Defining a concrete damaged plasticity model

From the menu bar in the Edit Material dialog box, select MechanicalPlasticityConcrete Damaged Plasticity.

(For information on displaying the Edit Material dialog box, see Creating or editing a material.)

Click the Plasticity tab, if necessary, to display the Plasticity tabbed page.

Toggle on Use temperature-dependent data to define data that depend on temperature.

A column labeled Temp appears in the Data table.

Click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables on which the data depend.

Enter the following data in the Data table:

Dilation Angle

Dilation angle, $\psi$, in the p–q plane. Enter the value in degrees.

Eccentricity

Flow potential eccentricity, $ϵ$. The eccentricity is a small positive number that defines the rate at which the hyperbolic flow potential approaches its asymptote. The default is $ϵ=0.1$.

fb0/fc0

${\sigma }_{b0}/{\sigma }_{c0}$, the ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress. The default value is $1.16$

K

$K_c$, the ratio of the second stress invariant on the tensile meridian, $q_{\left(\mathrm{TM}\right)}$, to that on the compressive meridian, $q_{\left(\mathrm{CM}\right)}$, at initial yield for any given value of the pressure invariant p such that the maximum principal stress is negative, ${\widehat{\sigma }}_{\max }<0$. It must satisfy the condition $0.5<K_c\le 1.0$. The default value is $2/3$.

Viscosity Parameter

Viscosity parameter, $\mu$, used for the visco-plastic regularization of the concrete constitutive equations in Abaqus/Standard analyses. This parameter is ignored in Abaqus/Explicit. The default value is $0.0$. (Units of $\mathrm{T}$.)

Temp

Temperature.

Field n

Predefined field variables.

Click the Compressive Behavior tab to display the Compressive Behavior tabbed page. (For information on compressive hardening, see Defining compressive behavior.)

Toggle on Use strain-rate-dependent data if the compressive stress data are a function of strain rate.

Toggle on Use temperature-dependent data to define data that depend on temperature.

A column labeled Temp appears in the Data table.

Click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables on which the data depend.

Enter the following data in the Data table:

Yield Stress

Yield stress in compression, ${\sigma }_c$. (Units of ${\text{FL}}^{-2}$.)

Inelastic Strain

Inelastic (crushing) strain, ${\tilde{\epsilon }}_c^{in}$.

Rate

Inelastic (crushing) strain rate, ${\dot{\tilde{\epsilon }}}_c^{in}$. (Units of ${\text{T}}^{-1}$.)

Temp

Temperature.

Field n

Predefined field variables.

If desired, select Compression Damage from the Suboptions menu to specify damage in tabular form. (If you omit damage data, the model behaves as a plasticity model.) See Defining concrete compression damage” for details.

Click the Tensile Behavior tab to display the Tensile Behavior tabbed page. (For information on tension stiffening, see Defining tension stiffening.)

Click the arrow to the right of the Type field, and select a method for defining the postcracking behavior:

• Select Strain to specify the postcracking behavior by entering the postfailure stress/cracking-strain relationship.

• Select Displacement to define the postcracking behavior by entering the postfailure stress/cracking-displacement relationship.

• Select GFI to define the postcracking behavior by entering the failure stress and the fracture energy.

Toggle on Use strain-rate-dependent data if the postcracking stress depends on strain rate.

Toggle on Use temperature-dependent data to define data that depend on temperature.

A column labeled Temp appears in the Data table.

Click the arrows to the right of the Number of field variables field to increase or decrease the number of field variables on which the data depend.

In the Data table, enter the data relevant to your Type choice from Step 13 (not all of the following will apply):

Yield Stress

If you selected Strain or Displacement from the list of Type options, enter the remaining direct stress after cracking, ${\sigma }_t$. (Units of ${\text{FL}}^{-2}$.)

If you selected GFI from the list of Type options, enter the failure stress, ${\sigma }_{t0}$. (Units of ${\text{FL}}^{-2}$.)

Cracking Strain

Direct cracking strain, ${\tilde{\epsilon }}_t^{ck}$.

Displacement

Direct cracking displacement, $u_t^{ck}$. (Units of L.)

Fracture Energy

Fracture energy, $G_f$. (Units of ${\text{FL}}^{-1}$.)

Rate

If you selected Strain from the list of Type options, enter the direct cracking strain rate, ${\dot{\tilde{\epsilon }}}_t^{ck}$. (Units of ${\text{T}}^{-1}$.)

If you selected Displacement or GFI from the list of Type options, enter the direct cracking displacement rate, ${\dot{u}}_t^{ck}$. (Units of ${\text{LT}}^{-1}$.)

Temp

Temperature.

Field n

Predefined field variables.

You may need to expand the dialog box to see all the columns in the Data table. For detailed information on how to enter data, see Entering tabular data.

If desired, select Tension Damage from the Suboptions menu to specify damage in tabular form. (If you omit damage data, the model behaves as a plasticity model.) See Defining concrete tension damage” for details.

Click OK to create the material and to close the Edit Material dialog box. Alternatively, you can select another material behavior to define from the menus in the Edit Material dialog box (see Browsing and modifying material behaviors, for more information).