Data Files for “Burger’s Contact Model: Stress Relaxation” Problem

burger.p2dat

;=============================================================================
; fname: burger.p2dat
;
; Relaxation test of Burger's contact model (initial 0.01 overlap) 
;=============================================================================
model new
;---------------------------
[k_set = 1.0e8]
[c_set = 1.0e8]
[f_set = 0.0  ]
[rad   = 0.05 ]
[un    = 0.01 ]
;---------------------------
fish define cal_cf
  cal_cf = comp.x(contact.prop(cpnt,'bur_force'))
  cal_age = mech.time.total - age0
end
;---------------------------
fish define compare_func
  local numPnt  = table.size(1)
  global errmax  = 0.0
  local a1 = c_set/k_set + c_set * (1.0/k_set + 1.0/k_set)
  local a2 = c_set*c_set/(k_set*k_set)
  local b1 = c_set
  local b2 = c_set*c_set/k_set
  local z1 = (-a1+math.sqrt(a1*a1-4.0*a2))/(2.0*a2)
  local z2 = (-a1-math.sqrt(a1*a1-4.0*a2))/(2.0*a2)
  local aa1 = (b2*z1+b1)/a2/(z1-z2)
  local aa2 = (b2*z2+b1)/a2/(z2-z1)
  loop n (1,numPnt)
    local tt = table.x(1,n)
    table.x(2,n) = table.x(1,n)
    table.y(2,n) = un*(aa1*math.exp(z1*tt)+aa2*math.exp(z2*tt))
    errmax  = math.max(errmax,math.abs(table.y(1,n)-table.y(2,n))/table.y(2,n))
  endLoop
  io.out(string.build(' Max. error = %1 %',string(errmax*100)))
end
;=====================================
contact cmat default model burger property ...
             'bur_knk' @k_set 'bur_cnk' @c_set 'bur_knm' @k_set ...
             'bur_cnm' @c_set 'bur_ksk' @k_set 'bur_csk' @c_set ...
             'bur_ksm' @k_set 'bur_csm' @c_set 'bur_fric' @f_set 
; --- Create two balls, assign properties and BCs.
model domain extent -1 1 
ball create id 1 rad @rad position-y 0.0
ball create id 2 rad @rad position-y [2.0*rad-un]
ball attribute density 2600.0
ball fix velocity-x velocity-y spin
model clean
[cpnt = contact.find('ball-ball',1)]
;
fish history name 1 @cal_cf
fish history name 2 @cal_age
history interval = 1000
[age0 = mech.time.total]
model mechanical timestep fix 2.840299219037086e-04
model solve time 10.0 
history export 1 vs 2 table 1
@compare_func
model save 'system-final.p2sav'
return
;=============================================================================
; eof: burger.p2dat

burger.p3dat

;=============================================================================
; fname: burger.p3dat
;
; Relaxation test of Burger's contact model (initial 0.01 overlap) 
;=============================================================================
model new
model title 'Relaxation test of Burger\'s contact model (initial 0.01 overlap)'
;---------------------------
[k_set = 1.0e8]
[c_set = 1.0e8]
[f_set = 0.0  ]
[rad   = 0.05 ]
[un    = 0.01 ]
;---------------------------
fish define cal_cf
  cal_cf = comp.x(contact.prop(cpnt,'bur_force'))
  cal_age = mech.time.total - age0
end
;---------------------------
fish define compare_func
  local numPnt  = table.size(1)
  global errmax  = 0.0
  local a1 = c_set/k_set + c_set * (1.0/k_set + 1.0/k_set)
  local a2 = c_set*c_set/(k_set*k_set)
  local b1 = c_set
  local b2 = c_set*c_set/k_set
  local z1 = (-a1+math.sqrt(a1*a1-4.0*a2))/(2.0*a2)
  local z2 = (-a1-math.sqrt(a1*a1-4.0*a2))/(2.0*a2)
  local aa1 = (b2*z1+b1)/a2/(z1-z2)
  local aa2 = (b2*z2+b1)/a2/(z2-z1)
  loop n (1,numPnt)
    local tt = table.x(1,n)
    table.x(2,n) = table.x(1,n)
    table.y(2,n) = un*(aa1*math.exp(z1*tt)+aa2*math.exp(z2*tt))
    errmax  = math.max(errmax,math.abs(table.y(1,n)-table.y(2,n))/table.y(2,n))
  endLoop
  io.out(string.build(' Max. error = %1 %',string(errmax*100)))
end
;=====================================
contact cmat default model burger property ...
             bur_knk @k_set bur_cnk @c_set bur_knm  @k_set ...
             bur_cnm @c_set bur_ksk @k_set bur_csk @c_set ...
             bur_ksm @k_set bur_csm @c_set bur_fric @f_set 
; --- Create two balls, assign properties and BCs.
model domain extent -1 1 
ball create id 1 rad @rad position-z 0.0
ball create id 2 rad @rad position-z [2.0*rad-un]
ball attribute density 2600.0
ball fix velocity-x velocity-y velocity-z spin
model clean
[cpnt = contact.find('ball-ball',1)
;
history fish @cal_cf
history fish @cal_age
history interval = 1000
[age0 = mech.time.total]
model mechanical timestep fix 1e-3
model solve time 10.0 
history export 1 vs 2 table 1
@compare_func
model save 'system-final.p3sav'
return
;=============================================================================
; eof: burger.p3dat
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