Concrete Damaged Plasticity

The concrete damaged plasticity material behavior enables you to model concrete and other quasi-brittle materials in beams, trusses, shells, and solids. You can define this material behavior by specifying a yield behavior and two separate hardening mechanisms (tension stiffening and compression hardening). The model also supports two optional damage behaviors and a failure mechanism. Concrete failure is active during explicit simulations only.

This page discusses:

Concrete Tension Stiffening
Concrete Compression Hardening
Concrete Tension Damage
Concrete Compression Damage
Concrete Failure

The concrete damaged plasticity material model is a continuum, plasticity-based, damage model for concrete. It assumes that the main two failure mechanisms are tensile cracking and compressive crushing of the concrete material. Two hardening variables control the evolution of the yield (or failure) surface: tensile equivalent plastic strain ( ${\tilde{ε}}_{t}^{p l}$ ) and compressive equivalent plastic strain ( ${\tilde{ε}}_{c}^{p l}$ ). These variables are linked to failure mechanisms under tension and compression loading, respectively.

The concrete damaged plasticity material option:

can be used for plain concrete, even though it is intended primarily for the analysis of reinforced concrete structures;
can be used with rebar to model concrete reinforcement;
is designed for applications in which concrete is subjected to monotonic, cyclic, and/or dynamic loading under low confining pressures;
consists of the combination of nonassociated multi-hardening plasticity and scalar (isotropic) damaged elasticity to describe the irreversible damage that occurs during the fracturing process;
allows user control of stiffness recovery effects during cyclic load reversals;
allows removal of elements based on material failure criteria;
can be defined to be sensitive to the rate of straining;
can be used in conjunction with a viscoplastic regularization of the constitutive equations in Abaqus/Standard to improve the convergence rate in the softening regime, and;
requires that the elastic behavior of the material be isotropic and linear.

The following parameters define flow potential, yield surface, and viscosity parameters for the concrete damaged plasticity material model.


Input Data	Description
Dilation Angle	Dilation angle measure, $ψ$ , in the p-q plane at high confining pressure.
Flow Potential Eccentricity	Eccentricity, $ϵ$ , which is a small positive number that defines the rate at which the hyperbolic flow potential approaches its asymptote.
Ratio of Yield Stresses	Ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress, $\frac{σ_{b 0}}{σ_{c 0}}$ .
Ratio of Stress Invariants	$K_{c}$ , ratio of the second stress invariant on the tensile meridian to that on the compressive meridian at initial yield for any given value of the pressure invariant, $p$ , such that the maximum principal stress is negative. It must satisfy the condition $0.5 < K_{c} \leq 1.0$ .
Viscosity	Visco-plastic regularization parameter, $μ$ , of the concrete constitutive equations used in implicit integration schemes. Ignored for explicit integration.
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.

Concrete Tension Stiffening

You can specify cracking and postcracking properties for the concrete damaged plasticity material model.

It also allows for the effects of the reinforcement interaction with concrete to be simulated in a simple manner. Tension stiffening is required in the concrete damaged plasticity model.

You can specify tension stiffening by means of a postfailure stress-strain relation, stress-displacement relation, or by applying a fracture energy cracking criterion.


Input Data	Description
Type	Type of tension stiffening. Strain specifies the postcracking behavior by entering the postfailure stress/cracking-strain relationship. Displacement specifies the postcracking behavior by entering the postfailure stress/cracking-displacement relationship. GFI specifies the postcracking behavior by entering the failure stress and the fracture energy.

Strain-based Postcracking Behavior Parameters


Input Data	Description
Cracking Stress	Remaining direct stress after cracking, $σ_{t}$ .
Cracking Strain	Direct cracking strain, ${\tilde{ε}}_{t}^{c k}$ .
Strain Rate	Direct cracking strain rate, ${\dot{\tilde{ε}}}_{t}^{c k}$ .
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.

Displacement-based Postcracking Behavior Parameters


Input Data	Description
Cracking Stress	Remaining direct stress after cracking, $σ_{t}$ .
Cracking Displacement	Direct cracking displacement, ${\tilde{u}}_{t}^{c k}$ .
Velocity	Direct cracking velocity, ${\dot{\tilde{u}}}_{t}^{c k}$ .
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.

GFI Postcracking Behavior Parameters


Input Data	Description
Failure Stress	Failure stress, $σ_{t 0}$ .
Fracture Energy	Fracture energy, $G_{f}$ .
Velocity	Direct cracking velocity, ${\dot{\tilde{u}}}_{t}^{c k}$ .
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.

Concrete Compression Hardening

You can specify compression hardening data for the concrete damaged plasticity material model.

