1.1. Defining the Multilinear Kinematic Hardening Model

Define the isotropic or anisotropic elastic behavior via MP commands. To specify the hardening behavior, define the material data table (TB) and as stress vs. total strain points or as stress vs. plastic strain points.

TB,MKIN -- Multilinear Kinematic Hardening Specifications

NTEMP:

Number of temperatures for which data will be provided. Default = 5. Maximum = 5.

NPTS:

t

Number of data points to be specified for a given temperature.

TBOPT:

Stress-strain options.

0 --

No stress relaxation with temperature increase (this is not recommended for nonisothermal problems); also produces thermal ratcheting. This value is the default.

1 --

Recalculate total plastic strain using new weight factors of the subvolume.

2 --

Scale layer plastic strains to keep total plastic strain constant; agrees with Rice's model (TB, BKIN) with TBOPT = 1). Produces stable stress-strain cycles.

TB,KINH -- Multilinear Kinematic Hardening Specifications

This material is the same as MKIN with TBOPT = 2, but with fewer restrictions on the number of points per curve and the number of temperatures.

NTEMP:

Number of temperatures for which data will be provided. Default = 1. Maximum = 40.

NPTS:

Number of data points to be specified for a given temperature. Default = 20. Maximum = 20.

TBOPT:

Use 0 or leave blank to define stress -vs- total strain curve.

Use 4 or enter "PLASTIC" to define stress -vs- plastic strain curve. This option supports only elements LINK180, SHELL181, PLANE182, PLANE183, SOLID185, SOLID186, SOLID187, BEAM188, BEAM189, SOLSH190, SHELL208, SHELL209, REINF264, REINF265, SOLID272, SOLID273, SOLID285, SHELL281, PIPE288, PIPE289, and ELBOW290, .

Specifying the Constants

Constant Meaning Property
P1 Strain value
P2 Stress value

The constants can be defined as a function of temperature (NTEMP, with temperatures specified for the table entries (TBTEMP).

When entering temperature-dependent stress-strain points, the set of data at each temperature must have the same number of points. Thermal softening for the multilinear kinematic hardening model is the same as that for bilinear kinematic hardening (TB,BKIN) with Rice's hardening rule.

Entering Stress vs. Total Strain Points

After defining the material data table (TB,KINH,,,,0), enter the stress-strain points (TBPT).

The slope of the first segment must correspond to the elastic modulus and no segment slope can be larger than the slope of the previous segment.

Example 1.1: Multilinear Kinematic Hardening with Stress vs. Total Strain

/prep7
TB,KINH,1,2,3                  ! Activate a data table
TBTEMP,20.0                    ! Temperature = 20.0
TBPT,,0.001,1.0                ! Strain = 0.001, Stress = 1.0
TBPT,,0.1012,1.2               ! Strain = 0.1012, Stress = 1.2
TBPT,,0.2013,1.3               ! Strain = 0.2013, Stress = 1.3
TBTEMP,40.0                    ! Temperature = 40.0
TBPT,,0.008,0.9                ! Strain = 0.008, Stress = 0.9
TBPT,,0.09088,1.0              ! Strain = 0.09088, Stress = 1.0
TBPT,,0.12926,1.05             ! Strain = 0.12926, Stress = 1.05