*HEADING
 : COULOMB FRICTION (2 SLIP DIRECTIONS, LAGRANGE MULTIPLIER METHOD)
*RESTART,WRITE,FREQ=0
*NODE, NSET=NALL
*ELEMENT,TYPE=B31,ELSET=BEAM
*BEAM SECTION,SECT=CIRC,ELSET=BEAM,MATERIAL=ELAS,TEMP=GRADIENTS
 0.564189584,
 0.,1.,0.,
*MATERIAL,NAME=ELAS
*ELASTIC
 30.E6,0.3
*INITIAL CONDITION,TYPE=TEMPERATURE
*rigid body,analytical surface=RS1,REFNODE=100
*surface,TYPE=CYLINDER,NAME=RS1
 START,0.,0.
 LINE,200.,0.
*surface,type=node,NAME=CN1
*surface,type=node,NAME=CN2
*CONTACT PAIR,INTERACTION=CI1
 CN1,RS1
*CONTACT PAIR,INTERACTION=CI2
 CN2,RS1
**
** CONTACT INTERACTION 1 (ANISOTROPIC MODEL)
**
** mu_1(p,t) = 0.005(t) + 2.5e-4*(p-100) with Tcrit = mu*p
** mu_2(p,t) = 0.005(t) + 3.3e-4*(p-100)
**
** where   mu    friction coefficient
**         p     contact pressure ( 100 < p < 1100)
**         t     temperature      (   0 < t < 20)
**
*SURFACE INTERACTION,NAME=CI1
 1.0,
*FRICTION, ANISOTROPIC, LAGRANGE, TAUMAX=1000.0
 0.000, 0.0000, 0.0,  100.0, 0
 0.025, 0.0330, 0.0,  200.0, 0
 0.050, 0.0660, 0.0,  300.0, 0
 0.075, 0.0990, 0.0,  400.0, 0
 0.100, 0.1320, 0.0,  500.0, 0
 0.125, 0.1650, 0.0,  600.0, 0
 0.150, 0.1980, 0.0,  700.0, 0
 0.175, 0.2310, 0.0,  800.0, 0
*GAP CONDUCTANCE
**
** CONTACT INTERACTION 2 (ZERO FRICTION)
**
*SURFACE INTERACTION,NAME=CI2
 1.0,
*FRICTION, ROUGH
*AMPLITUDE,NAME=AMP1
 0.0, 0.0, 0.2, 0.0625, 0.4, 0.1250, 0.6, 0.2500,
 0.8, 0.5, 1.0, 1.0
**
** STEP 1: ESTABLISH CONTACT (PRESCRIBED DISPLACEMENT)
**
*STEP, NLGEOM
 ESTABLISH CONTACT (PRECRIBED DISPLACEMENT)
*STATIC
 1.,1.
*BOUNDARY
 100,1,6,0.0
 2,1,1,0.0
 2,2,2,0.0
 2,4,6,0.0
 2,3,3,-1.e-5
 4,1,2,0.0
 4,3,3,-1.e-5
 4,4,6,0.0
*EL PRINT,F=0
*NODE PRINT,F=0
*OUTPUT,FIELD,FREQ=0
*ELEMENT OUTPUT
*OUTPUT,FIELD,FREQ=0
*NODE OUTPUT
*PRINT,CONTACT=YES
*OUTPUT,FIELD,FREQ=0
*CONTACT OUTPUT,VARIABLE=PRESELECT,SLAVE=CN1,MASTER=RS1
*OUTPUT,FIELD,FREQ=0
*CONTACT OUTPUT,VARIABLE=PRESELECT,SLAVE=CN2,MASTER=RS1
*CONTACT PRINT,F=0,SLAVE=CN1,MASTER=RS1
*CONTACT PRINT,F=0,SLAVE=CN2,MASTER=RS1
*END STEP
**
** STEP 2: ESTABLISH CONTACT (APPLY NORMAL PRESSURE = 300)
**
*STEP, NLGEOM
 ESTABLISH CONTACT (APPLY NORMAL PRESSURE = 300)
*STATIC
 1.,1.
*BOUNDARY,OP=NEW
 100,1,6,0.0
 2,1,1,0.0
 2,2,2,0.0
 2,4,6,0.0
 4,1,2,0.0
 4,4,6,0.0
*CLOAD
 2,3,-300.0
 4,3,-300.0
*END STEP
**                                                       _     _
** STEP 3: APPLY SHEAR FORCE IN THE X- AND Y-DIRECTIONS (Teq < Tcrit)
**         INCREASE PRESSURE FROM 300 to 450
**
** Given:    P=450.0, Ave. Temp=10.0, Tau_1=29.0, Tau_2=58.0,
** Results:  mu_1=0.1375, mu_2=0.1655
**           _          _
**           Teq=62.23, Tcrit=68.44   --> "Sticking"
**
*STEP, NLGEOM
 APPLY SHEAR FORCE IN THE X- AND Y-DIRECTIONS (Teq < Tcrit)
*STATIC
 .1,1.
*BOUNDARY,OP=NEW
 100,1,6,0.0
 2,4,6,0.0
 4,1,2,0.0
 4,4,6,0.0
*CLOAD, OP=NEW
 2,1,29.0
 2,2,58.0
 2,3,-450.0
 4,3,-300.0
*OUTPUT,FIELD,FREQ=1
*CONTACT OUTPUT,VARIABLE=PRESELECT,SLAVE=CN1,MASTER=RS1
CSTRESS,CDISP
*CONTACT PRINT,F=1, SLAVE=CN1,MASTER=RS1
*PRINT,CONTACT=YES
*END STEP
**
** STEP 4: REMOVE SHEAR FORCES
**
*STEP, NLGEOM
 REMOVE SHEAR FORCES
*STATIC
 .1,1.
