suanPan-manual
  • Introduction
  • Basic
    • Obtain Application
    • Configure Application
    • Perform Analysis
    • Model Syntax
    • Model Structure
    • Tweak Performance
    • Compile Application
    • Build Documentation
    • Architecture Design
    • On Clusters
  • Example
    • Developer
      • element template
      • material template
    • Solid
      • wave propagation
    • Geotechnical
      • triaxial compression of sand
      • slope analysis
    • Structural
      • Statics
        • bending of a cantilever beam
        • bifurcation of a cantilever beam
        • double-edge notched specimen
        • lees frame
        • notched beam under cyclic loading
        • rc section analysis
        • truss roof
        • uniform tension of a rubber specimen
        • thin-walled section analysis for frame structures
        • calibration of subloading surface model
      • Dynamics
        • bouncing of a ball
        • mass-spring-dashpot system
        • dynamic analysis of a portal frame
        • elemental damping
        • particle collision
        • response history analysis of an elastic coupled wall
        • multi-support excitation
        • triple pendulum
        • computing response spectrum
        • integrate with python
        • process ground motion
      • Hybrid
        • vibration of a displaced beam
      • Buckling
        • buckling analysis of a cantilever beam
      • Contact
        • contact between beam and block
        • contact in 3d space
      • Optimization
        • evolutionary structural optimization
      • Isogeometric Analysis
        • linear analysis of a single element
    • Miscellaneous
      • batch execution for automation
  • Command Collection
    • Define
      • amplitude
      • bc
      • domain
      • element
      • expression
      • file
      • generate
      • group
      • import
      • initial
      • load
      • material
      • modifier
      • node
      • recorder
      • section
    • Configure
      • analyze
      • converger
      • criterion
      • integrator
      • precheck
      • step
    • Process
      • benchmark
      • clear
      • command
      • enable
      • exit
      • materialtest
      • materialtestbyload
      • sectiontest
      • peek
      • plot
      • protect
      • pwd
      • reset
      • save
      • set
      • upsampling
      • sdof_response
      • response_spectrum
  • Amplitude
    • Amplitude
    • Special
      • NZStrongMotion
    • Universal
      • Combine
      • Constant
      • Decay
      • Linear
      • Modulated
      • Tabular
      • TabularSpline
      • Trig
  • Constraint
    • MPC
    • ParticleCollision
    • RigidWall
    • RestitutionWall
    • FixedLength
    • MaxForce
    • NodeLine
    • NodeFacet
    • Embed2D
    • Embed3D
    • LJPotential2D
    • MaximumGap2D
    • MinimumGap2D
    • MaximumGap3D
    • MinimumGap3D
  • Converger
    • Converger
    • Absolute
      • AbsDisp
      • AbsError
      • AbsIncreDisp
      • AbsIncreAcc
      • AbsIncreEnergy
      • AbsResidual
    • Other
      • FixedNumber
      • Logic
    • Relative
      • RelDisp
      • RelError
      • RelIncreDisp
      • RelIncreAcc
      • RelIncreEnergy
      • RelResidual
  • Criterion
    • Criterion
    • MaxDisplacement
    • MaxHistory
    • MaxResistance
    • MinDisplacement
    • MinResistance
    • StrainEnergyEvolution
  • Element
    • Beam
      • B21
      • B21E
      • B21H
      • B31
      • B31OS
      • EB21
      • EB31OS
      • F21
      • F21H
      • F31
      • NMB21
      • NMB21E
      • NMB31
      • MVLEM
      • Orientation
    • Cube
      • C3D20
      • C3D4
      • C3D8
      • C3D8I
      • CIN3D8
      • DC3D4
      • DC3D8
    • Membrane
      • Couple Stress
      • Phase Field
        • DCP3
        • DCP4
      • Axisymmetric
        • CAX3
        • CAX4
        • CAX8
      • Plane
        • CP3
        • CP4
        • CP4I
        • CP5
        • CP6
        • CP7
        • CP8
      • Mixed
        • PS
        • QE2
      • Drilling
        • Allman
        • GCMQ
        • GQ12
      • Infinite
        • CINP4
      • Geotechnical
        • PCPE4DC
        • PCPE4UC
        • PCPE8DC
        • PCPE8UC
      • Membrane
    • Modifier
      • Modifier
      • ElementalLee
      • ElementalNonviscous
      • LinearViscosity
    • Patch
      • Patch
      • PatchCube
      • PatchQuad
    • Plate
      • DKT3
      • DKT4
      • Mindlin
    • Shell
      • DKTS3
      • DKTS4
      • S4
      • SGCMS
      • ShellBase
    • Special
      • Contact2D
      • Contact3D
      • Damper01
      • Damper02
      • Embedded2D
      • Embedded3D
      • Joint
      • Mass
      • SingleSection
      • Spring01
      • Spring02
      • Tie
      • TranslationConnector
    • Truss
      • T2D2
      • T2D2S
      • T3D2
      • T3D2S
