FLAC3D Theory and Background • Constitutive Models

Single Zone Uniaxial and Simple Shear Test

Note

To view this project in FLAC3D, use the menu command Help ► Examples…. The project’s main data file is shown at the end of this example.

In this example to test the von-mises model, a 1 m x 1 m single zone is generated, and the following elastic material properties are assigned: Young’s modulus \(E\) = 2 x 10⁵ Pa, Poisson’s ratio \(\nu\) = 0.2, and yield strength \(\sigma_Y\) = 1000 Pa. The properties are listed in Table 1.

Table 1: Von Mises Model Properties

Parameter	Value
\(E\) (Pa)	2e5
\(\nu\)	0.25
\(\sigma_Y\) (Pa)	100

The first test is the uniaxial loading with an unloading-reloading cycle. This test inputs a hardening modulus \(H\) = 0.5e5 Pa. Figure 1 presents the result. The uniaxial yield strengths in the extension and compression directions are compatible to the input value 100 Pa. The pre-yielding slope of the uniaxial stress vs. uniaxial strain is exactly the input Young’s modulus. The elasto-plastic tangent modulus (see von-mises model) is exactly \(EH/(E+H)\) = 0.4e5 Pa.

The second test is the simple shear loading with an unloading-reloading cycle. This test inputs a zero hardening modulus. Figure 2 presents the result. The simple shear yield strengths in the extension and compression directions are compatible to the input value \(\sigma_Y/\sqrt{3} = 57.735\) Pa. The pre-yielding slope of the shear stress vs. shear strain is exactly the shear modulus \(G = 8e4\) Pa.

Figure 1: Uniaxial stress vs. uniaxial strain.

Figure 2: Shear stress vs. shear strain.

Data File

SingleZoneUniAxialVonMises.dat

; single zone uniaxial von-mises test
model new
model large-strain off
model title "Single Zone Uniaxial Test - Swell Model"
model gravity (0,0,-10)
;
zone create brick size 1 1 1
zone face skin
zone cmodel assign von-mises
zone property density 1000 young 2e5 poisson 0.25 strength-yield 100 ...
              modulus-plastic 0.5e5
zone face apply velocity-z 0.0 range group 'Bottom'
zone gridpoint fix velocity(0,0,0) range id 1
;
history interval 100
zone history displacement-z position (1,1,1)
zone history stress-zz position (0.5,0.5,0.5)
;
zone face apply velocity-z  1e-7 range group 'top'
model step 10000
zone face apply velocity-z -1e-7 range group 'top'
model step 20000
zone face apply velocity-z  1e-7 range group 'top'
model step 20000

model save 'vm-uniaxial'

SingleZoneSimpleShearVonMises.dat

; single zone simple shear von-mises test
model new
model large-strain off
model title "Single Zone Simple Shear Test - Swell Model"
model gravity (0,0,-10)
;
zone create brick size 1 1 1
zone face skin
zone cmodel assign von-mises
zone property density 1000 young 2e5 poisson 0.25 strength-yield 100 
zone gridpoint fix velocity
;
history interval 100
zone history displacement-x position (1,1,1)
zone history stress-xz position (0.5,0.5,0.5)
;
zone face apply velocity-x  1e-7 range group 'top'
model step 10000
zone face apply velocity-x -1e-7 range group 'top'
model step 20000
zone face apply velocity-x  1e-7 range group 'top'
model step 20000

model save 'vm-ss'