*CONCRETE DAMAGED PLASTICITY

Optional parameters

DEPENDENCIES: Set this parameter equal to the number of field variable dependencies included in the definition of the material parameters other than temperature. If this parameter is omitted, it is assumed that the material parameters depend only on temperature. See Material Data Definition for more information.
REF LENGTH: Set this parameter equal to the specimen length, $l_{0}$ , used to properly account for the length units when converting the cracking displacement values to “plastic” displacement values. By default, the value is $l_{0} = 1.0$ , which means one unit length. (Units of L.)

Data lines to define concrete damaged plasticity flow potential, yield surface, and viscosity parameters

First line

Dilation angle, $ψ$ , in the p–q plane. Give the value in degrees.
Flow potential eccentricity, $ϵ$ . The eccentricity is a small positive number that defines the rate at which the hyperbolic flow potential approaches its asymptote. If this field is left blank or a value of 0.0 is entered, the default of $ϵ = 0.1$ is used.
$σ_{b 0} / σ_{c 0}$ , the ratio of initial equibiaxial compressive yield stress to initial uniaxial compressive yield stress. If this field is left blank or a value of 0.0 is entered, the default of $1.16$ is used.
$K_{c}$ , the ratio of the second stress invariant on the tensile meridian, $q_{(TM)}$ , to that on the compressive meridian, $q_{(CM)}$ , at initial yield for any given value of the pressure invariant p such that the maximum principal stress is negative, ${\hat{σ}}_{\max} < 0$ . It must satisfy the condition $0.5 < K_{c} \leq 1.0$ . If this field is left blank or a value of 0.0 is entered, the default of $2 / 3$ is used.
Viscosity parameter, $μ$ , 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 $T$ .)
Temperature.
First field variable.
Second field variable.

Subsequent lines (only needed if the DEPENDENCIES parameter has a value greater than two)

Third field variable.
Etc., up to eight field variables per line.

Repeat this set of data lines as often as necessary to define the dependence of the material parameters on temperature and other predefined field variables.