor.

This keyword interprets the code block to generate two methods:

Note

If the user provide a way of computing the stress at the end of the time step through the @ComputeFinalStress keyword, we consider that the use of @ComputeStress is meaningless and advice the user to rather compute explicitly the stress as part of the integration step.

Example

@ComputeStress{
  sig = (1-d)*(lambda*trace(eel)*Stensor::Id()+2*mu*eel);
}

The @ComputeStressFreeExpansion keyword

The ComputeStressFreeExansion keyword introduces a code block which allows the user to define an arbitrary expansion.

The code block is meant to update two symmetric tensors dl0_l0 and dl1_l0 which respectively stands for the value of the expansion at the beginning and at the end of the time step.

Note

Example

@ExternalStateVariable real tau;
tau.setGlossaryName("BurnUp (at.%)");

@Parameter Ctau = 0.6e-2;
Ctau.setEntryName("SolidSwellingCoefficient");

@ComputeStressFreeExpansion{
  dl0_l0 += Ctau*tau*StrainStensor::Id();
  dl1_l0 += Ctau*(tau+dtau)*StrainStensor::Id();
}

The @ComputeThermalExpansion keyword

The ComputeThermalExansion keyword is followed either by a material property description or an array of material descriptions (othotropic behaviours) giving the mean linear thermal expansion coefficient.

A material description is either a floating point number, a formula or the name of an external MFront file.

The thermal expansion is computed as follows: \[ \frac{\Delta\,l}{l_{T^{i}}} = \frac{1}{1+\alpha\left(T^{i}\right)\,\left(T^{i}-T^{\alpha}\right)}\,\left[\alpha\left(T\right)\,\left(T-T^{\alpha}\right)-\alpha\left(T^{i}\right)\,\left(T^{i}-T^{\alpha}\right)\right] \]

where:

Definition of the reference temperature for the thermal expansion

The reference temperature for the thermal expansion \(T^{\alpha}\) is intrinsically linked to the definition of the thermal expansion coefficient.

One may use the following syntax to define \(T^{\alpha}\):

@Parameter a0 = 2.e-5;
@Parameter a1 = 4.e-8;
@ComputeThermalExpansion "a0+a1*(T-273.15)"{
 reference_temperature : 273.15
};

However, if the mean linear thermal expansion coefficient is given by an external MFront file, it is recommended to define a static variable called ReferenceTemperature in this file.

Whatever the way used to defined \(T^{\alpha}\), a parameter called ThermalExpansionReferenceTemperature is automatically defined.

Note

If \(T^{\alpha}\) is not explicitly defined, a default value of \(293.15\,K\) is used.

Parameter associated with the reference temperature for the geometry

The reference temperature at which of the geometry has been measured, \(T^{i}\), has a default value of \(293.15\,K\). This can be changed using the automatically defined ReferenceTemperatureForInitialGeometry parameter.

Orthotropic axis convention

For orthotropic behaviours, the orthotropic axes convention is taken into account (see OrthotropicBehaviour).

Example

@ComputeThermalExpansion 1.e-5;
@ComputeThermalExpansion "UO2_ThermalExpansion.mfront"
@ComputeThermalExpansion {1.e-5,0.2e-5,1.2e-5};

The @ComputedVar keyword

The keyword @ComputedVar is not documented yet

The @CrystalStructure keyword

The crystal structure must be defined through the @CrystalStructure keyword. This keyword is followed by one of the following value:

Example

@CrystalStructure FCC;

The @DSL keyword

The @DSL keyword specify the domain specific language (dsl) used.

The list of available dsl’s is returned by the --list-dsl option of mfront:

$ mfront --list-dsl

As the time of writing this notice, the following dsl’s are available:

DSL options

A DSL’s behaviour may be changed using options defined either in the MFront file using a JSON-like syntax or as a command line argument.

The options related to a specific DSL can be retrieved using the --list-dsl-options command line argument, as follows:

$ mfront --list-dsl-options=Model
- parameters_as_static_variables: boolean stating if the parameter shall be treated as static variables.
- build_identifier              : string specifying a build identifier. This option shall only be specified on the command line.

Defining DSL options in the MFront file

Options can be passed to a DSL as follows:

@DSL Default{
  parameters_as_static_variables : true
};

Defining DSL options on the command line:

MFront have various command line arguments to define options passed to DSLs:

For example, the --dsl-option can be used as follows:

$ mfront --obuild --interface=cyrano --dsl-option=build_identifier:\"Cyrano-3.2\" Elasticity.mfront

This example illustrates that special care must be taken when defining an option expecting a string value.

Options common to all DSLs

The following options are available for all DSLs:

Example

@DSL Implicit;

The @Date keyword

The @Date keyword allows the user to precise when the mfront file was written.

All the following words are appended to the date up to a final semicolon.

Example

@Date 2008-11-17;

The @Description keyword

The @Description describes the material property, behaviour or model which is implemented in a mfront file.

This keyword is followed by a block containing all the relevant piece of information including:

Example

@Description
{
  Corrélation établie sur la nuance V-4Cr-4Ti.

  Propriétés extraites du document :

  Propriétés et comportement mécanique d alliages
   de Vanadium avant, après et sous irradiation

  Marion Le Flem, Jean-Luc Bechade, Annick Bougault,
  Aurore Michaux, Lionel Gosmain, Jean-Louis Seran
  DMN/SRMA/LA2M/NT/2008-2967/A
}

The @DislocationsMeanFreePathInteractionMatrix keyword

The interaction matrix associated with the effects of the dislocations on the mean free path of the dislocations of a specific system can be defined though the @DislocationsMeanFreePathInteractionMatrix keyword.

This keyword follows the same conventions as the @InteractionMatrix keyword. In particular, the structure of the matrix is fully described in the description of @InteractionMatrix.

See the @InteractionMatrix keyword for details.

The @DissipatedEnergy keyword

The @DissipatedEnergy keyword allows the computation of the internal energy per unit of volume in the reference configuration.