  • Group
    • CustomNodeGroup
    • NodeGroup
    • ElementGroup
    • GroupGroup
  • Integrator
    • Implicit
      • Linear
      • BatheTwoStep
      • GeneralizedAlpha
      • OALTS
      • GSSSS
      • Newmark
        • LeeNewmark
        • LeeElementalNewmark
        • LeeNewmarkFull
        • LeeNewmarkIterative
        • Newmark
        • RayleighNewmark
        • WilsonPenzienNewmark
        • NonviscousNewmark
    • Explicit
      • Tchamwa
      • BatheExplicit
      • GeneralizedAlphaExplicit
  • Material
    • Guide
      • Metal
      • Customisation
    • Material1D
      • Concrete
        • ConcreteCM
        • ConcreteExp
        • ConcreteTsai
        • ConcreteTable
        • ConcreteK4
      • Degradation
        • Degradation
        • CustomStrainDegradation
        • CustomStressDegradation
        • Dhakal
        • TrilinearStrainDegradation
      • Elastic
        • BilinearElastic1D
        • Elastic1D
        • AsymmElastic1D
        • MultilinearElastic1D
        • PolyElastic1D
        • NLE1D01
        • Sinh1D
        • Tanh1D
        • CustomElastic1D
      • Hysteresis
        • AFC
        • AFCN
        • BilinearOO
        • BilinearPO
        • BoucWen
        • BWBN
        • Flag
        • MPF
        • MultilinearOO
        • MultilinearPO
        • RambergOsgood
        • SimpleHysteresis
        • SlipLock
        • SteelBRB
        • Trivial
        • Gap01
      • Viscosity
        • Kelvin
        • Maxwell
        • NonlinearViscosity
        • BilinearViscosity
        • CustomViscosity
        • Viscosity01
        • Viscosity02
        • CoulombFriction
        • Nonviscous01
      • vonMises
        • Subloading1D
        • ArmstrongFrederick1D
        • AFCO1D
        • Bilinear1D
        • BilinearMises1D
        • CustomGurson1D
        • CustomMises1D
        • ExpGurson1D
        • ExpMises1D
        • Mises1D
        • Multilinear1D
        • NonlinearGurson1D
        • VAFCRP1D
    • Material2D
      • AxisymmetricElastic
      • Concrete21
      • Concrete22
      • DuncanSelig
      • Elastic2D
      • Rebar2D
    • Material3D
      • CamClay
        • BilinearCC
        • ExpCC
        • NonlinearCamClay
        • ParabolicCC
      • Concrete
        • CDP
        • CDPM2
        • Rebar3D
        • TableCDP
        • CustomCDP
      • Damage
        • IsotropicDamage
        • LinearDamage
      • DruckerPrager
        • BilinearDP
        • ExpDP
        • CustomDP
        • NonlinearDruckerPrager
      • Elastic
        • BlatzKo
        • IsotropicElastic3D
        • IsotropicNonlinearElastic3D
        • MooneyRivlin
        • NLE3D01
        • OrthotropicElastic3D
        • Yeoh
      • Hoffman
        • BilinearHoffman
        • ExpHoffman
        • CustomHoffman
        • NonlinearHill
        • NonlinearHoffman
        • TimberPD
      • Sand
        • SimpleSand
        • DafalisaManzari
      • vonMises
        • ArmstrongFrederick
        • BilinearJ2
        • BilinearPeric
        • CustomGurson
        • TableGurson
        • CustomJ2
        • ExpGurson
        • ExpJ2
        • MultilinearJ2
        • NonlinearGurson
        • NonlinearJ2
        • NonlinearPeric
        • PolyJ2
        • VAFCRP
        • Subloading
    • MaterialOS
      • ElasticOS
    • Wrapper
      • Axisymmetric
      • Laminated
      • Parallel
      • PlaneStrain
      • PlaneSymmetric
      • PlaneStress
      • Rotation2D
      • Rotation3D
      • Sequential
      • Stacked
      • Uniaxial
      • OS146
      • OS146S
      • Substepping
  • Recorder
    • Recorder
    • OutputType
  • Section
    • Code
      • EU
      • NZ
      • US
    • Section1D
      • Circle1D
      • Fibre1D
      • Rectangle1D
      • TrussSection
    • Section2D
      • Bar2D
      • Box2D
      • Circle2D
      • CircularHollow2D
      • Fibre2D
      • HSection2D
      • ISection2D
      • Rectangle2D
      • TSection2D
    • Section3D
      • Bar3D
      • Box3D
      • Circle3D
      • CircularHollow3D
      • Fibre3D
      • ISection3D
      • Rectangle3D
      • TSection3D
    • SectionOS
      • Cell3DOS
      • Fibre3DOS
    • SectionNM
      • SectionNM
      • NM2D1
      • NM2D2
      • NM2D3
      • NM2D3K
      • NM3D1
      • NM3D2
      • NM3D3
      • NM3D3K
  • Solver
    • BFGS
    • MPDC
    • Newton
    • AICN
    • Ramm
  • Step
    • Overview
    • ArcLength
    • Buckle
    • Dynamic
    • Frequency
    • Optimization
    • Static
  • Developer
    • Prerequisites
    • C Style Interface
      • material
    • CPP Style Interface
      • material
      • element
      • constraint
Powered by GitBook
On this page
  • Syntax
  • Remarks
  • History Variable Layout
  • General Description of the Model
  • Unload from backbone
  • Reload from unload branch
  • Determination of Parameters
Edit on GitHub
  1. Material
  2. Material1D
  3. Concrete

