- alpha-1Initial slope of the exponential softening curve at crack initiation. If not specified, it is equal to the negative of the Young's modulus.
Default:-1

C++ Type:double

Description:Initial slope of the exponential softening curve at crack initiation. If not specified, it is equal to the negative of the Young's modulus.

- beta1Multiplier applied to alpha to control the exponential softening behavior.
Default:1

C++ Type:double

Description:Multiplier applied to alpha to control the exponential softening behavior.

- residual_stress0The fraction of the cracking stress allowed to be maintained following a crack.
Default:0

C++ Type:double

Description:The fraction of the cracking stress allowed to be maintained following a crack.

- 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

# Exponential Softening

Softening model with an exponential softening response upon cracking. This class is intended to be used with ComputeSmearedCrackingStress.

## Description

The material `ExponentialSoftening`

computes the reduced stress and stiffness in the direction of a crack according to a exponential function. The computed cracked stiffness ratio softens the tensile response of the material once the principle stress 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 an exponential function of the crack strain (1) where the calculated stress, is the principle stress along the direction of the crack, is the stress threshold beyond which cracking occurs, is the residual stress retained after full softening due to the crack is completed, is the initial slope of the exponential curve, is a fitting parameter, is the maximum strain in the direction of crack, and is the strain in direction of crack when crack initiation occurred. The ratio of the current stiffness to the original material stiffness is computed using the result of Eq. 1 (2) where the definitions for the variables are the same here as in Eq. 1. The stiffness ratio is passed back to the ComputeSmearedCrackingStress to compute the softened cracked material stiffness.

## Example Input File

```
[./exponential_softening]
type = ExponentialSoftening
[../]
```

(moose/modules/tensor_mechanics/test/tests/smeared_cracking/cracking_rotation.i)`ExponentialSoftening`

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

```
[./cracking_stress]
type = ComputeSmearedCrackingStress
shear_retention_factor = 0.1
cracking_stress = 3.e9
softening_models = exponential_softening
[../]
```

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