The code provided must update a variable called Psi_d.

This update is called at the end of the behaviour integration, if convergence was reached, after that:

Example

@DissipatedEnergy{
    Psi_d += sig|(deto-deel)
    // If would have been better to store the initial value of the
    // stress in a local variable sig0 and then used 

}
@DissipatedEnergy{
    // Here, we have stored the initial value of the
    // stress in a local variable sig0 
    Psi_d += (sig0+sig)|(deto-deel)/2
}

The @ElasticMaterialProperties keyword

The @ElasticMaterialProperties keyword is used give the material properties for standard mechanical behaviours.

This keyword is followed by an array which values can be either a string referring to a formula, an external MFront file or a numerical value. After this array, a semicolon is expected.

If an entry refers to an external MFront file or a formula, all the inputs of this material property must be either:

of the behaviour.

Elastic material properties are used by behaviours bricks.

Isotropic case

In the isotropic case, two entries are expected in the array, in that order:

In domain specific languages providing an implicit scheme (Implicit,ImplicitII, ImplicitFiniteStrain), the following local variables are automatically defined and computed:

Orthotropic case

In the orthotropic case, 9 entries are expected in the array, in that order:

In the orthoropic case, behaviours bricks will rely on the definition of an orthotropic convention to compute the stiffness tensor. For example, the Pipe orthotropic convention will lead to automatically exchange the second and first axes when computing the stiffness tensor for the plane strain, plane stress and generalised plane strain hypotheses.

Example

@ElasticMaterialProperties {"AISI348_YoungModulus.mfront",0.3};

The @Epsilon keyword

The @Epsilon keyword let the user define the convergence criterion value. It is followed by a positive floating-point number.

The epsilon parameter

The @Epsilon keyword defines the default value for the epsilon parameter. This parameter can be changed at runtime.

Example

@Epsilon 1.e-12;

The @ExternalStateVar keyword

The @ExternalStateVar keyword is a deprecated synonymous of @ExternalStateVariable.

The @ExternalStateVariable keyword

The ExternalStateVariable keyword introduces one or several new external state variables. It is followed by a type name and the name(s) of the variable(s) declared, separated by commas.

The external state variables names must be valid C++ identifiers.

The following characters are legal as the first character of an identifier, or any subsequent character:

_ a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The following characters are legal as any character in an identifier except the first:

0 1 2 3 4 5 6 7 8 9

Arrays

One may declare an array of external state variables by specifying the array size after the external state variable name.

External names

It is recommended to associate to an external state variable a glossary or an entry name through the methods setGlossaryName or setEntryName respectively.

Example

// scalar external state variable
@ExternalStateVariable strain s;

The @GlidingSystem keyword

A synonym of @SlipSystem. See @SlipSystem for details.

The @GlidingSystems keyword

A synonym of @SlipSystems. See @SlipSystems for details.

The @HillTensor keyword

The keyword @HillTensor is not documented yet

The @Import keyword

The @Import keyword allows the inclusion of one or several (external) mfront files. This keyword is followed by a string or an array of strings. Each string stands for a mfront file name that is meant to be imported.

This instruction interrupts the treatment of the current file and starts the sequential treatment of each file to be imported.

Search paths

Files to be imported are searched, in that order:

Example

@Import "SlidingSystemsCC.mfront";

The @Includes keyword

The @Includes introduces a block were the user may define some preprocessor directives, typically #include directives (hence the name).

Example

@Includes{
#include<fstream>
}

The @InitJacobian keyword

The @InitJacobian keyword is a deprecated synonymous of @InitializeJacobian.

The @InitJacobianInvert keyword

The @InitJacobianInvert keyword is a deprecated synonymous of @InitializeJacobianInvert.

The @InitLocalVariables keyword

The @InitLocalVariables keyword is a deprecated synonymous of @InitializeLocalVariables.

The @InitLocalVars keyword

The @InitLocalVars keyword is a deprecated synonymous of @InitializeLocalVariables.

The @Initialize keyword

The keyword @Initialize is not documented yet

The @InitializeFunction keyword

The @InitializeFunction keyword introduces a code block that can be used to initialize internal state variables at the very beginning of the computation. Initialize functions may have user so-called initialize function variables.

In this version, only the generic interface generates functions associated with initialize functions (See Section [sec?]::tfel_4.1:system:elm:initialize_functions to see how to retrieve the initialize functions generated by the generic interfaces).

Because initialize functions are called before any behaviour integration, special care to the meaning of the variables must be taken:

Concerning material properties, they have their values at the beginning of the time step.

About initialisation of local variables

The code block defined by the @InitLocalVariables code block shall be called before the execution of an initialize function.

Example of usage

The following code defines an initializer function which initializes the elastic strain from the value of stress:

@InitializeFunction ElasticStrainFromInitialStress{
  const auto K = 2 / (3 * (1 - 2 * nu));
  const auto pr = trace(sig) / 3;
  const auto s = deviator(sig);
  eel = eval((pr / K) * Stensor::Id() + s / mu);
}

The @InitializeFunctionVariable keyword

Initialize function variables are introduced by the @InitializeFunctionVariable keyword.

Initialize function variables are only defined in initialize functions, and can’t be used in the other code blocks.

Contrary most variables (internal state variables, external state variables, etc.), initialize function variables can be defined after the first code block. However, care must be taken to declare initialize function variables before their use in an initialize function.

Note that an initialize function variable can be used in different initialize function.

The @InitializeJacobian keyword

The @InitializeJacobian keyword let the user introduce an initial estimate for the jacobian matrix used by quasi-newton methods, such as the first Broyden method.

Example

@InitializeJacobian{
  // setting the jacobian to identity (which is the default)
  fill(this->jacobian.begin(),this->jacobian.end(),real(0));
  for(unsigned short i=0;i!=this->jacobian.size();++i){
    this->jacobian(i,i)=real(1);
  }
}

The @InitializeJacobianInvert keyword

The @InitializeJacobianInvert keyword let the user introduce an initial estimate for the jacobian matrix used by quasi-newton methods, such as the second Broyden method.

