WIPP-Drucker Model: Compression Test Showing Localization

Note

To view this project in FLAC3D, use the menu command Help ? Examples…. Choose “Creep/CompressionWIPPDrucker” and select “CompressionWIPPDrucker.f3dprj” to load. The project’s main data files are shown at the end of this example.

A compression test is performed with the viscoplastic model (WIPP-Drucker model) to demonstrate that the model is capable of simulating localization given an appropriate loading rate.

It causes FLAC3D to perform an unconfined compression test on a sample in which one of the material strength parameters (cohesion-drucker) reduces with increasing plastic strain. Under a low strain-rate, the response is monotonic, and the sample deforms in a uniform manner (Figure 1). If a similar test is performed at ten times the rate, localization occurs, even though the same boundary displacement is applied. Figure 2 shows that shear bands have formed in the rapid-loading case. The maximum load is nearly the same for the two loading-rate tests. However, the latter test exhibits global softening behavior.

Figure 1: Contours of strength parameter cohesion-drucker for slow-loading case.

Figure 2: Contours of strength parameter cohesion-drucker for rapid-loading case.

Data File

;------------------------------------------------------------------
;       Compression test -- WIPP-Drucker creep model
;-------------------------------------------------------------------
model new
model largestrain off
fish automatic-create off
model title "Compression test -- WIPP-Drucker creep model"
model configure creep
;
zone create brick size 20 1 60
zone cmodel wipp-drucker
call 'softening'
fish set @max_strength = 3.5e6,  @soft_rep=0
zone gridpoint fix velocity-y
zone gridpoint fix velocity-x range position-z 0
zone gridpoint fix velocity-z range position-z 0
zone gridpoint fix velocity-x range position-z 60 
zone gridpoint fix velocity-z range position-z 60 
;
zone property density 2600 shear 12.4e9 bulk 20.7e9 tension 1e15 ...
              friction-drucker 0.75 dilation-drucker 0.0 cohesion-drucker @max_strength ...
              constant-gas 1.987 activation-energy 12e3 exponent 4.9 ...
              constant-d 5.79e-36 constant-a 4.56 constant-b 127 ...
              creep-rate-critical 5.39e-8 temperature 300
;
model history creep time-total
zone history displacement-z position 0,0,0
zone history stress-zz position 10,0.5,0
zone history stress-zz position 10,0.5,60
model save 'ini'
; --- Slow test
model restore 'ini'
model creep timestep fix 100                   
zone gridpoint initialize velocity-z  7.5e-8 grad 0 0 -2.5e-9 
model cycle 5000
model save 'slow'
; --- Fast test
model restore 'ini'
model creep timestep fix 10
zone gridpoint initialize velocity-z 7.5e-7 grad 0 0 -2.5e-8   
model cycle 5000
model save 'fast'
;
return