# Compute Smeared Cracking Stress

Compute stress using a fixed smeared cracking model

## Description

This class implements a fixed smeared cracking model, which represents cracking as a softening stress-strain law at the material points as opposed to introducing topographic changes to the mesh, as would be the case with a discrete cracking model.

In this model, principal stresses are compared to a critical stress. If one of the principal stresses exceeds the critical stress, the material point is considered cracked in that direction, and the model transitions to an orthotropic model, in which the stress in the cracked direction is decreased according to a softening law. Material behavior in the cracking direction is affected in two ways: reduction of the stiffness in that direction, and adjusting the stress to follow the softening curve.

### Interaction with Inelastic Models

This class derives from ComputeMultipleInelasticStrain, and prior to cracking, allows multiple inelastic models to be active. Once cracking occurs, the inelastic strains at that material point are preserved, but those models are no longer called for the duration of the simulation, and inelastic strains from those other models are no longer permitted to evolve.

### Cracking Direction Determination

The orientation of the principal coordinate system is determined from the eigenvectors of the elastic strain tensor. However, once a crack direction is determined, that direction remains fixed and further cracks are considered in directions perpendicular to the original crack direction. Note that for axisymmetric problems, one crack direction is known a priori. The theta or out-of-plane direction is not coupled to the and directions (i.e., no or shear strain/stress exists) and is therefore a known or principal direction.

If we store a scalar value, , for each of the three possible crack directions at a material point, these in combination with the principal directions (eigenvectors or rotation tensor) provide a convenient way to eliminate stress in cracked directions. A value of 1 for indicates that the material point has not cracked in that direction. A value very close to zero (not zero for numerical reasons) indicates that cracking has occurred.

We define a cracking tensor in the cracked orientation as : (1) The rotation tensor is defined in terms of the eigenvectors : (2) This leads to a transformation operator : (3)

is useful for transforming uncracked tensors in the global frame to cracked tensors in the same frame. For example, the cracked stress in terms of the stress is (subscript indicates cracked, local frame, and global frame): (4)

When many material points have multiple cracks, the solution becomes difficult to obtain numerically. For this reason, controls are available to limit the number and direction of cracks that are allowed. Also, there are options to control the amount of shear retention and amount of stress correction during softening, both of which can significantly affect convergence.

## Example Input File Syntax

[./elastic_stress]
type = ComputeSmearedCrackingStress
cracking_stress = 1.68e6
softening_models = abrupt_softening
[../]

(modules/tensor_mechanics/test/tests/smeared_cracking/cracking.i)

## Input Parameters

• cracking_stressThe stress threshold beyond which cracking occurs. Negative values prevent cracking.

C++ Type:std::vector

Options:

Description:The stress threshold beyond which cracking occurs. Negative values prevent cracking.

• inelastic_modelsThe material objects to use to calculate stress and inelastic strains. Note: specify creep models first and plasticity models second.

C++ Type:std::vector

Options:

Description:The material objects to use to calculate stress and inelastic strains. Note: specify creep models first and plasticity models second.

### Required Parameters

• relative_tolerance1e-05Relative convergence tolerance for the stress update iterations over the stress change after all update materials are called

Default:1e-05

C++ Type:double

Options:

Description:Relative convergence tolerance for the stress update iterations over the stress change after all update materials are called

• computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

Default:True

C++ Type:bool

Options:

Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the Material via MaterialPropertyInterface::getMaterial(). Non-computed Materials are not sorted for dependencies.

• base_nameOptional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

C++ Type:std::string

Options:

Description:Optional parameter that allows the user to define multiple mechanics material systems on the same block, i.e. for multiple phases

• tangent_operatornonlinearType of tangent operator to return. 'elastic': return the elasticity tensor. 'nonlinear': return the full, general consistent tangent operator.

Default:nonlinear

C++ Type:MooseEnum

Options:elastic nonlinear

Description:Type of tangent operator to return. 'elastic': return the elasticity tensor. 'nonlinear': return the full, general consistent tangent operator.

• max_stress_correction1Maximum permitted correction to the predicted stress as a ratio of the stress change to the predicted stress from the previous step's damage level. Values less than 1 will improve robustness, but not be as accurate.

Default:1

C++ Type:double

Options:

Description:Maximum permitted correction to the predicted stress as a ratio of the stress change to the predicted stress from the previous step's damage level. Values less than 1 will improve robustness, but not be as accurate.