Example

@InitializeJacobianInvert{
  // setting the inverse of the jacobian (still called jacobian by the
  // way) to identity (which is the default)
  fill(this->jacobian.begin(),this->jacobian.end(),real(0));
  for(unsigned short i=0;i!=this->jacobian.size();++i){
    this->jacobian(i,i)=real(1);
  }
}

The @InitializeLocalVariables keyword

The @InitializeLocalVariables introduces a code block meant to initialize the local variables (see the @LocalVariable keyword).

Example

//! volumic fraction of each phase
@LocalVariable real  fv[Np];
//! interaction matrix
@LocalVariable tfel::math::tmatrix<Nss,Nss,real> mh;

@InitLocalVariables<Append>{
  // volumic fraction of each phase
  for(unsigned short i=0;i!=Np;++i){
    fv[i]=1.0/static_cast<real>(Np) ; 
  }
  // interaction matrix
  const real h1 = 1.;
  const real h2 = 1.;
  const real h3 = 1.;
  const real h4 = 1.;
  const real h5 = 1.;
  const real h6 = 1.;
  mh = InteractionMatrix::getInteractionMatrix(h1,h2,h3,
                           h4,h5,h6);
}

The @IntegerConstant keyword

The keyword @IntegerConstant is not documented yet

The @IntegrationVariable keyword

The IntegrationVariable keyword introduces one or several new integration variables. It is followed by a type name and the name(s) of the variable(s) declared, separated by commas.

The integration variables names must be valid C++ identifiers.

The following characters are legal as the first character of an identifier, or any subsequent character:

_ a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The following characters are legal as any character in an identifier except the first:

0 1 2 3 4 5 6 7 8 9

Arrays

One may declare an array of integration variables by specifying the array size after the integration variable name.

Example

// scalar integration variable
@IntegrationVariables strain p;
// symmetric tensors integration variable
@IntegrationVariables StrainStensor evp,evp2;

The @Integrator keyword

The keyword @Integrator is not documented yet

The @InteractionMatrix keyword

The @InteractionMatrix keyword let the user specify an interaction matrix. By convention, this matrix is associated with hardening.

The interaction matrix associated with the effects of the dislocations on the mean free path of the dislocations of a specific system can be defined though the @DislocationsMeanFreePathInteractionMatrix keyword.

Structure of the interaction matrix

Since many interactions between slip systems are equivalent, the interaction matrix only contains a few independent coefficients.

Consider the following example:

@DSL       ImplicitFiniteStrain;
@Behaviour SlipSystemGenerationTest;
@Brick     FiniteStrainSingleCrystal;
@CrystalStructure FCC;
@SlidingSystem <1,-1,0>{1,1,1};

Using mfront-query, one may have access to the whole matrix using the --interaction-matrix query:

$ mfront-query --interaction-matrix SlipSystemGenerationTest.mfront 
| 0 1 2 2 3 4 5 6 5 6 4 3 |
| 1 0 2 2 6 5 4 3 4 3 5 6 |
| 2 2 0 1 5 6 3 4 6 5 3 4 |
| 2 2 1 0 4 3 6 5 3 4 6 5 |
| 3 4 5 6 0 1 2 2 6 5 4 3 |
| 6 5 4 3 1 0 2 2 3 4 5 6 |
| 5 6 3 4 2 2 0 1 5 6 3 4 |
| 4 3 6 5 2 2 1 0 4 3 6 5 |
| 5 6 4 3 4 3 5 6 0 1 2 2 |
| 4 3 5 6 5 6 4 3 1 0 2 2 |
| 6 5 3 4 6 5 3 4 2 2 0 1 |
| 3 4 6 5 3 4 6 5 2 2 1 0 |

Here only \(7\) coefficients are needed. The number corresponding to a pair of slip systems defines the rank of the interaction.

The mfront-query also provides the --interaction-matrix-structure query which displays the number of independent coefficients and sorts the pair of slip systems by rank:

$ mfront-query --interaction-matrix-structure SlipSystemGenerationTest.mfront 
- number of independent coefficients: 7
- rank 0: ([0,1,-1](1,1,1):[0,1,-1](1,1,1)) ([1,0,-1](1,1,1):[1,0,-1](1,1,1)) ([1,-1,0](1,1,1):[1,-1,0](1,1,1)) ([0,1,1](1,1,-1):[0,1,1](1,1,-1)) ([1,0,1](1,1,-1):[1,0,1](1,1,-1)) ([1,-1,0](1,1,-1):[1,-1,0](1,1,-1)) ([0,1,-1](1,-1,-1):[0,1,-1](1,-1,-1)) ([1,0,1](1,-1,-1):[1,0,1](1,-1,-1)) ([1,1,0](1,-1,-1):[1,1,0](1,-1,-1)) ([0,1,1](1,-1,1):[0,1,1](1,-1,1)) ([1,0,-1](1,-1,1):[1,0,-1](1,-1,1)) ([1,1,0](1,-1,1):[1,1,0](1,-1,1))
- rank 1: ([0,1,-1](1,1,1):[1,0,-1](1,1,1)) ([0,1,-1](1,1,1):[1,-1,0](1,1,1)) ([1,0,-1](1,1,1):[0,1,-1](1,1,1)) ([1,0,-1](1,1,1):[1,-1,0](1,1,1)) ([1,-1,0](1,1,1):[0,1,-1](1,1,1)) ([1,-1,0](1,1,1):[1,0,-1](1,1,1)) ([0,1,1](1,1,-1):[1,0,1](1,1,-1)) ([0,1,1](1,1,-1):[1,-1,0](1,1,-1)) ([1,0,1](1,1,-1):[0,1,1](1,1,-1)) ([1,0,1](1,1,-1):[1,-1,0](1,1,-1)) ([1,-1,0](1,1,-1):[0,1,1](1,1,-1)) ([1,-1,0](1,1,-1):[1,0,1](1,1,-1)) ([0,1,-1](1,-1,-1):[1,0,1](1,-1,-1)) ([0,1,-1](1,-1,-1):[1,1,0](1,-1,-1)) ([1,0,1](1,-1,-1):[0,1,-1](1,-1,-1)) ([1,0,1](1,-1,-1):[1,1,0](1,-1,-1)) ([1,1,0](1,-1,-1):[0,1,-1](1,-1,-1)) ([1,1,0](1,-1,-1):[1,0,1](1,-1,-1)) ([0,1,1](1,-1,1):[1,0,-1](1,-1,1)) ([0,1,1](1,-1,1):[1,1,0](1,-1,1)) ([1,0,-1](1,-1,1):[0,1,1](1,-1,1)) ([1,0,-1](1,-1,1):[1,1,0](1,-1,1)) ([1,1,0](1,-1,1):[0,1,1](1,-1,1)) ([1,1,0](1,-1,1):[1,0,-1](1,-1,1))
.....

