3.1.5.18. HystereticSM Material

This command is used to construct a uniaxial multilinear hysteretic material object with pinching of force and deformation, damage due to ductility and energy, and degraded unloading stiffness based on ductility. - This material is an extension of the Hysteretic Material – the envelope can be defined 2,3, 4,5,6 or 7 points, while the original one only had 2 or 3. - The positive and negative backbone of this material do not need to have the same number of segments. - This material also has the option to degrade the envelope using the degEnv parameters – these parameters must be used in combination with the damage parameters - This material also has additional DCR-type recorder output (this is still a work in progress).

3.1.5.18.1. Input Command:

OpenSeesPy

uniaxialMaterial('HystereticSM',matTag,
   '-posEnv',s1p,e1p,s2p,e2p <,s3p,e3p> <,s4p,e4p><,s5p,e5p><,s6p,e6p><,s7p,e7p>
   <,'-negEnv',s1n,e1n,s2n,e2n <,s3n,e3n> <,s4n,e4n> <,s5n,e5n> <,s6n,e6n> <,s7n,e7n>>
   <,'-pinch',pinchX,pinchY>
   <,'-damage',damage1,damage2>
   <,'-beta',beta>
   <,'-degEnv',degEnvP <,degEnvN>>
   <,'-defoLimitStates',lsD1 <$lsD2>...>
   <,'-forceLimitStates',lsF1 <,$lsF2>...>
   <,'-printInput'>
   <,'-XYorder'>
 )

Tcl interpreter

uniaxialMaterial HystereticSM $matTag \
   -posEnv $s1p $e1p $s2p $e2p <$s3p $e3p> <$s4p $e4p> <$s5p $e5p> <$s6p $e6p> <$s7p $e7p> \
   <-negEnv $s1n $e1n $s2n $e2n <$s3n $e3n> <$s4n $e4n> <$s5n $e5n> <$s6n $e6n> <$s7n $e7n>> \
   <-pinch $pinchX $pinchY> \
   <-damage $damage1 $damage2> \
   <-beta $beta> \
   <-degEnv degEnvP <degEnvN>> \
   <-defoLimitStates $lsD1 <$lsD2>...> \
   <-forceLimitStates $lsF1 <$lsF2>...> \
   <-printInput> \
   <-XYorder>

You can use the following input format as it is compatible with Hysteretic material. Note that in this case you must have the same number of positive and negative segments. I have made this format (make sure you test it) to make the transition from Hysteretic to HystereticSM easy:

OpenSeesPy

uniaxialMaterial('HystereticSM',matTag,s1p,e1p,s2p,e2p <,s3p,e3p> <,s4p,e4p> <,s5p,e5p> <,s6p,e6p> <,s7p,e7p>,
   s1n,e1n,s2n,e2n <,s3n,e3n> <,s4n,e4n> <,s5n,e5n> <,s6n,e6n> <,s7n,e7n>,
   pinchX,pinchY,damage1,damage2 <,beta>
   <,'-degEnv',degEnvP <,degEnvN>>
   <,'-defoLimitStates',lsD1 <$lsD2>...>
   <,'-forceLimitStates',lsF1 <,$lsF2>...>
   <,'-printInput'>
   <,'-XYorder'>)

Tcl interpreter

uniaxialMaterial HystereticSM $matTag $s1p $e1p $s2p $e2p <$s3p $e3p> <$s4p $e4p> <$s5p $e5p> <$s6p $e6p> <$s7p $e7p> \
   $s1n $e1n $s2n $e2n <$s3n $e3n> <$s4n $e4n> <$s5n $e5n> <$s6n $e6n> <$s7n $e7n> \
   $pinchX $pinchY $damage1 $damage2 <$beta> \
   <-degEnv degEnvP <degEnvN>> \
   <-defoLimitStates lsD1? <lsD2?>...> \
   <-forceLimitStates lsF1? <lsF2?>...> \
   <-printInput> \
   <-XYorder>