Compressive stress data are provided as a tabular function of inelastic (or crushing) strain, ${\tilde{ε}}_{c}^{i n}$ , and, if desired, strain rate, temperature, and field variables. Positive (absolute) values should be given for the compressive stress and strain. The stress-strain curve can be defined beyond the ultimate stress, into the strain-softening regime. Compression hardening is required in the concrete damaged plasticity model.


Input Data	Description
Yield Stress	Yield stress in compression, $σ_{c}$ .
Plastic Strain	Inelastic crushing strain, ${\tilde{ε}}_{c}^{i n}$ .
Strain Rate	Inelastic crushing strain rate, ${\dot{\tilde{ε}}}_{c}^{i n}$ .
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.

Concrete Tension Damage

You can define postcracking damage (or stiffness degradation) properties for the concrete damaged plasticity material model.

The compression recovery variable, $w_{c}$ , determines the amount of compression stiffness that is recovered as the loading changes from tension to compression. If $w_{c} = 1$ , the material fully recovers the compressive stiffness; if $w_{c} = 0$ , there is no stiffness recovery. Intermediate values of $w_{c}$ in the range $(0 < w_{c} < 1)$ result in partial recovery of the compressive stiffness.

You can define the uniaxial tension damage variable, $d_{t}$ , as a tabular function of either cracking strain or cracking displacement.


Input Data	Description
Compression recovery	Compression recovery variable, $w_{c}$ . This variable must be in the range $(0 \leq w_{c} \leq 1)$ .
Type	Type of tension damage. Select Strain to specify the tensile damage variable as a function of cracking strain.describes cracking strain. Select Displacement to specify the tensile damage variable as a function of cracking displacement.

Strain-based Concrete Tension Damage


Input Data	Description
Tensile Damage Variable	Tensile damage variable, $d_{t}$ .
Cracking Strain	Direct cracking strain, ${\tilde{ε}}_{t}^{c k}$ .
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.

Displacement-based Concrete Tension Damage


Input Data	Description
Tensile Damage Variable	Tensile damage variable, $d_{t}$ .
Cracking Displacement	Direct cracking displacement, ${\tilde{u}}_{t}^{c k}$ .
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.

Concrete Compression Damage

You can specify compression damage (or stiffness degradation) properties for the concrete damaged plasticity material model.

The tension recovery variable, $w_{t}$ , determines the amount of tension stiffness that is recovered as the loading changes from compression to tension. If $w_{t} = 1$ , the material fully recovers the tensile stiffness; if $w_{t} = 0$ , there is no stiffness recovery. Intermediate values of $w_{t}$ in the range $(0 < w_{t} < 1)$ result in partial recovery of the compressive stiffness.

You can define the uniaxial compression damage variable, $d_{c}$ , as a tabular function of inelastic (crushing) strain.


Input Data	Description
Tension recovery	Specify $(0 \leq w_{t} \leq 1)$ .
Compressive Damage Variable	Compression damage variable, $d_{c}$ .
Crushing Strain	Inelastic crushing strain, ${\tilde{ε}}_{c}^{i n}$ .
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.

Concrete Failure

You can define the material failure criteria for the concrete damaged plasticity material model when explicit time integration is used.

The Type options specify the failure model:


Input Data	Description
Type	Failure model. Strain specifies the tensile and compressive failure based on a tensile cracking strain and compressive crushing strain criterion. Displacement specifies the tensile and compressive failure based on a tensile cracking displacement and compressive crushing strain criterion.

Strain-based Concrete Failure Options


Input Data	Description
Tensile Failure Strain	Tensile cracking strain at failure, ${({\tilde{ε}}_{t}^{c k})}_{f}$ .
Compressive Failure Strain	Compressive inelastic (crushing) strain at failure, ${({\tilde{ε}}_{c}^{i n})}_{f}$ .
Tensile Damage Variable	Tensile damage variable at failure, ${(d_{t})}_{f}$ , if the Concrete Tension Damage option is specified for the material.
Compressive Damage Variable	Compressive damage variable at failure, ${(d_{c})}_{f}$ , if the Concrete Compression Damage option is specified for the material.
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.

Displacement-based Concrete Failure Options


Input Data	Description
Cracking Displacement	Tensile cracking displacement at failure, ${({\tilde{u}}_{t}^{c k})}_{f}$ .
Compressive Failure Strain	Compressive inelastic (crushing) strain at failure, ${({\tilde{ε}}_{c}^{i n})}_{f}$ .
Tensile Damage Variable	Tensile damage variable at failure, ${(d_{t})}_{f}$ , if the Concrete Tension Damage option is specified for the material.
Compressive Damage Variable	Compressive damage variable at failure, ${(d_{c})}_{f}$ , if the Concrete Compression Damage option is specified for the material.
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.