In this example, the rank \(0\) contains all the interactions of a slip system with itself.

Definition of the interaction matrix

The interaction matrix is defined through the @InteractionMatrix keyword.

This keyword is followed by an array of values, ordered by growing rank.

The @Interface keyword

The @Interface keyword let the user specify interfaces to be used. The keyword is followed by a list of interface name, separated by commas.

Using this keyword is considered a bad practice. The user shall use the --interface command line argument to specify which interface shall be used.

Example

@Interface castem;

The @InternalEnergy keyword

The @InternalEnergy keyword allows the computation of the internal energy density per unit of volume in the reference configuration.

The code provided must update a variable called Psi_s.

This update is called at the end of the behaviour integration, if convergence was reached, after that:

Example

@InternalEnergy{
  // updating the previous value
  // of the stored energy
  Psi_s += (sig|deel)/2;
}
@InternalEnergy{
    Psi_s = (sig|eel)/2;
}
@InternalEnergy{
    const strain tr = trace(eel);
    Psi_s = lambda*tr*tr/2+mu*(eel|eel);
}

The @IsTangentOperatorSymmetric keyword

The keyword @IsTangentOperatorSymmetric is not documented yet

The @IsotropicBehaviour keyword

The @IsotropicBehaviour declares the behaviour to be isotropic. As this symmetry is the default one, this keyword is seldom used.

Example

@IsotropicBehaviour;

The @IsotropicElasticBehaviour keyword

The @IsotropicElasticBehaviour is used to declare that the elastic behaviour is isotropic even though the material as been declared orthotropic. This declaration affects the @RequireStiffnessTensor behaviour.

Example

@IsotropicElasticBehaviour;

The @IterMax keyword

The @IterMax keyword is a deprecated synonymous of @MaximumNumberOfIterations.

The @JacobianComparisonCriterion keyword

The @JacobianComparisonCriterion keyword defines the criterion value used for the comparison of the user-defined jacobian to a numerically computed one. This keyword must be followed by a positive floating-point number.

The jacobianComparisonCriterion parameter

The @JacobianComparisonCriterion keyword defines the default value for the jacobianComparisonCriterion parameter. This parameter can be changed at runtime.

Example

@JacobianComparisonCriterion 1.e-6;

The @JacobianComparisonCriterium keyword

The @JacobianComparisonCriterium keyword is a deprecated synonymous of @JacobianComparisonCriterion.

The @Library keyword

The @Library keyword let the user specify part of the generated library name. This keyword is followed by the name of library.

This name must be a valid C++ identifier. The following characters are legal as the first character of an identifier, or any subsequent character:

_ a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The following characters are legal as any character in an identifier except the first:

0 1 2 3 4 5 6 7 8 9

Example

@Library AlcyoneLibrary;

The @Link keyword

The @Link keyword let the user specify additional linker flags used to build their shared library/executables. This keyword must be followed by a string or an array of strings.

Usage of the @Link keyword is deprecated a linker flags are not portable. The user may prefer using the LDFLAGS environment variable.

Example

// explicit link with libm.so
// (not necessary in pratice)
@Link "-lm";

The @LocalVar keyword

The @LocalVar keyword is a deprecated synonymous of @LocalVariable.

The @LocalVariable keyword

The keyword @LocalVariable is not documented yet

The @MFront keyword

The keyword @MFront is not documented yet

The @Material keyword

The @Material keyword let the user specify which material is treated by the current file. This keyword is followed by the name of the material.

This name must be a valid C++ identifier. The following characters are legal as the first character of an identifier, or any subsequent character:

_ a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The following characters are legal as any character in an identifier except the first:

0 1 2 3 4 5 6 7 8 9

Example

@Material UO2;

The @MaterialLaw keyword

The @MaterialLaw keyword imports the definition of a material law defined in a mfront file and compiles, as part of the current library, a function using the mfront interface. This function is available in every standard code blocks.

The @MaterialLaw keyword is followed by a string or an array of string identifying mfront files.

Search paths

Files to be imported are searched, in that order:

Note

The mfront interface has been created to avoid names conflict.

For internal reasons, mfront reports the creation of an auxiliary library which is of no use.

Example

@MaterialLaw "UO2_YoungModulus.mfront";

The @MaterialProperty keyword

The @MaterialProperty keyword let the user define one or several material properties. This keyword is followed by the type of the material property and a list of material properties names separated by commas.

The material properties names must be valid C++ identifiers.

The following characters are legal as the first character of an identifier, or any subsequent character:

_ a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The following characters are legal as any character in an identifier except the first:

0 1 2 3 4 5 6 7 8 9

Arrays

One may declare an array of material properties by specifying the array size after the material property name.

External names

It is recommended to associate to a material property a glossary or an entry name through the methods setGlossaryName or setEntryName respectively.

Example

// scalar material property
@MaterialProperty stress young;
young.setGlossaryName("YoungModulus");

The @MaximalTimeStepScalingFactor keyword

The @MaximalTimeStepScalingFactor let the user define the default value of the maximal_time_step_scaling_factor parameter.

