- stiffness_reductionFactor multiplied by the current stiffness each time a new crack forms
C++ Type:double

Description:Factor multiplied by the current stiffness each time a new crack forms

# Power Law Softening

Softening model with an abrupt stress release upon cracking. This class is intended to be used with ComputeSmearedCrackingStress.

## Description

The material `PowerLawSoftening`

computes the reduced stress and stiffness along the direction of a crack according to a power law equation. The computed reduced stiffness softens the tensile response of the material once the principle stress applied to a material exceeds the cracking stress threshold of the material.

As with the other smeared cracking softening models, which all follow the nomenclature convention of using the `Softening`

suffix, this model is intended to be used with the ComputeSmearedCrackingStress material.

### Softening Model

The tensile stress response to cracking is calculated as a function of the number cracks, where the number of cracks reduces the stress reponse of the cracked material. The calculated stress is the principle stress in the single direction of the crack. (1) where is the reduction factor applied to the initial stiffness each time a new crack initiates, is the Youngs' modulus, and is the strain along the direction of the crack. The reduction factor in Eq. 1 is a function of the number of cracks (2) where is the initial cracking reduction factor and is the number of cracks. The form of Eq. 2 gives the `PowerLawSoftening`

model its name.

In the context of the smeared cracking modeling approach, individual cracks are not tracked; therefore, Eq. 2 is approximated by a single constant input parameter. The user should consult additional resources to determine a reasonable value for the initial stiffness reduction factor.

## Example Input File

```
[./power_law_softening]
type = PowerLawSoftening
stiffness_reduction = 0.3333
[../]
```

(moose/modules/tensor_mechanics/test/tests/smeared_cracking/cracking_power.i)`PowerLawSoftening`

must be run in conjunction with the fixed smeared cracking material model as shown below:

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

(moose/modules/tensor_mechanics/test/tests/smeared_cracking/cracking_power.i)## Input Parameters

- boundaryThe list of boundary IDs from the mesh where this boundary condition applies
C++ Type:std::vector

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

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

### Optional Parameters

- enableTrueSet the enabled status of the MooseObject.
Default:True

C++ Type:bool

Description:Set the enabled status of the MooseObject.

- use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False

C++ Type:bool

Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

- control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector

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

- seed0The seed for the master random number generator
Default:0

C++ Type:unsigned int

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

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

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

### Advanced Parameters

- output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector

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

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