3.1.5.18.2. Input Arguments:

Argument

Type

Description

$matTag

integer

Integer tag identifying material

$s1p $e1p

float

stress and strain (or force & deformation) at first point of the envelope in the positive direction

$s2p $e2p

float

stress and strain (or force & deformation) at second point of the envelope in the positive direction

$s3p $e3p

float

stress and strain (or force & deformation) at third point of the envelope in the positive direction (optional)

($s4p $e4p …. $s7p $e7p)

float

stress and strain (or force & deformation) at 4th-7th points of the envelope in the positive direction (optional)

$s1n $e1n

float

stress and strain (or force & deformation) at first point of the envelope in the negative direction

$s2n $e2n

float

stress and strain (or force & deformation) at second point of the envelope in the negative direction

$s3n $e3n

float

stress and strain (or force & deformation) at third point of the envelope in the negative direction (optional)

($s4n $e4n …. $s7n $e7n)

float

stress and strain (or force & deformation) at 4th-7th points of the envelope in the negative direction (optional)

$pinchx

float

pinching factor for strain (or deformation) during reloading

$pinchy

float

pinching factor for stress (or force) during reloading

$damage1

float

damage due to ductility: D1(mu-1)

$damage2

float

damage due to energy: D2(Eii/Eult)

$beta

float

power used to determine the degraded unloading stiffness based on ductility, mu-beta (optional, default=0.0)

$degEnvP

float

envelope-degredation factor. This factor works with the damage parameters to degrade the POSITIVE envelope. A positive value degrades both strength and strain values, a negative values degrades only strength. The factor is applied to points 3+ (optional, default=0.0)

$degEnvN

float

envelope-degredation factor. This factor works with the damage parameters to degrade the NEGATIVE envelope. A positive value degrades both strength and strain values, a negative values degrades only strength. The factor is applied to points 3+ (optional, default=degEnvP, if defined, =0. otherwise)

($lsD1,$lsD2..)

float

list of user-defined strain/deformation limits for computing deformation DCRs (optional)

($lsF1,$lsF2..)

float

list of user-defined stress/force limits for computing force DCRs (optional)

-printInput

string

program will output input-parameter values (optional)

-XYorder

string

invert backbone-envelope points to be strain-stress instead of stress-strain (optional). This flag has the same effect as using -posEnvXY and the optional -negEnvXY, so it should be used with the -posEnv and -negEnv flags.

Note

  • posEnv is defined using positive, INCREASING points –> strain values must be unique.

  • negEnv is defined using negative, DECREASING points –> strain values must be unique.

  • For symmetric response: do not enter -negEnv data.

  • If the last stress point is higher than the previous one, the curve will extrapolate linearly. If it is less than, the curve will extrapolate at a constant value equal to the last stress value

  • If you would like to enter strain-stress pairs use -posEnvXY (and optional -negEnvXY) instead of -posEnv (-negEnv) OR the flag XYorder.

  • The values for damage and envelope-degradation factors depend on the amplitude of your input values, so you should calibrate them.

3.1.5.18.3. Recorder Options:

Argument

Label

Description

MU1

Ductility Ratio

ratio of current strain to first point in strain/deformation envelope (if CurrentStrain positive: CurrentStrain/e1p, if CurrentStrain negative: CurrentStrain/e1n) (MUy also works)

defoPlastic

Plastic Deformation

CurrentStrain/defo - ElasticStrain/defo (ElasticStrain is defined by the elastic stiffness s1p/e1p, if CurrentStrain is positive, or s2p/e2p, if negative, and the current stress/force)

defoDCR

deformation DCR on Envelope Points

7-component array with the ratio of the CURRENT strain to each of the envelope strain points (if positive: positive points, if negative: negative points)

defoDCRMax

Maximum-deformation DCR on Envelope Points

14-component array with the ratio of the MAXIMUM strain to each of the envelope strain points (emaxP/e1p,….emaxP/e7p,emaxN/e1n,…emaxN/e7n)