ConcreteCM

Chang-Mander Concrete Model

Syntax

material ConcreteCM (1) (2) (3) (4) (5) (6) [7] [8] [9] [10]
# (1) int, unique material tag
# (2) double, elastic modulus
# (3) double, compression strength, should be negative but sign insensitive
# (4) double, tension strength, should be positive but sign insensitive
# (5) double, NC
# (6) double, NT
# [7] double, strain at compression strength, default: -2E-3
# [8] double, strain at tension strength, default: 1E-4
# [9] bool string, linear transition switch, default: false
# [10] double, density, default: 0.0

Remarks

  1. The Chang-Mander concrete model uses Tsai's equation as backbone curves for both tension and compression.

  2. Parameters NC and NT control the shapes of backbone curves. A detailed explanation is presented later.

  3. In the original model, the transition between compression and tension could sometimes have larger stiffness than initial stiffness. This is unlikely to be true in reality.

  4. A linear behaviour of part of hysteresis behaviour can be applied by turning on the linear transition switch. It shall be noted that a linear hysteresis rule is much more stable than the original version.

  5. The original CM model has some undefined behaviour which may cause stability issues. This is a simplified model.

History Variable Layout

location
value

initial_history(0)

unload_c_strain

initial_history(1)

unload_c_stress

initial_history(2)

reverse_c_strain

initial_history(3)

reverse_c_stress

initial_history(4)

residual_c_strain

initial_history(5)

residual_c_stiffness

initial_history(6)

unload_t_strain

initial_history(7)

unload_t_stress

initial_history(8)

reverse_t_strain

initial_history(9)

reverse_t_stress

initial_history(10)

residual_t_strain

initial_history(11)

residual_t_stiffness

initial_history(12)

connect_c_stress

initial_history(13)

connect_c_stiffness

initial_history(14)

connect_t_stress

initial_history(15)

connect_t_stiffness

initial_history(16)

inter_strain

initial_history(17)

inter_stress

initial_history(18)

reload_c_stiffness

initial_history(19)

reload_t_stiffness

General Description of the Model

Unload from backbone

Reload from unload branch

Reload before residual

Reload between two residuals

Reload after the opposite residual

Small Cycle

Determination of Parameters

The Tsai's equation (Tsai, 1988) can be expressed as

y=mx1+(m−nn−1)x+xnn−1.y=\dfrac{mx}{1+(m-\dfrac{n}{n-1})x+\dfrac{x^n}{n-1}}.y=1+(m−n−1n​)x+n−1xn​mx​.

where x=ε/εcx=\varepsilon/\varepsilon_cx=ε/εc​ or x=ε/εtx=\varepsilon/\varepsilon_tx=ε/εt​ is normalized strain and y=f/fcy=f/f_cy=f/fc​ and y=f/fty=f/f_ty=f/ft​ are normalized stress. The stress decreases to zero if m(n−1)>nm(n-1)>nm(n−1)>n and n>1n>1n>1. The initial stiffness is related to mtm_tmt​ and mcm_cmc​ by

E0=mEs=mtftεt=mcfcεc.E_0=mE_s=m_t\dfrac{f_t}{\varepsilon_t}=m_c\dfrac{f_c}{\varepsilon_c}.E0​=mEs​=mt​εt​ft​​=mc​εc​fc​​.

Once E0E_0E0​ is given, mcm_cmc​ and mtm_tmt​ are determined automatically.

The parameter nnn controls the slope of descending branch, normally nt>ncn_t>n_cnt​>nc​. Some empirical expressions are available to determine both mmm and nnn. But most are unit dependent. Users shall do manual conversion. For example,

mc=1+17.9fcfc in MPa,m_c=1+\dfrac{17.9}{f_c}\quad{}f_c\text{ in MPa},mc​=1+fc​17.9​fc​ in MPa,
mc=1+2600fcfc in psi,m_c=1+\dfrac{2600}{f_c}\quad{}f_c\text{ in psi},mc​=1+fc​2600​fc​ in psi,
nc=fc6.68−1.85>1fc in MPa,n_c=\dfrac{f_c}{6.68}-1.85>1\quad{}f_c\text{ in MPa},nc​=6.68fc​​−1.85>1fc​ in MPa,
nc=fc970−1.85>1fc in psi.n_c=\dfrac{f_c}{970}-1.85>1\quad{}f_c\text{ in psi}.nc​=970fc​​−1.85>1fc​ in psi.
PreviousConcreteNextConcreteExp

Last updated 2 years ago

example one
example two
example three
example four
example five
example six