This parameter defines the maximal value by which the time step will be increase in case of convergence. This parameter acts as a lower bound for the value returned by the @APosterioriTimeStepScalingFactor code block.

This keyword is followed by a number which must be strictly greater than one.

Note

By default (i.e. if the @MaximalTimeStepScalingFactor is not used), the default value for maximal_time_step_scaling_factor parameter will be very large so that the value returned by the @APosterioriTimeStepScalingFactor code block will not be bounded.

Example

@MaximalTimeStepScalingFactor 1.2;

The @MaximumIncrementValuePerIteration keyword

The keyword @MaximumIncrementValuePerIteration is not documented yet

The @MaximumNumberOfIterations keyword

The @MaximumNumberOfIterations keyword let the user define the maximum number of iterations allowed. It is followed by a positive integer.

The iterMax parameter

The @MaximumNumberOfIterations keyword defines the default value for the itermax parameter. This parameter can be changed at runtime.

Example

@MaximumNumberOfIterations 200;

The @Members keyword

The keyword @Members is not documented yet

The @MinimalTimeStepScalingFactor keyword

The @MinimalTimeStepScalingFactor let the user define the default value of the minimal_time_step_scaling_factor parameter.

This parameter defines the minimal value by which the time step will be reduced in case of non convergence or when the time step is rejected by one of the @APrioriTimeStepScalingFactor or @APosterioriTimeStepScalingFactor code blocks.

This keyword is followed by a number which must be strictly positive and strictly lower than one.

Note

By default (i.e. if the @MinimalTimeStepScalingFactor is not used), the default value for minimal_time_step_scaling_factor parameter will be 0.1.

Example

@MinimalTimeStepScalingFactor 0.5;

The @Model keyword

The @Model keyword is used to call an external model from a behaviour. This model is called before any code block defining the behaviour.

This model is meant to make evolve one or more state variables of the material.

From the behaviour point of view, those state variables are declared as additional auxiliary state variables, but their values and their increments over the time step are known. Those variables are meant to be used like external state variables.

Note

In the behaviour, the names of the variables described by the model are the same as in the model.

The entry/glossary names of those variables shall be defined in the model.

Example

// Evolution of the \(\beta\) phase
@Model "M5PhaseTransformation_EdgarV3_SRMA2017.mfront";

The @ModellingHypotheses keyword

The keyword @ModellingHypotheses is not documented yet

The @ModellingHypothesis keyword

The keyword @ModellingHypothesis is not documented yet

The @NumericallyComputedJacobianBlocks keyword

The @NumericallyComputedJacobianBlocks keyword is used to give a list of jacobian blocks that have to be computed numerically.

This keyword can optionally be followed by a list of modelling hypotheses. The list of jacobian blocks is given as an array.

Notes

Example

@NumericallyComputedJacobianBlocks {dfp_ddeel,dfeel_ddeel};

The @OrthotropicBehaviour keyword

The @OrthotropicBehaviour declares the behaviour to be orthotropic.

As an option, the orthotropic behaviour can be followed by an orthotropic axes convention. Three orthotropic axes convention are currently supported:

Examples

@OrthotropicBehaviour;
@OrthotropicBehaviour<Pipe>;

The @Parameter keyword

The @Parameter keyword declares a new parameter or a list of new parameters. Optionally, the default value of the declared parameters may also be given following various C++ standard assignment syntaxes.

The default value of a parameter can also be declared after its declaration using the setDefaultValue method.

Example

@Parameter  R0 = 500;
@Parameter  Q1{1000000000},b1{0.000001};
@Parameter  Q2(0),b2(0);
@Parameter  fc;
fc.setDefaultValue(1.e-2);

The @Parser keyword

The @Paser keyword is a deprecated synonymous of @DSL.

The @PerturbationValueForNumericalJacobianComputation keyword

The @PerturbationValueForNumericalJacobianComputation keyword let the user defines the perturbation value used to compute the numerical jacobian.

If \(Y\) is the vector of integration variables and \(F\) the function defining the implicit system, the \(j^{\text{th}}\) column of the numerical jacobian \(J^{n}\) is defined by the centered finite difference formulae: \[ J^{n}(i,j)=\frac{F(Y_{i}^{+\epsilon})-F(Y_{i}^{-\epsilon})}{2\,\epsilon} \] where: \[ Y_{i}^{+\epsilon}(j)= \left\{ \begin{aligned} Y(j) & \text{ si } &j \neq i \\ Y(i)+\epsilon & \text{ si } &j = i \end{aligned} \right. \]

Example

@PerturbationValueForNumericalJacobianComputation 1.e-7;

The @PhysicalBounds keyword

The @PhysicalBounds keyword let the use define the physical domain of a variable.

The @PhysicalBounds keyword is followed by a variable name, the keyword in and an interval. The interval may contain the infinity, represented by the ’*’ character.

Effect

In implicit schemes, if physical bounds are set on an integration variable, this variable is bounded to satisfy them during the internal iterations.

If a variable is found to be out of its physical bounds, the computations are stopped. The tests are performed at different stages of the integration depending on the nature of the variable.

Example

// a temperature (in Kelvin) can't be negative
@PhysicalBounds T in [0:*[;

The @PostProcessing keyword

The @PostProcessing keyword introduces a code block that can be used to perform computations independently of the behaviour integration.

The outputs of post-processing are stored in so-called post-processing variables. See the @PostProcessingVariable for details.

Post-processing is typically meant to be called at the end of a time step, when the equilibrium has been reached.

Because post-processing is called independently of the behaviour integration step, special care to the meaning of the variables must be taken:

The values of the thermodynamic forces, state variables, auxiliary state variables at the beginning of the time step are available in a special data structure named initial_state.

Concerning material properties, they have their values at the end of the time step as usual.

For the gradients and external state variables have their values at the end of the time step. Their values at the beginning of the time step are available in the initial_state data structure (if defined). Their increments have their usual values.