defoLimitStates

User-Defined Deformation Limit States

return array of user-defined deformation limit states

forceLimitStates

User-Defined Force Limit States

return array of user-defined force limit states

defoLimitStatesDCR

deformation DCR on User-Defined Limit States

array with the ratio of the CURRENT strain to each of the user-defined deformation limit states

defoLimitStatesDCRMax

Maximum-deformation DCR on User-Defined Limit States

array with the ratio of the MAXIMUM strain to each of the user-defined deformation limit states (positive limit-state value emaxP/els, negative value emaxN/els)

defoLimitStatesDCRMaxAbs

MaximumAbsolute-deformation DCR on User-Defined Limit States

array with the ratio of the MAXIMUM strain to each of the envelope strain points (max(emaxP,abs(emaxN))/els)

forceLimitStatesDCR

force DCR on User-Defined Limit States

array with the ratio of the CURRENT stress/force to each of the user-defined force limit states

allData

All relevant Data

all relevant data at current step (mom1p, rot1p, mom2p, rot2p, mom3p, rot3p, mom4p, rot4p, mom5p, rot5p, mom6p, rot6p, mom7p, rot7p, mom1n, rot1n, mom2n, rot2n, mom3n, rot3n, mom4n, rot4n, mom5n, rot5n, mom6n, rot6n, mom7n, rot7n, pinchX, pinchY, damfc1, damfc2, beta, CrotMax, CrotMin, CrotPu, CrotNu, CenergyD, CloadIndicator, Cstress, Cstrain, Ttangent)

3.1.5.18.4. Backbone Curve for material:

Backbone curve for Symmetric material behavior.

../../../../_images/HystereticSM_backbone_Symm.jpg

Backbone curve for Unsymmetric material behavior.

../../../../_images/HystereticSM_backbone_nonSymm.jpg

3.1.5.18.5. Examples:

You have endless options with this material. Here are a few demos:

Jupyter Notebook

Open or download Jupyter the notebook with example of HystereticSM material, used generate the figures CLICK HERE!

Example Input

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
  '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
  '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
  '-pinch', 1, 1,
  '-damage', 0.1, 0.01,
  '-beta', 0,
  '-defoLimitStates', 0.01, -0.01, 0.02, -0.02,
  '-forceLimitStates', 2772.0, -2772.0, 3104.6, -3104.6,
  '-printInput'
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM 99 \
  -posEnv 2772.0 0.01 3104.6 0.02 1663.2 0.04 1663.2 0.06 277.2 0.08 200.0 0.1 0 0.12 \
  -negEnv -2772.0 -0.01 -3104.6 -0.02 -1663.2 -0.04 \
  -pinch 1 1 \
  -damage 0.1 0.01 \
  -beta 0 \
  -defoLimitStates 0.01 -0.01 0.02 -0.02 \
  -forceLimitStates 2772.0 -2772.0 3104.6 -3104.6 \
  -printInput

3.1.5.18.6. Input-Parameters Study:

Pinching

  1. pinch=[1, 1]

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
    '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.10, 0, 0.12,
    '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
    '-pinch', 1, 1
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM 99 \
    -posEnv 2772.0 0.01 3104.6 0.02 1663.2 0.04 1663.2 0.06 277.2 0.08 200.0 0.10 0 0.12 \
    -negEnv -2772.0 -0.01 -3104.6 -0.02 -1663.2 -0.04 \
    -pinch 1 1

  1. pinch=[0.2, 0.8]

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
  '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
  '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
  '-pinch', 0.2, 0.8
  )

  • Tcl Interpreter

    uniaxialMaterial HystereticSM  99  \
    -posEnv  2772.0  0.01  3104.6  0.02  1663.2  0.04  1663.2  0.06  277.2  0.08  200.0  0.1  0  0.12  \
    -negEnv  -2772.0  -0.01  -3104.6  -0.02  -1663.2  -0.04  \
    -pinch  0.2  0.8

