WIPP-Drucker Model: Compression Test Showing Localization (FLAC2D)

Model Verification

The project file for this example may be viewed/run in FLAC2D.[1] The main data file used is shown at the end of this example.

How To Read and Use Examples

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 FLAC2D 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 large-strain off
fish automatic-create off
model title "Compression test -- WIPP-Drucker creep model"
model configure creep
;
zone create quadrilateral size 20 60
zone cmodel wipp-drucker
program call 'softening'
[global max_strength = 3.5e6]
[global soft_rep = 0]

zone gridpoint fix velocity-x range position-y 0
zone gridpoint fix velocity-y range position-y 0
zone gridpoint fix velocity-x range position-y 60
zone gridpoint fix velocity-y range position-y 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-y position 0,0
zone history stress-yy position 10,0
zone history stress-yy position 10,60
zone mech safety-factor 3.1
model save 'ini'
; --- Slow test
model restore 'ini'
model creep timestep fix 100
zone gridpoint initialize velocity-y  7.5e-8 gradient 0 -2.5e-9
model cycle 5000
model save 'slow'
; --- Fast test
model restore 'ini'
model creep timestep fix 5
zone gridpoint initialize velocity-y 7.5e-7 gradient 0 -2.5e-8
model cycle 4450
model save 'fast'

Endnote

[1]

This example is listed under the present document title in the i Examples dialog (use the menu command Help -> Examples… to access).