About initialisation of local variables

The code block defined by the @InitLocalVariables code block shall be called before the execution of the post-processing. However, this code block will be called with the thermodynamic forces, state variables, auxiliary state variables at the end of the time step.

Example of usage

The following code defines a post-processing computing the principal strain at the end of the time step:

//! principal strains
@PostProcessingVariable tvector<3u,strain> εᵖ;
εᵖ.setEntryName("PrincipalStrain");
//! compute the principal strain
@PostProcessing PrincipalStrain {
  εᵖ = eto.computeEigenValues();
}

The @PostProcessingVariable keyword

Post-processing variables are introduced by the @PostProcessingVariable keyword.

Post-processing variables are only defined in post-processing, and can’t be used in the other code blocks.

Contrary most variables (internal state variables, external state variables, etc.), post-processing variables can be defined after the first code block. However, care must be taken to declare post-processing variables before their use in a post-processing.

Note that a post-processing variable can be used in different post-processing. Typically, one may compute the principal strains in a dedicated post-processing and in a post-processing computing the principal strains and the strain eigen vectors.

Exemple of usage

//! principal strains
@PostProcessingVariable tvector<3u,strain> εᵖ;

The @PredictionOperator keyword

The keyword @PredictionOperator is not documented yet

The @Predictor keyword

The keyword @Predictor is not documented yet

The @Private keyword

The @Private keyword let the user define private methods or members of in the generated behaviour class.

Example

@Private{
  void display(void) const{
    std::cout << "eto " << this->eto << std::endl;
  }
} // end of @Private

The @ProcessNewCorrection keyword

The @ProcessNewCorrection keyword introduces a code block called when a new correction of the increments of the integration variables is available.

This method can be used to:

This increment is stored in an array called delta_zeros. The delta_zeros variable is not meant to be used directly by the users and views to the corrections of the increments of the integration variables are automatically declared in this code block.

Let v be an integration variable, then the variable delta_dv is a view to the correction of the increment of this variable. If Unicode notations are used, let υ be the symbolic name of v, then δΔv is an alias for delta_dv.

The increments of the integration variables are not updated at this stage of the resolution algorithm.

Example

The following code limits the amplitude of the correction given to the increment of the elastic strain:

@ProcessNewCorrection{
 constexpr const real δΔεᵉˡ_m = 1.e-4;
 const auto e = abs(δΔεᵉˡ);
 if(e > δΔεᵉˡ_m){
   δΔεᵉˡ *= e / δΔεᵉˡ_m;
 }
}

The @ProcessNewEstimate keyword

The @ProcessNewEstimate keyword introduces a code block called after the update of the increments of the integration variables.

This method may be used to compute local variables dependent on the updated value of the integration variables.

For example, MFront may define or update this code block to evaluate material properties dependent on the value of the state variable (for example, a Young modulus depending of the porosity), if any.

The @Profiling keyword

The @Profiling keyword is followed by a boolean. If true, several high resolutions clocks will be introduced in the generated code to profile performance bottlenecks. The total time spend in various portions of the generated code will be stored and displayed when the calling process exits.

Example

@Profiling true;

The @RejectCurrentCorrection keyword

The @RejectCurrentCorrection keyword introduces a code block called when the current correction is rejected.

This method can be used to reject the decondensation step when some integration variables were eliminated by static condensation.

This increment is stored in an array called delta_zeros. The delta_zeros variable is not meant to be used directly by the users and views to the corrections of the increments of the integration variables are automatically declared in this code block.

The @Relocation keyword

The @Relocation keyword can be used to impose a boundary condition specific the fuel performances describing the rigid body translation of fuel pellet fragment as an additional strain.

Modelling hypotheses affected

This keyword is only effective in:

No expansion are added in the tridimensional and axisymmetrical modelling hypotheses.

Physical description

The value of the relocation expansion \(r\) is converted in an additional expansion in the radial and orthoradial directions:

\[ \left\{ \begin{aligned} \frac{\Delta\,l_{r}}{l_{r}} &= \frac{r}{2} \\ \frac{\Delta\,l_{\theta}}{l_{\theta}} &= \frac{r}{2} \end{aligned} \right. \].

This additional expansion is such that it does not create any stress in the fuel pellet for an isotropic elastic material with constant material properties.

The axial axis is the second direction in \(1D\) hypotheses and the third direction in \(2D\) hypotheses.

Examples

// relocation defined by an external model
@Relocation 'UO2Relocation.mfront';
// relocation defined by an external state variable
@ExternalStateVariable real r;
r.setEntryName("Relocation");
@Relocation r;

The @RequireStiffnessOperator keyword

The @RequireStiffnessOperator keyword is a deprecated synonymous of @RequireStiffnessTensor.

The @RequireStiffnessTensor keyword

The @RequireStiffnessTensor keyword requires the stiffness tensor to be computed by the calling code. This generally means that some extra material properties will be introduced and handled by the interface before the behaviour integration.

By default, the stiffness tensor will have the same symmetry as the behaviour (see @IsotropicElasticBehaviour to change this in the case of an orthotropic behaviour).

@RequireStiffnessTensor true;

The @RequireThermalExpansionCoefficientTensor keyword

The @RequireThermalExpansionCoefficientTensor keyword requires the thermal expansion coefficient tensor to be computed by the calling code. This generally means that some extra material properties will be introduced and handled by the interface before the behaviour integration.

The thermal expansion tensor will have the same symmetry as the behaviour. For example, for an isotropic behaviour, the thermal expansion tensor will be proportional to the identity. For an orthotropic behaviour, the thermal expansion tensor is diagonal and expressed in the material frame.

@RequireThermalExpansionCoefficientTensor true;

The @SlidingSystem keyword

A synonym of @SlipSystem. See @SlipSystem for details.

The @SlidingSystems keyword

A synonym of @SlipSystems. See @SlipSystems for details.

The @SlipSystem keyword

A single slip systems family can be defined by one of the following keywords: @SlidingSystem, @GlidingSystem or @SlipSystem. Those keywords are followed by the definition of one family of slip systems.