  1. pinch=[0.8, 0.2]

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
'-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
'-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
'-pinch', 0.8, 0.2
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM  99  \
    -posEnv  2772.0  0.01  3104.6  0.02  1663.2  0.04  1663.2  0.06  277.2  0.08  200.0  0.1  0  0.12  \
    -negEnv  -2772.0  -0.01  -3104.6  -0.02  -1663.2  -0.04  \
    -pinch  0.8  0.2
../../../../_images/HystereticSM_pinch_strainDip.jpg
../../../../_images/HystereticSM_pinch_symmCycles.jpg
../../../../_images/HystereticSM_pinch_strainOneSidedPush.jpg
../../../../_images/HystereticSM_pinch_strainOneSidedPull.jpg

Damage1

  1. damage1=0

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
  '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
  '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
  '-damage', 0, 0
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM  99  \
  -posEnv  2772.0  0.01  3104.6  0.02  1663.2  0.04  1663.2  0.06  277.2  0.08  200.0  0.1  0  0.12  \
  -negEnv  -2772.0  -0.01  -3104.6  -0.02  -1663.2  -0.04  \
  -damage  0  0

  1. damage1=0.01

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
  '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
  '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
  '-damage', 0.01, 0
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM  99  \
  -posEnv  2772.0  0.01  3104.6  0.02  1663.2  0.04  1663.2  0.06  277.2  0.08  200.0  0.1  0  0.12  \
  -negEnv  -2772.0  -0.01  -3104.6  -0.02  -1663.2  -0.04  \
  -damage  0.01  0

  1. damage1=0.1

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
  '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
  '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
  '-damage', 0.1, 0
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM  99  \
    -posEnv  2772.0  0.01  3104.6  0.02  1663.2  0.04  1663.2  0.06  277.2  0.08  200.0  0.1  0  0.12  \
    -negEnv  -2772.0  -0.01  -3104.6  -0.02  -1663.2  -0.04  \
    -damage  0.1  0
../../../../_images/HystereticSM_damage1_strainDip.jpg
../../../../_images/HystereticSM_damage1_symmCycles.jpg
../../../../_images/HystereticSM_damage1_strainOneSidedPush.jpg
../../../../_images/HystereticSM_damage1_strainOneSidedPull.jpg

Damage2

  1. damage2=0

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
  '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
  '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
  '-damage', 0, 0
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM  99  \
    -posEnv  2772.0  0.01  3104.6  0.02  1663.2  0.04  1663.2  0.06  277.2  0.08  200.0  0.1  0  0.12  \
    -negEnv  -2772.0  -0.01  -3104.6  -0.02  -1663.2  -0.04  \
    -damage  0  0

  1. damage2=0.01

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
  '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
  '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
  '-damage', 0, 0.01
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM  99  \
    -posEnv  2772.0  0.01  3104.6  0.02  1663.2  0.04  1663.2  0.06  277.2  0.08  200.0  0.1  0  0.12  \
    -negEnv  -2772.0  -0.01  -3104.6  -0.02  -1663.2  -0.04  \
    -damage  0  0.01

  1. damage2=0.1

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
  '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
  '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
  '-damage', 0, 0.1
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM  99  \
    -posEnv  2772.0  0.01  3104.6  0.02  1663.2  0.04  1663.2  0.06  277.2  0.08  200.0  0.1  0  0.12  \
    -negEnv  -2772.0  -0.01  -3104.6  -0.02  -1663.2  -0.04  \
    -damage  0  0.1
../../../../_images/HystereticSM_damage2_strainDip.jpg
../../../../_images/HystereticSM_damage2_symmCycles.jpg
../../../../_images/HystereticSM_damage2_strainOneSidedPush.jpg
../../../../_images/HystereticSM_damage2_strainOneSidedPull.jpg

beta

  1. beta=0

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
  '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
  '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
  '-beta', 0
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM  99  \
  -posEnv  2772.0  0.01  3104.6  0.02  1663.2  0.04  1663.2  0.06  277.2  0.08  200.0  0.1  0  0.12  \
  -negEnv  -2772.0  -0.01  -3104.6  -0.02  -1663.2  -0.04  \
  -beta  0

