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 (
) and compressive equivalent plastic strain (
). 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,
, in the p-q plane at high confining pressure. |
Flow Potential Eccentricity |
Eccentricity,
, 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,
. |
Ratio of Stress Invariants |
, 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,
, such that the maximum principal stress is negative. It must satisfy
the condition
. |
Viscosity |
Visco-plastic regularization parameter,
, 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,
. |
Cracking Strain |
Direct cracking strain,
. |
Strain Rate |
Direct cracking strain rate,
. |
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,
. |
Cracking Displacement |
Direct cracking displacement,
. |
Velocity |
Direct cracking velocity,
. |
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,
. |
Fracture Energy |
Fracture energy,
. |
Velocity |
Direct cracking velocity,
. |
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,
, 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,
. |
Plastic Strain |
Inelastic crushing strain,
. |
Strain Rate |
Inelastic crushing strain rate,
. |
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,
, determines the amount of compression stiffness that is recovered as the
loading changes from tension to compression. If
, the material fully recovers the compressive stiffness; if
, there is no stiffness recovery. Intermediate values of
in the range
result in partial recovery of the compressive stiffness.
You can define the uniaxial tension damage variable,
, as a tabular function of either cracking strain or cracking
displacement.
Input Data |
Description |
Compression recovery |
Compression recovery variable,
. This variable must be in the range
. |
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,
. |
Cracking Strain |
Direct cracking strain,
. |
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,
. |
Cracking Displacement |
Direct cracking displacement,
. |
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,
, determines the amount of tension stiffness that is recovered as the
loading changes from compression to tension. If
, the material fully recovers the tensile stiffness; if
, there is no stiffness recovery. Intermediate values of
in the range
result in partial recovery of the compressive stiffness.
You can define the uniaxial compression damage variable,
, as a tabular function of inelastic (crushing) strain.
Input Data |
Description |
Tension recovery |
Specify
. |
Compressive Damage Variable |
Compression damage variable,
. |
Crushing Strain |
Inelastic crushing strain,
. |
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,
. |
Compressive Failure Strain |
Compressive inelastic (crushing) strain at failure,
. |
Tensile Damage Variable |
Tensile damage variable at failure,
, if the Concrete Tension Damage option is specified for the
material. |
Compressive Damage Variable |
Compressive damage variable at failure,
, 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,
. |
Compressive Failure Strain |
Compressive inelastic (crushing) strain at failure,
. |
Tensile Damage Variable |
Tensile damage variable at failure,
, if the Concrete Tension Damage option is specified for the
material. |
Compressive Damage Variable |
Compressive damage variable at failure,
, 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. |
|