A slip system is defined by its plane and its Burgers’vector as follows, for a Cubic and FCC crystal structures:

<1,-1,0>{1,1,1}

For hexagonal structures, the slip systems are defined through a four indices notation.

Example

Thus, an example of the usage of the @SlidingSystem keyword is:

@SlidingSystem <1,-1,0>{1,1,1};

For a given slip systems family, a set of slip systems are generated by symmetry using code extracted from the NUMODIS code. The previous example defines \(12\) slip systems.

Once the sliding system families has been defined, a static integer variable called Nss is available which contains the total number of slip systems defined. In the previous example, Nss value is \(12\).

This value can be used to define additional state variables:

//! equivalent plastic strain on each slip system
@AuxiliaryStateVariable real p[Nss];

For post-processing reasons, one needs to know in which order the slip systems are defined. This question is treated in the next paragraph.

Also, note that for the \(i^{\text{th}}\) slip systems family, a static integer variable beginning by Nss and followed by the value of \(i\) is defined. In the previous example, a unique slip systems family is defined and a variable Nss0 is made available. Of course, in this case Nss0 is equal to Nss. Those variables may be useful to define variables specific to a slip system family.

Getting information about the generated slip systems

The list of the generated slip systems can be retrieved using mfront-query.

Consider the following example:

@DSL       ImplicitFiniteStrain;
@Behaviour SlipSystemGenerationTest;
@Brick     FiniteStrainSingleCrystal;
@CrystalStructure FCC;
@SlidingSystem <1,-1,0>{1,1,1};

If the previous code is saved a file called SlipSystemGenerationTest.mfront, one may use mfront-query as follows:

$ mfront-query --slip-systems SlipSystemGenerationTest.mfront
- <1,-1,0>{1,1,1}: [0,1,-1](1,1,1) [1,0,-1](1,1,1) [1,-1,0](1,1,1) [0,1,1](1,1,-1) [1,0,1](1,1,-1) [1,-1,0](1,1,-1) [0,1,-1](1,-1,-1) [1,0,1](1,-1,-1) [1,1,0](1,-1,-1) [0,1,1](1,-1,1) [1,0,-1](1,-1,1) [1,1,0](1,-1,1)

The output shows that \(12\) slip systems were generated. All those systems are equivalent by symmetry.

Concerning slip systems, the following queries are available:

$ mfront-query --help-behaviour-queries-list |grep slip
--slip-systems          : list all the slip systems, sorted by family
--slip-systems-by-index : list all the slip systems

The --slip-systems-by-index query gives the index associated to a given slip system, which is helpful for postprocessing purposes. For this example:

$ mfront-query --slip-systems-by-index SlipSystemGenerationTest.mfront
- 0: [0,1,-1](1,1,1)
- 1: [1,0,-1](1,1,1)
- 2: [1,-1,0](1,1,1)
- 3: [0,1,1](1,1,-1)
- 4: [1,0,1](1,1,-1)
- 5: [1,-1,0](1,1,-1)
- 6: [0,1,-1](1,-1,-1)
- 7: [1,0,1](1,-1,-1)
- 8: [1,1,0](1,-1,-1)
- 9: [0,1,1](1,-1,1)
- 10: [1,0,-1](1,-1,1)
- 11: [1,1,0](1,-1,1)

Getting information about the orientation tensors

Concerning the orientation tensors, the following queries are available:

Getting information about the Schmid factors

Concerning the Schmid factors, the following queries are available:

$ mfront-query --schmid-factors-by-index='<1,1,1>' SlipSystemGenerationTest.mfront

Note In this example, the direction must be surrounded by simple quote to avoid interpretation by the shell.

The @SlipSystems keyword

The @SlipSystems can be used to define several families of slip systems. This keyword is followed by an array defining the various slip systems. The user can refer to the description of the @SlipSystem keyword for a detailed description.

The @Sources keyword

The @Sources keyword let the user define a code block that will be integrated in the generated sources of a behaviour. This allows the user to implement their own classes or functions. These declarations of such classes or functions can be made in a code block introduced by the @Includes keyword.

@Includes{
  //! declaration of the function f
  void f(void);
}

@Sources{
  // source of the function
  void f(void){
    std::cout << "Example of a function " << std::endl;
  } // end of f
}

The @SpeedOfSound keyword

The @SpeedOfSound keyword introduces the computation of an upper bound of the speed of sound in a material. This quantity is mostly meant to be used by explicit mechanical solvers to evaluate an upper bound of the critical time step.

The code block must compute a variable called v_sound (or vₛ if UTF-8 encoding is used).

The mass density in the initial configuration is available in a variable called rho_m0 (or ρₘ₀ if UTF-8 encoding is used).

Example

@SpeedOfSound{
 v_sound = sqrt(young / rho_m0);
} 
@SpeedOfSound{
 vₛ = sqrt(young / ρₘ₀);
}

The @StateVar keyword

The @StateVar keyword is a deprecated synonymous of @StateVariable.

The @StateVariable keyword

The StateVariable keyword introduces one or several new state variables. It is followed by a type name and the name(s) of the variable(s) declared, separated by commas.

The state variables names must be valid C++ identifiers.

The following characters are legal as the first character of an identifier, or any subsequent character:

_ a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The following characters are legal as any character in an identifier except the first:

0 1 2 3 4 5 6 7 8 9

Arrays

One may declare an array of state variables by specifying the array size after the state variable name.

External names

It is recommended to associate to a state variable a glossary or an entry name through the methods setGlossaryName or setEntryName respectively.

Example

// scalar state variable
@StateVariables strain p;
// symmetric tensors state variable
@StateVariables StrainStensor evp,evp2;

The @StaticVar keyword

The @StaticVar keyword is a deprecated synonymous of @StaticVariable.

The @StaticVariable keyword

The @StaticVariable keyword let the user define a constant value. Unlike parameters (see the @Parameter keyword), static variables’ values can’t be changed after compilation.