  1. beta=0.5

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
  '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
  '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
  '-beta', 0.5
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM  99  \
  -posEnv  2772.0  0.01  3104.6  0.02  1663.2  0.04  1663.2  0.06  277.2  0.08  200.0  0.1  0  0.12  \
  -negEnv  -2772.0  -0.01  -3104.6  -0.02  -1663.2  -0.04  \
  -beta  0.5

  1. beta=1

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
  '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
  '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
  '-beta', 1
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM  99  \
  -posEnv  2772.0  0.01  3104.6  0.02  1663.2  0.04  1663.2  0.06  277.2  0.08  200.0  0.1  0  0.12  \
  -negEnv  -2772.0  -0.01  -3104.6  -0.02  -1663.2  -0.04  \
  -beta  1
../../../../_images/HystereticSM_beta_strainDip.jpg
../../../../_images/HystereticSM_beta_symmCycles.jpg
../../../../_images/HystereticSM_beta_strainOneSidedPush.jpg
../../../../_images/HystereticSM_beta_strainOneSidedPull.jpg

degEnv

  1. degEnv=0

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
  '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
  '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
  '-damage', 0.005, 0.002,
  '-degEnv', 0, 0
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM  99  \
  -posEnv  2772.0  0.01  3104.6  0.02  1663.2  0.04  1663.2  0.06  277.2  0.08  200.0  0.1  0  0.12  \
  -negEnv  -2772.0  -0.01  -3104.6  -0.02  -1663.2  -0.04  \
  -damage  0.005  0.002  \
  -degEnv  0  0

  1. degEnv=1

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
  '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
  '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
  '-damage', 0.005, 0.002,
  '-degEnv', 1, -1
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM  99  \
  -posEnv  2772.0  0.01  3104.6  0.02  1663.2  0.04  1663.2  0.06  277.2  0.08  200.0  0.1  0  0.12  \
  -negEnv  -2772.0  -0.01  -3104.6  -0.02  -1663.2  -0.04  \
  -damage  0.005  0.002  \
  -degEnv  1  -1

  1. degEnv=5

  • OpenSeesPy

    ops.uniaxialMaterial('HystereticSM', 99,
  '-posEnv', 2772.0, 0.01, 3104.6, 0.02, 1663.2, 0.04, 1663.2, 0.06, 277.2, 0.08, 200.0, 0.1, 0, 0.12,
  '-negEnv', -2772.0, -0.01, -3104.6, -0.02, -1663.2, -0.04,
  '-damage', 0.005, 0.002,
  '-degEnv', 5, -5
)

  • Tcl Interpreter

    uniaxialMaterial HystereticSM  99  \
  -posEnv  2772.0  0.01  3104.6  0.02  1663.2  0.04  1663.2  0.06  277.2  0.08  200.0  0.1  0  0.12  \
  -negEnv  -2772.0  -0.01  -3104.6  -0.02  -1663.2  -0.04  \
  -damage  0.005  0.002  \
  -degEnv  5  -5
../../../../_images/HystereticSM_degEnv_strainDip.jpg
../../../../_images/HystereticSM_degEnv_symmCycles.jpg
../../../../_images/HystereticSM_degEnv_strainOneSidedPush.jpg
../../../../_images/HystereticSM_degEnv_strainOneSidedPull.jpg
HystereticSM Code Developed (2022) by: Silvia Mazzoni (Silvia’s Brainery)
Original Hysteretic-Material Code Developed by: Michael H. Scott & Filip Filippou (UC Berkeley)