• perform_finite_strain_rotationsTrueTensors are correctly rotated in finite-strain simulations. For optimal performance you can set this to 'false' if you are only ever using small strains

Default:True

C++ Type:bool

Options:

Description:Tensors are correctly rotated in finite-strain simulations. For optimal performance you can set this to 'false' if you are only ever using small strains

• cracking_neg_fraction0The fraction of the cracking strain at which a transitition begins during decreasing strain to the original stiffness.

Default:0

C++ Type:double

Options:

Description:The fraction of the cracking strain at which a transitition begins during decreasing strain to the original stiffness.

• prescribed_crack_directionsPrescribed directions of first cracks

C++ Type:MultiMooseEnum

Options:x y z

Description:Prescribed directions of first cracks

• cycle_modelsFalseAt timestep N use only inelastic model N % num_models.

Default:False

C++ Type:bool

Options:

Description:At timestep N use only inelastic model N % num_models.

• softening_modelsThe material objects used to compute softening behavior for loading a crack.Either 1 or 3 models must be specified. If a single model is specified, it isused for all directions. If 3 models are specified, they will be used for the3 crack directions in sequence

C++ Type:std::vector

Options:

Description:The material objects used to compute softening behavior for loading a crack.Either 1 or 3 models must be specified. If a single model is specified, it isused for all directions. If 3 models are specified, they will be used for the3 crack directions in sequence

• combined_inelastic_strain_weightsThe combined_inelastic_strain Material Property is a weighted sum of the model inelastic strains. This parameter is a vector of weights, of the same length as inelastic_models. Default = '1 1 ... 1'. This parameter is set to 1 if the number of models = 1

C++ Type:std::vector

Options:

Description:The combined_inelastic_strain Material Property is a weighted sum of the model inelastic strains. This parameter is a vector of weights, of the same length as inelastic_models. Default = '1 1 ... 1'. This parameter is set to 1 if the number of models = 1

• max_cracks3The maximum number of cracks allowed at a material point.

Default:3

C++ Type:unsigned int

Options:

Description:The maximum number of cracks allowed at a material point.

• internal_solve_full_iteration_historyFalseSet to true to output stress update iteration information over the stress change

Default:False

C++ Type:bool

Options:

Description:Set to true to output stress update iteration information over the stress change

• absolute_tolerance1e-05Absolute convergence tolerance for the stress update iterations over the stress change after all update materials are called

Default:1e-05

C++ Type:double

Options:

Description:Absolute convergence tolerance for the stress update iterations over the stress change after all update materials are called

• shear_retention_factor0Fraction of original shear stiffness to be retained after cracking

Default:0

C++ Type:double

Options:

Description:Fraction of original shear stiffness to be retained after cracking

• boundaryThe list of boundary IDs from the mesh where this boundary condition applies

C++ Type:std::vector

Options:

Description:The list of boundary IDs from the mesh where this boundary condition applies

• blockThe list of block ids (SubdomainID) that this object will be applied

C++ Type:std::vector

Options:

Description:The list of block ids (SubdomainID) that this object will be applied

• max_iterations30Maximum number of the stress update iterations over the stress change after all update materials are called

Default:30

C++ Type:unsigned int

Options:

Description:Maximum number of the stress update iterations over the stress change after all update materials are called

### Optional Parameters

• control_tagsAdds user-defined labels for accessing object parameters via control logic.

C++ Type:std::vector

Options:

Description:Adds user-defined labels for accessing object parameters via control logic.

• enableTrueSet the enabled status of the MooseObject.

Default:True

C++ Type:bool

Options:

Description:Set the enabled status of the MooseObject.

• seed0The seed for the master random number generator

Default:0

C++ Type:unsigned int

Options:

Description:The seed for the master random number generator

• implicitTrueDetermines whether this object is calculated using an implicit or explicit form

Default:True

C++ Type:bool

Options:

Description:Determines whether this object is calculated using an implicit or explicit form

• constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

Default:NONE

C++ Type:MooseEnum

Options:NONE ELEMENT SUBDOMAIN

Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeSubdomainProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped

• output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)

C++ Type:std::vector

Options:

Description:List of material properties, from this material, to output (outputs must also be defined to an output type)

• outputsnone Vector of output names were you would like to restrict the output of variables(s) associated with this object

Default:none

C++ Type:std::vector

Options:

Description:Vector of output names were you would like to restrict the output of variables(s) associated with this object