Brittle Cracking

The Brittle Cracking model:

provides a capability for modeling concrete in all types of structures: beams, trusses, shells, and solids;
works with applications in which tensile cracking dominates the behavior;
assumes that the compressive behavior is always linear elastic;
uses the linear elastic material model, which also defines the material behavior completely before cracking;
is most accurate in applications where the brittle behavior dominates such that the assumption that the material is linear elastic in compression is adequate;
primarily used to analyze reinforced concrete structures but also models plain concrete; and
allows removal of elements based on a brittle failure criterion.

Brittle Cracking

You can specify the postfailure behavior for direct straining across cracks by means of a postfailure stress-strain relation or by applying a fracture energy cracking criterion.

Strain: Specify the postcracking behavior by entering the postfailure stress/cracking-strain relationship.
Displacement: Specify the postcracking behavior by entering the postfailure stress/cracking-displacement relationship.
GFI: Specify the postcracking behavior by entering the failure stress and the fracture energy.

Table 1. Type=Strain
Input Data	Description
Direct Stress After Cracking	Remaining direct stress after cracking, $σ_{t}^{I}$ .
Direct Cracking Strain	Direct cracking strain, $e_{n n}^{c k}$ .
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables	Specifies material parameters that depend on one or more independent field variables. A Field column appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.

Table 2. Type=Displacement
Input Data	Description
Direct Stress After Cracking	Remaining direct stress after cracking, $σ_{t}^{I}$ .
Direct Cracking Displacement	Direct cracking displacement, $u_{n}^{c k}$ .
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables	Specifies material parameters that depend on one or more independent field variables. A Field column appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.

Table 3. Type=GFI
Input Data	Description
Failure Stress	Failure stress, $σ_{t u}^{I}$ .
Mode I Fracture Energy	Mode I fracture energy, $G_{f}^{I}$ .
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables	Specifies material parameters that depend on one or more independent field variables. A Field column appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.

Brittle Shear

An important feature of the brittle cracking model is that, whereas crack initiation is based on Mode I fracture only, postcracked behavior includes Mode II as well as Mode I. The Mode II shear behavior is based on the common observation that the shear behavior depends on the amount of crack opening. More specifically, the cracked shear modulus reduces as the crack opens. Define the shear retention model as a function of the opening strain across the crack. Define the shear retention model in the cracking model, but do not use zero shear retention. You can define shear retention using one of the following two options:

In these models, the dependence is defined by expressing the postcracking shear modulus, $G_{c}$ , as a fraction of the uncracked shear modulus:

G_{c} = ρ (e_{n n}^{c k}) G

where

G

is the shear modulus of the uncracked material and the shear retention factor,

ρ (e_{n n}^{c k})

, depends on the crack opening strain,

e_{n n}^{c k}

. You can define the dependence using a piecewise linear form, or you can use the following power law:

ρ (e_{n n}^{c k}) = {(1 - \frac{e_{n n}^{c k}}{e_{\max}^{c k}})}^{p}

where

p

and

e_{\max}^{c k}

are material parameters.

Retention Factor: Specify the postcracking shear behavior by entering a linear piecewise relationship between the shear retention factor, $ρ$ , and crack opening, $e_{n n}^{c k}$ .
Power Law: Specify the postcracking shear behavior by entering the material parameters $p$ and $e_{\max}^{c k}$ for the power law shear retention model.

Table 4. Type=Retention Factor
Input Data	Description
Shear Retention Factor	Shear retention factor, $ρ$ .
Crack Opening Strain	Direct cracking strain, $e_{n n}^{c k}$ .
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables	Specifies material parameters that depend on one or more independent field variables. A Field column appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.

Table 5. Type=Power Law
Input Data	Description
e	Material parameters $p$ .
p	Material parameters $e_{\max}^{c k}$ .
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables	Specifies material parameters that depend on one or more independent field variables. A Field column appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.

Brittle Failure

You can define brittle failure of the material. When one, two, or all three local direct cracking strain (displacement) components at a material point reach the value defined as the failure strain (displacement), the material point fails and all the stress components are set to zero. An element is removed from a mesh on material failure.


Input Data	Description
Failure Criteria	Set to Unidirectional to indicate that an element is removed when any local direct cracking strain component reaches the failure value. Set to Bidirectional to indicate that an element is removed when any two direct cracking strain components reach the failure value. Set to Tridirectional to indicate that an element is removed when all three possible direct cracking strain components reach the failure value. Note: Only Unidirectional can be used for beam or truss elements. Only Unidirectional and Bidirectional can be used for plane stress and shell elements, and any option can be used for three-dimensional, plane strain, and axisymmetric elements.

If you define the postfailure relation in terms of stress versus strain, you must give the failure strain as the failure criterion. If you define the postfailure relation in terms of stress versus displacement or stress versus fracture energy, you must give the failure displacement as the failure criterion. You can specify the failure strain (displacement) as a function of temperature and predefined field variables.

You can control how many cracks at a material point must fail before the material point fails. The number of cracks that must fail can only be one for beam and truss elements. The number cannot be greater than two for plane stress and shell elements, and it cannot be greater than three otherwise.

Table 6. TYPE=STRAIN
Input Data	Description
Direct Cracking Failure Strain	Direct cracking failure strain, ${(e_{n n}^{c k})}_{f}$ .
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables	Specifies material parameters that depend on one or more independent field variables. A Field column appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.

Table 7. TYPE=DISPLACEMENT or TYPE=GFI
Input Data	Description
Direct Cracking Displacement	Direct cracking failure displacement, ${(u_{n}^{c k})}_{f}$ .
Use temperature-dependent data	Specifies material parameters that depend on temperature. A Temperature field appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.
Number of field variables	Specifies material parameters that depend on one or more independent field variables. A Field column appears in the data table. For more information, see Specifying Material Data as a Function of Temperature and Independent Field Variables.