Results for 2D RJB model

For the 2D RJB model the parameters we are using are K_C = 100, K_L = 1, \sigma_F = 1, and \sigma_R is random distributed in the range 0.0 to 0.5 . These parameters are the same as M. Anghel et al. (cond-mat/0002459).

Results for the 2D RJB model with zero loading velocity

• Cluster size distribution for N = 256 x 256 at R = 30 (see plot) after decomposing into three ranges which are similar as M. Anghel's.
• Metrics for N = 64 x 64 at R = 1 and R = 10 (see energy metric plot, stress metric plot and displacement metric plot).
• Radius of gyration of an event as a function of cluster size for N = 64 x 64 at R = 1 and R = 10 (see plot).
• Average stress just before rupture within a radius r of the initiator for N = 64 x 64 at R = 1 and R = 10. See plot for average over all events. Generally speaking, with the increase of r, the average stress for R = 1 drops to the backgound stress more quickly than that of R = 10. Because the correlation length may be differen for different event sizes we plot R = 1 and R = 10 for average over certain cluster size within 10 percentage variant). For R = 1, the average stressesdrop to the backgound stress quickly, showing a small correlation length around r = 5. While, the average stresse for R = 10 drops gradually to the backgound, showing a bigger correlation length around r = 20.
• Average stress over all blocks involved in an event just before rupture as the function of cluster size for N = 64 x 64 at R = 1 and R = 10 (see plot). For R = 1, the averager stress drops to the back ground stress quickly with the increase of cluster size. While it drops to the back ground much slowlier for R = 10.
• Minimum stress of all blocks involved in an event just before rupture as the function of cluster size shows the similar behaviour as average stress over all blocks involved in an event shown above except droping to the zero stress. See plot for N = 64 x 64 at R = 1 and R = 10.
• Radius of gyration of a tipical event with the number of failed blocks (4000) almost equals to the system size N =64 x 64 = 4096 as the function of evolution time (see plot ). The corresponding sites involved are shown in plots of event 1, event 2, event 3, event 4, and event 5. We also calculated the average stress just before rupture of an event as function of evloution time, see plot for all five events. The average stress are over sites which failed between two points of evlution time.
• Radius of gyrations of three tipical events with the number of failed blocks (s =45204, 42147, and 40163) close to the system size N =256 x 256 = 65536 (R = 30) as the function of evolution time (see plot). Plots of event 1, event 2, and event 3 show the evolutions of failed sites. The corresponding evolutions of average stress over sites at time t are shown in the plot. When the system is in the state right before the first fail of a block, the colored distributions of stresses are shown in event 1 (x = 137, y = 59 for the first failed block), event 2 (x = 52, y = 96 for the first failed block), and event 3 (x = 116, y = 50 for first failed block), and the averaged stress over sites within a radius of r centered at first failed site is shown in linear-linear plot or log-log plot for all such events (The individual plot is plot 1, plot 2, and plot 3 ).
• The evolution of corresponding quantities for two different kind of events are shown in the plots in the table below. The center of mass is calculated from all sites failed already at that time. 

  size of event	s = 3178	s = 45204
  graphic stress distribution at (t = 0)	plot	plot
  position of initiator (t =0)	x =2, y = 167	x = 137, y = 59
  number of failed sites at time t	plot	plot
  total # of failed sites for t = 0 to t	plot	plot
  radius of gyration	plot	plot
  center of mass (all failed sites till t)	plot	plot
  avrg Stress at t = 0	plot	plot
  avrg Stress within a radius (t =1)	plot	plot
  avrg Stress within a radius (t =2)	plot	plot
  avrg Stress within a radius (t =3)	plot	plot
  avrg Stress within a radius (t =4)	plot	plot
  avrg Stress within a radius (t =5)	plot	plot
  avrg Stress within a radius (t =6)	plot	plot
  avrg Stress within a radius (t =7)	plot	plot
  avrg Stress within a radius (t =8)	plot	plot
  avrg Stress within a radius (t =9)	plot	plot
  avrg Stress within a radius (t =10)	plot	plot
  avrg Stress within a radius (t =11)	plot	plot
  avrg Stress within a radius (t =12)	plot	plot
  avrg Stress within a radius (t =13)	plot	plot
  avrg Stress within a radius (t =14)	plot	plot
  avrg Stress within a radius (t =15)	plot	plot
  avrg Stress within a radius (t =16)	plot	plot
  avrg Stress within a radius (t =17)	plot	plot
  avrg Stress within a radius (t =18)	plot	plot
  avrg Stress within a radius (t =19)	plot	plot
  avrg Stress within a radius (t =20)	plot	plot
  avrg Stress within a radius (t =30)	plot	plot
  avrg Stress within a radius (t =40)	plot	plot
  avrg Stress within a radius (t =50)	plot	plot
  avrg Stress within a radius (t =60)	plot	plot
  avrg Stress within a radius (t =70)	plot	plot
  avrg Stress within a radius (t =80)	plot	plot
  avrg Stress within a radius (t =90)	plot	plot
  avrg Stress within a radius (t =100)	plot	plot
  avrg Stress within a radius (t =110)	plot	plot
  avrg Stress within a radius (t =120)	plot	plot
  avrg Stress within a radius (t =130)	last plot at t =129	plot
  avrg Stress within a radius (t =140)		plot
  avrg Stress within a radius (t =150)		plot
  avrg Stress within a radius (t =200)		plot
  avrg Stress within a radius (t =250)		plot
  avrg Stress within a radius (t =300)		plot
  avrg Stress within a radius (t =370)		plot at t = 370

  
  

Updated on 20 Feburary 2003.