Steel4 Material

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This command is used to construct a general uniaxial material with combined kinematic and isotropic hardening and optional non-symmetric behavior.
uniaxialMaterial Steel4 $matTag $f_y $E_0 < -asym > < -kin $b_k $R_0 $r_1 $r_2 < $b_kc $R_0c $r_1c $r_2c > > < -iso $b_i $rho_i $b_l $R_i $l_yp < $b_ic $rho_ic $b_lc $R_ic> > < -ult $f_u $R_u < $f_uc $R_uc > > < -init $sig_init > < -mem $cycNum >


$matTag unique material object integer tag
$f_y yield strength (assumed identical in tension and compression)
$E_0 initial stiffness (Young's modulus)
optional features:
-kin apply kinematic hardening
Kinematic hardening is based on the Menegotto-Pinto model. The parameters and their use is identical to those of the Steel02 material. Steel4 param kin.png
$b_k hardening ratio (E_k/E_0)
$R_0 control the exponential transition from linear elastic to hardening asymptote

recommended values: $R_0 = 20 $r_1 = 0.90 $r_2 = 0.15

-iso apply isotropic hardening
Isotropic hardening increases the yield strength of the material. The applied increase is calculated as a function of the accumulated plastic strain. The following parameters control that function. Steel4 param iso.png
$b_i initial hardening ratio (E_i/E_0)
$b_l saturated hardening ratio (E_is/E_0)
$rho_i specifies the position of the intersection point between initial and saturated hardening asymptotes
$R_i control the exponential transition from initial to saturated asymptote
$l_yp length of the yield plateau in eps_y0 = f_y / E_0 units
-ult apply an ultimate strength limit
The ultimate strength limit serves as an upper limit of material resistance. After the limit is reached the material behaves in a perfectly plastic manner. Exponential transition is provided from the kinematic hardening to the perfectly plastic asymptote. Steel4 param ult.png
Note that isotropic hardening is also limited by the ultimate strength, but the transition from the isotropic hardening to the perfectly plastic asymptote is instantaneous.
$f_u ultimate strength
$R_u control the exponential transition from kinematic hardening to perfectly plastic asymptote
-asym assume non-symmetric behavior
If non-symmetric behavior is assumed, material response under tension and compression will be controlled by two different parameter sets. The normal parameters control behavior under tension. Additional parameters shall be specified to describe behavior under compression. The following parameters are expected after the normal parameters when the options below are used. Steel4 param asymk.png
-kin $b_kc $R_0c $r_1c $r_2c
-iso $b_ic $rho_ic $b_lc $R_ic
-ult $f_uc $R_uc
Steel4 param asymi.png
-init apply initial stress
Initial stress is assumed at 0 strain at the beginning of the loading process. The absolute value of the initial stress is assumed to be less than the yield strength of the material. Steel4 param init.png
$sig_init initial stress value
-mem configure the load history memory
The load history memory is a database of preceding load cycles. It is updated at every load reversal point during the loading process. It is turned on by default. Turning it off will reduce the memory consumption of Steel4. Steel4 param mem.png
The available data on preceding cycles is currently used to correct a typical error in the Steel02 material. The error stems from the formulation of the Menegotto-Pinto kinematic hardening model. It leads to overestimation of the stress response after small unloading-reloading cycles. This phenomenon is important, because the seismic response of structures typically includes a large number of such small cycles. The error is avoided by forcing the kinematic hardening component of the response to converge to previous load cycles.
The load history memory can be used in the future to describe other characteristics of the response that depend on preceding load cycles.
$cycNum expected number of half-cycles during the loading process
Efficiency of the material can be slightly increased by correctly setting this value. The default value is $cycNum = 50
Load history memory can be turned off by setting $cycNum = 0.


Coming soon...

Author: Adam Zsarnóczay: