/MAT/LAW24 (CONC)

Block Format Keyword This material law models brittle elastic-plastic behavior of concrete. A yield surface is deduced from an Ottosen triaxial failure surface. Orthotropic damage is modeled and cracks can open and close.

An optional embedded model allows to take into account steel rebars into a homogenized model. Otherwise, rebars are usually meshed with 1D or 3D elements.

This material law is compatible with solid elements only.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW24/mat_ID/unit_ID or /MAT/CONC/mat_ID/unit_ID
mat_title
ρ i                
Ec ν Icap          
fc ft/fc fb/fc f2/fc s0/fc
Ht Dsup ε max        
ky ρ t ρ c Hbp Etc
α y α f vmax        
fk f0 Hv0 Eps0 hfac
E σ y Et        
α 1 α 2 α 3        

Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

 
unit_ID Unit Identifier.

(Integer, maximum 10 digits)

 
mat_title Material title.

(Character, maximum 100 characters)

 
ρ i Initial density.

(Real)

[ kg m 3 ]
Ec Concrete elasticity Young's modulus.

(Real)

[ Pa ]
ν Poisson's ratio.

(Real)

 
Icap Cap formulation flag. 8
= 0 (Default)
Improved cap formulation.
= 1
Original cap formulation (initial formulation used in Radioss 14.0 and older).
= 2
Cap model with updated multi-axial and hydrostatic load representation (recommended).

(Integer)

 
fc Concrete uniaxial compression strength.

(Real)

[ Pa ]
ft/fc Concrete tensile strength ratio.

Default = 0.10 (Real)

 
fb/fc Concrete biaxial strength ratio.

Default = 1.20 (Real)

 
f2/fc Concrete confined strength ratio.

Default = 4.00, if Icap = 0 or 1

Default = 7.00 if Icap = 2

(Real)

 
s0/fc Concrete confining stress ratio.

Default = 1.25 (Real)

 
Ht Concrete tensile tangent modulus.

Default = -Ec (Real)

[ Pa ]
Dsup Concrete maximum damage.

Default = 0.99999 (Real)

 
ε max Concrete data total failure strain.

Default = 1020 (Real)

 
ky Concrete plasticity initial value of hardening parameter (first part).

Default = 0.5 (Real)

 
ρ t Concrete plasticity failure/plastic transition pressure (first part).

Default = 0.0 (Real)

[ Pa ]
ρ c Concrete plasticity proportional yield transition pressure (first part).

Default = -fc/3 (Real)

[ Pa ]
Hbp Concrete plasticity base plastic modulus (first part). 3

Default is computed by Starter (Real)

[ Pa ]
Etc Concrete plastic modulus. 3

(Real)

[ Pa ]
α y Concrete plasticity dilatancy factor at yield (second part).

Default = -0.2, if Icap= 0 or 2

Default = 0.0, if Icap= 1

(Real)

 
α f Concrete plasticity dilatancy factor at failure (second part).

Default = 0.0 (Real)

 
vmax Concrete plasticity maximum volumetric compaction ( < 0 ) (second part).

Default = -0.35 (Real)

 
fk Initial beginning of cap. 7

Default = -fc/3 (Real)

[ Pa ]
f0 Initial end of cap. 7

Default = -0.8 fc, if Icap = 0 or 1

Default = -2 fc, if Icap = 2

(Real)

[ Pa ]
Hv0 Initial triaxial plastic modulus.

Default = 0.2 Ec (Real)

[ Pa ]
Eps0 Reference plastic strain for plastic hardening (Icap = 2 only).

Default = 0.02 (Real)

 
hfac Reduction factor for plastic hardening default (Icap = 2 only).

Default = 0.1 (Real)

 
E Steel properties Young's modulus.

(Real)

[ Pa ]
σ y Yield strength.

(Real)

[ Pa ]
Et Tangent modulus.

(Real)

[ Pa ]
α 1 Rebar section fraction of reinforcement in direction 1.

(Real)

 
α 2 Rebar section fraction of reinforcement in direction 2.

(Real)

 
α 3 Rebar section fraction of reinforcement in direction 3.

(Real)

 

Example (Concrete)

#RADIOSS STARTER
/UNIT/1
unit for mat
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  2. MATERIALS:
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/CONC/1/1
concrete - air dry
#              RHO_I
               .0024  
#                E_c                  NU      Icap
               41200                  .2         0
#                 fc            ft_on_fc            fb_on_fc            f2_on_fc            s0_on_fc
                  44                   0                   0                   0                   0
#                H_t               D_sup             EPS_max
                   0                   0                   0
#                k_y                 r_t                 r_c                H_bp
                   0                   0                   0                   0
#            ALPHA_y             ALPHA_F               V_max
                -0.2                -0.1                   0
#                f_k                 f_0                H_v0                eps0               h_fac
                   0                   0                   0
#                  E             sigma_y                 E_t
                   0                   0                   0
#             ALPHA1              ALPHA2              ALPHA3
                   0                   0                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

  1. This material law can be used with only four parameters: ρ i , E c , ν MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqyWdi3aaS baaSqaaiaadMgaaeqaaOGaaiilaiaadweadaWgaaWcbaGaam4yaaqa baGccaGGSaGaeqyVd4gaaa@3DDA@ and f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOza8aadaWgaaWcbaWdbiaadogaa8aabeaaaaa@3839@ . Values f t ,   f b ,   f 2 ,   s 0   MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOza8aadaWgaaWcbaWdbiaadshaa8aabeaak8qacaGGSaGaaeii aiaadAgapaWaaSbaaSqaa8qacaWGIbaapaqabaGcpeGaaiilaiaabc cacaWGMbWdamaaBaaaleaapeGaaGOmaaWdaeqaaOWdbiaacYcacaqG GaGaam4Ca8aadaWgaaWcbaWdbiaaicdaa8aabeaak8qacaGGGcaaaa@4408@ are input as ratios of f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOza8aadaWgaaWcbaWdbiaadogaa8aabeaaaaa@3839@ and are based on the failure of a typical concrete material.
  2. The parameters for the damage model are:

    tensile_damage
    Figure 1. Stress Strain Curve for LAW24 Damage Model. meridians of failure and yield surfaces

    Where, f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape GaamOza8aadaWgaaWcbaWdbiaadogaa8aabeaaaaa@3839@ is the uniaxial compression strength.

  3. The default value of the plastic modulus in compression is defined as:(1)
    E tc = ( 1 k y ) E c 2.10 3 E c k y f c MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamyra8aadaWgaaWcbaWdbiaadshacaWGJbaapaqabaGcpeGaeyyp a0ZaaSaaa8aabaWdbmaabmaapaqaa8qacaaIXaGaeyOeI0Iaam4Aa8 aadaWgaaWcbaWdbiaadMhaa8aabeaaaOWdbiaawIcacaGLPaaacaWG fbWdamaaBaaaleaapeGaam4yaaWdaeqaaaGcbaWdbiaaikdacaGGUa GaaGymaiaaicdapaWaaWbaaSqabeaapeGaeyOeI0IaaG4maaaakiaa dweapaWaaSbaaSqaa8qacaWGJbaapaqabaGcpeGaeyOeI0Iaam4Aa8 aadaWgaaWcbaWdbiaadMhaa8aabeaak8qacaWGMbWdamaaBaaaleaa peGaam4yaaWdaeqaaaaaaaa@4EBD@
    The base plastic modulus is then calculated:(2)
    H p b = E c E tc ( E c E tc ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVCI8FfYJH8YrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbb a9q8WqFfeaY=biLkVcLq=JHqpepeea0=as0Fb9pgeaYRXxe9vr0=vr 0=vqpWqaaeaabiGaciaacaqabeaadaqaaqaaaOqaaabaaaaaaaaape Gaamisa8aadaqhaaWcbaWdbiaadchaa8aabaWdbiaadkgaaaGccqGH 9aqpdaWcaaWdaeaapeGaamyra8aadaWgaaWcbaWdbiaadogaa8aabe aak8qacaWGfbWdamaaBaaaleaapeGaamiDaiaadogaa8aabeaaaOqa a8qadaqadaWdaeaapeGaamyra8aadaWgaaWcbaWdbiaadogaa8aabe aak8qacqGHsislcaWGfbWdamaaBaaaleaapeGaamiDaiaadogaa8aa beaaaOWdbiaawIcacaGLPaaaaaaaaa@477E@


    Figure 2.
  4. The yield envelope is derived from the failure envelope using a scale factor k ( σ m , k 0 ) .
    (3)
    f = r k ( σ m , k 0 ) r f = 0
  5. The scale factor k ( σ m , k 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4Aamaabm aabaGaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaOGaaiilaiaadUgadaWg aaWcbaGaaGimaaqabaaakiaawIcacaGLPaaaaaa@3DEB@ is a function of mean stress (pressure), and k 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4AamaaBa aaleaacaaIWaaabeaaaaa@37CC@ models the hardening effect. It is related to the surface where elasticity domain reaches its limit. In tension k ( σ m , k 0 ) = 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4Aamaabm aabaGaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaOGaaiilaiaadUgadaWg aaWcbaGaaGimaaqabaaakiaawIcacaGLPaaacqGH9aqpcaaIXaaaaa@3FAC@ and the yield envelope and failure envelope are superimposed. In compression the scale factor k ( σ m , k 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4Aamaabm aabaGaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaOGaaiilaiaadUgadaWg aaWcbaGaaGimaaqabaaakiaawIcacaGLPaaaaaa@3DEB@ depends on Icap value (0, 1 or 2).


    Figure 3. Scale factor k ( σ m , k 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaci4Aamaabm aabaGaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaOGaaiilaiaadUgadaWg aaWcbaGaaGimaaqabaaakiaawIcacaGLPaaaaaa@3DEB@ shapes the yield surface from the failure surface
    • For Icap =0 or 1: (4)
      k y k σ m , k 0 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4AamaaBa aaleaacaWG5baabeaakiaaykW7cqGHKjYOcaaMc8Uaam4Aamaabmaa baGaeq4Wdm3aaSbaaSqaaiaad2gaaeqaaOGaaGPaVlaacYcacaaMc8 Uaam4AamaaBaaaleaacaaIWaaabeaaaOGaayjkaiaawMcaaiaaykW7 cqGHKjYOcaaMc8UaaGymaaaa@4D72@


      Figure 4.
    • For Icap =2 (with cap): (5)
      0k σ m , k 0 1 MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGimaiaayk W7cqGHKjYOcaaMc8Uaam4AamaabmaabaGaeq4Wdm3aaSbaaSqaaiaa d2gaaeqaaOGaaGPaVlaacYcacaaMc8Uaam4AamaaBaaaleaacaaIWa aabeaaaOGaayjkaiaawMcaaiaaykW7cqGHKjYOcaaMc8UaaGymaaaa @4C08@


      Figure 5.

    Where, r = 2 J 2 = 2 3 σ V M and σ m = I 1 3 is mean stress (pressure), I 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamysamaaBa aaleaacaaIXaaabeaaaaa@37AB@ and J 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOsamaaBa aaleaacaaIYaaabeaaaaa@37AD@ are the first and second stress invariant. The factor k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4Aaaaa@36C6@ can be output in time history file under VK keyword.

  6. There is no cap effect when α y = α f = 0 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaadMhaaeqaaOGaeyypa0JaeqySde2aaSbaaSqaaiaadAga aeqaaOGaeyypa0JaaGimaaaa@3E4F@ because there is no compaction. The default values of dilatancy parameters α y MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaadMhaaeqaaaaa@38BF@ and α f MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaadMhaaeqaaaaa@38BF@ were modified for Icap = 0 or 2 in Radioss 2017. These parameters should be negative with recommended values of -0.2 and -0.1, respectively. The default cap formulation was updated in Radioss 2017. To enable the original cap formulation used in Radioss 14.0 and older, set Icap = 1. The Icap =2 formulation is more accurate for triaxial and hydrostatic loadings. The cap hardening is a function of the compaction coefficient. The shear hardening modulus is reduced in the transition region which assures better stability. Icap = 2 must be used to output plastic strain using /ANIM/BRICK/EPSP or /H3D/SOLID/EPSP.
  7. The embedded rebar model is optional. It uses an elastic-plastic with hardening material model. When defining rebar section fractions, a homogenized behavior is assumed for each element. The element should be large enough to stand for a Representative Elementary Volume (REV). This homogenized model is mostly used with large structures and a coarse mesh. Otherwise, rebar can be modeled with trusses, springs, beams, or even brick elements. the section ratio of rebars must be provided α 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaaigdaaeqaaaaa@387C@ , α 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaaigdaaeqaaaaa@387C@ , and α 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS baaSqaaiaaigdaaeqaaaaa@387C@ :


    Figure 6.
  8. The rebar directions must be defined in the orthotropic solid property /PROP/TYPE6. Otherwise, the local element coordinate r, s, and t are taken respectively as directions 1, 2, and 3; unless Isolid = 1 or 2 is used with Iframe = 2; in which case the orthotropic directions 1, 2 and 3 are defined with the local co-rotating element coordinate r, s, and t, when time = 0.
  9. In an axisymmetrical analysis, direction 3 is the θ direction.
  10. The 10 node tetrahedron elements are compatible with this law.