This keyword must be followed by the type of the constant, its name, an equal sign and its value.

Example

@StaticVariable real A = 1.234e56;

The @StrainMeasure keyword

This keyword let the user choose to the strain measure. This choice also defines the meaning of the stress tensor by energetic duality.

The following values are supported:

Two options can be specified:

If requested, the auxiliary state variables saved_strain_measure and saved_dual_stress are updated at the beginning of the @UpdateAuxiliaryStateVariables code block. For orthotropic behaviours, it is worth mentioning that those variables are expressed in the material frame.

Note

  1. The computation of the strain measure and its dual and the convertion of the tangent operator is delegated to the interface, because several finite element solver already provides those operations natively (Code_Aster, ZebuloN, etc…)

Example

@StrainMeasure Hencky;
@StrainMeasure{
  save_strain: true,
  save_stress: true
};

The @Swelling keyword

The @Swelling keyword allow the user to specify that an additional stress-free expansion must be taken into account.

This keyword has the following options:

The @Swelling keyword is then followed by one or three definition of stress-free expansion.

If one stress-free expansion is defined, the swelling is computed as an isotropic second order tensor.

If three stress-free expansions are defined, the swelling is computed as a diagonal second order tensor: \[ s = \left( \begin{array}{ccc} \left.\frac{\Delta\,l}{l_{0}}\right|_{0} & 0 & 0 \\ 0 & \left.\frac{\Delta\,l}{l_{0}}\right|_{1} & 0 \\ 0 & 0 & \left.\frac{\Delta\,l}{l_{0}}\right|_{2} \\ \end{array} \right) \]

A stress-free expansion is either defined by:

Notes

A null swelling is not allowed when only one stress-free expansion

The definition of three stress-free expansion is only valid for orthotropic behaviours and is not compatible with the Volume option.

Examples

@ExternalStateVariable strain s;
s.setGlossaryName("SolidSwelling");
@Swelling<Volume> s;

The @TangentOperator keyword

The TangentOperator keyword introduces a code block used to define the tangent operator. This code is called once the integration variables, the stresses and the auxiliary state variables (see the @UpdateAuxiliaryStateVariables keyword) have been updated.

The kind of tangent operator requested is given by variable named smt (stiffness matrix type). As the time of writing this notice, the possible values for smt are the following:

Example

@TangentOperator{
  using namespace tfel::material::lame;
  if((smt==ELASTIC)||(smt==SECANTOPERATOR)){
    computeAlteredElasticStiffness<hypothesis,Type>::exe(Dt,lambda,mu);
  } else if (smt==CONSISTENTTANGENTOPERATOR){
    StiffnessTensor De;
    Stensor4 Je;
    computeElasticStiffness<N,Type>::exe(De,lambda,mu);
    getPartialJacobianInvert(Je);
    Dt = De*Je;
  } else {
    return false;
  }
}

The @Theta keyword

The Theta keyword is used to define the default value of \(\theta\) parameter used by implicit schemes. If the Theta keyword is not used, implicit domain specific languages provide their own specific default value (either \(0.5\) or \(1\)).

The value given to \(\theta\) must be in the range (]0:1]).

The value of \(\theta\) can be changed at runtime by modifying the theta parameter (see the @Parameter keyword).

Example

@Theta 0.5;

The @UnitSystem keyword

The @UnitSystem keyword declares that the state variables, external state variables and parameters are expressed in a given unit system. In the current version of MFront, the only supported unit system is the international system of units, denoted SI.

One advantage of declaring a unit system is that physical bounds of variables associated with a glossary entry can automatically be declared by MFront.

For instance the declaration of the physical bounds for the temperature and the porosity is automatic if the SI unit system is used.

Example of usage

@UnitSystem SI;

The @UpdateAuxiliaryStateVariables keyword

The UpdateAuxiliaryStateVariables introduces a code block meant to update the auxiliary state variables after integration.

In implicit domain specific languages, the code declared by UpdateAuxiliaryStateVariables is called once the integration variables (including state variables) and stresses (see the @ComputeFinalStress keyword) have been updated. The external state variables are not updated.

In Runge-Kutta domain specific languages, the code declared by UpdateAuxiliaryStateVariables is called after each successful time step. Keep in mind that most Runge-Kutta algorithms performs internal substepping: in this case, the code declared by UpdateAuxiliaryStateVariables may be called several time during the behaviour integration. An additional variable called dt_, which is lower than the total time step increment dt if substepping is performed, gives the current time increment. The external state variables are set to their values at the current date.

Example (Implicit dsl)

@UpdateAuxiliaryStateVariables{
  // valeur de milieu de pas, q ayant
  // déjà été mis à jour
  const real q_ = q-(1-theta)*dq;
  const real Q = Q0 + (Qm - Q0) * (1 - exp(-2 * Mu * q_) );
  R+=b*(Q-R)*dp;
}

Example (Runge-Kutta dsl)

@UpdateAuxiliaryStateVariables{
  sigeq = sqrt(sig|sig);
}

The @UpdateAuxiliaryStateVars keyword

The @UpdateAuxiliaryStateVars keyword is a deprecated synonymous of @UpdateAuxiliaryStateVariables.

The @UsableInPurelyImplicitResolution keyword

The @UsableInPurelyImplicitResolution is a specifier which states that the behaviour is usable in a purely implicit resolution, i.e. if we can call the behaviour by only providing the values of external state variables at the end of the time step and by setting their increments to zero.

This behaviour characteristic may or may not have any influence depending on the calling code. As the time of writing this notice, only the Licos fuel performance code take advantage of this characteristic. If true, the Licos code will simplify the definition of the external state variables (called material loadings in this context) which may result in some gain in time and memory space.

Example

@UsableInPurelyImplicitResolution true;

The @UseQt keyword

The UseQt keyword (use quantities) specify if the behaviour compilation should perform compile-time units checks. It is followed by a boolean.

Note

This feature is still experimental and is disabled in most cases.

Example

@UseQt true;