*BOUNDARY,OP=NEW
 100,1,6,0.0
 2,4,6,0.0
 4,1,2,0.0
 4,4,6,0.0
*CLOAD, OP=NEW
 2,3,-450.0
 4,3,-300.0
*END STEP
**
** STEP 5: CHANGE FRICTION TO AN ISOTROPIC MODEL AND APPLY
**         SHEAR FORCES IN X- AND Y-DIRECTION. PRESSURE IS
**         INCREASED TO 550.
**
** Given:    P=550.0, Ave. Temp=10.0, Tau_1=-25.0, Tau_2=-50.0
** Results:  mu=0.2125, Tcrit=116.875
**           Teq=55.9          Teq < Tcrit  --> Sticking
**           ks=Tcrit/Gcrit=46,750.0
**
*STEP, NLGEOM
 CHANGE FRICTION TO AN ISOTROPIC MODEL
*STATIC
 .1,1.0
**
** NEW FRICTION MODEL FOR CONTACT INTERACTION CN1
**
** mu(p,t)=0.002(t) + 3.3e-4(p)                100 < p <= 500
** mu(p,t)=0.1650 + 0.002(t) + 5.5e-4(p-500)   500 < p <= 800
**                                             0 <= t <= 100
**
*CHANGE FRICTION, INTERACTION=CI1
*FRICTION, LAGRANGE
 0.0330, , 100.0,   0.0
 0.0660, , 200.0,   0.0
 0.0990, , 300.0,   0.0
 0.1320, , 400.0,   0.0
 0.1650, , 500.0,   0.0
 0.2200, , 600.0,   0.0
 0.3300, , 800.0,   0.0
 0.2330, , 100.0, 100.0
*BOUNDARY,OP=NEW
 100,1,6,0.0
 2,4,6,0.0
 4,1,2,0.0
 4,4,6,0.0
*CLOAD, OP=NEW
 2,1,-25.0
 2,2,-50.0
 2,3,-550.0
 4,3,-300.0
*END STEP
**
**  STEP 6: REMOVE SHEAR FORCES
**
*STEP, NLGEOM
 REMOVE SHEAR FORCES (2)
*STATIC
 .1,1.0
*BOUNDARY,OP=NEW
 100,1,6,0.0
 2,4,6,0.0
 4,1,2,0.0
 4,4,6,0.0
*CLOAD, OP=NEW
 2,3,-550.0
 4,3,-300.0
*END STEP
**
** STEP 7: RESET THE FRICTION MODEL TO THE ORIGINAL MODEL
**         AND APPLY A SLIP IN THE X AND Y DIRECTIONS.
**         PRESSURE IS INCREASED TO 850.
**
** Given:   P=850, Temp=10.0, G_1=0.2, G_2=0.4
** Results: mu_1=0.2375, mu_2=0.2975
**          _       _
**          Tcrit = Teq = 228.82   "slipping"
**          T_1=74.8, T_2=234.9
**
*STEP, NLGEOM
 RESET THE FRICTION MODEL TO THE ORIGINAL MODEL
*STATIC
 .1,1.0
*CHANGE FRICTION, RESET, INTERACTION=CI1
*BOUNDARY,OP=NEW
 100,1,6,0.0
 2,4,6,0.0
 2,1,1,0.2
 2,2,2,0.4
 4,1,2,0.0
 4,4,6,0.0
*CLOAD, OP=NEW
 2,3,-850.0
 4,3,-300.0
*END STEP
**
** STEP 8: CHANGE FRICTION TO A SLIP VELOCITY DEPENDENT MODEL
**
*STEP, NLGEOM, AMP=STEP
 CHANGE FRICTION TO A SLIP VELOCITY DEPENDENT MODEL
*STATIC
 ,1.0
*CHANGE FRICTION, INTERACTION=CI1
*FRICTION, ROUGH
*CHANGE FRICTION, INTERACTION=CI2
*FRICTION, LAGRANGE
 0.2, 0.0, 100
 0.0, 2.0, 100
 0.4, 0.0, 500
 0.2, 2.0, 500
*BOUNDARY, OP=NEW
 100,1,6,0.0
 2,1,2,0.0
 2,4,6,0.0
 4,1,2,0.0
 4,4,6,0.0
*CLOAD, OP=NEW
 2,3,-300.0
 4,3,-300.0
*CONTACT PRINT,F=0,SLAVE=CN2,MASTER=RS1
*OUTPUT,FIELD,FREQ=0
*CONTACT OUTPUT,VARIABLE=PRESELECT,SLAVE=CN2,MASTER=RS1
*END STEP
**
** STEP 9: SLIP IN THE X DIRECTION WITH VARIABLE SLIP RATE
**
** Given:   P=300
** Results: mu_s=0.3 and mu_k=0.1
**          Tau=30.0
**
*STEP, NLGEOM
 SLIP IN THE X DIRECTION WITH A VARIABLE SLIP RATE
*STATIC
 .1,1.0
*BOUNDARY, OP=MOD, AMP=AMP1
 4,1,1,1.0
*CONTACT PRINT,F=9999,SLAVE=CN2,MASTER=RS1
*OUTPUT,FIELD,FREQ=9999
*CONTACT OUTPUT,VARIABLE=PRESELECT,SLAVE=CN2,MASTER=RS1
CSTRESS,CDISP
*END STEP