Steel4
This command is used to construct a general uniaxial material with
combined kinematic and isotropic hardening and optional non-symmetric
behavior.
Model.uniaxial(“Steel04”, name, fy, E)
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fy
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float
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Yield stress.
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E
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float
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Young’s modulus of elasticity
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kin
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[b_k,R_0,r_1,r_2], 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 recommended values: R_0 = 20,
r_1 = 0.90, r_2 = 0.15
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b_k
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float
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hardening ratio (E_k/E_0)
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R_0
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float
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control the exponential transition from linear elastic to hardening
asymptote
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r_1
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float
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r_2
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float
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iso
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[b_i,b_l,rho_i,R_i,l_yp], 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
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b_i
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float
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initial hardening ratio (E_i/E_0)
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b_l
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float
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saturated hardening ratio (E_is/E_0)
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rho_i
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float
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specifies the position of the intersection point between initial and
saturated hardening asymptotes
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R_i
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float
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control the exponential transition from initial to saturated asymptote
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l_yp
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float
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length of the yield plateau in \(\varepsilon_{y0} = f_y / E_0\) units
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ult
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[f_u,R_u], 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. 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. Steel4
param ult.png
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f_u
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float
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ultimate strength
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R_u
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float
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control the exponential transition from kinematic hardening to perfectly
plastic asymptote
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asym
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[[kin1,kin2,kin3,kin4],[iso1,iso2,iso3,iso4],[ult1,ult2]],
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
asymi.png Steel4 param asymk.png
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kin
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[kin1,kin2,kin3,kin4],
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kin1
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float
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kin2
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float
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kin3
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float
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kin4
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float
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iso
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[iso1,iso2,iso3,iso4],
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iso1
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float
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iso2
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float
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iso3
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float
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iso4
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float
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ult
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[ult1,ult2],
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sig_init
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float
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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
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cycNum
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int
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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.
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Examples
Under development…
Code developed by: Adam Zsarnóczay,
zsarnoczay@vbt.bme.hu