J2CyclicBoundingSurface Material

This command is used to construct a multi-dimensional J2CyclicBoundingSurface material. nDmaterial J2CyclicBoundingSurface $matTag $G $K $Su $Den $h $m $ho $k_in $beta $matTag integer tag identifying material $G0 shear modulus $K bulk modulus $Su undrained shear strength $Den mass density of the material $h hardening parameter $m hardening exponent $ho initial hardening parameter $k_in initial damping (viscous) = 2 psi_o/ omega (psi_o = damping ratio at zero strain, omega = angular frequency) $beta integration variable (0 = explicit, 1 = implicit, 0.5 = midpoint rule

The material formulations for the J2CyclicBoundingSurface object are "ThreeDimensional" and "PlaneStrain"

Code Developed by: Alborz Ghofrani, Pedro Arduino, U Washington Contents [hide]

   1 Notes
   2 Theory
       2.1 Elasticity
       2.2 Critical State Line
       2.3 Yield Surface
       2.4 Plastic Strain Increment
   3 Example
   4 References

[edit] Notes

   Valid Element Recorder queries are
       stress, strain

e.g.

recorder Element -eleRange 1 $numElem -time -file stress.out  stress

   Elastic or Elastoplastic response could be enforced by 

           Elastic: 	updateMaterialStage -material $matTag -stage 0
           Elastoplastic: 	updateMaterialStage -material $matTag -stage 1 

[edit] Theory

[edit] Example

This example, provides an undrained confined triaxial compression test using one 8-node SSPBrickUP element and ManzariDafalias material model.

1. HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH #
2. 3D Conventional Triaxial Compression Test Using One Element #
3. University of Washington, Department of Civil and Environmental Eng #
4. Computational Geotechnics Eng Group, A. Ghofrani, P. Arduino - Dec 2013 #
5. Basic units are m, Ton(metric), s #
6. HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH #

set strains {0.05}

for {set ii 0} {$ii < [llength $strains]} {incr ii} { # debug material model wipe

# ################################# # build model: -ndm 3 -ndf 3 # ################################# model BasicBuilder -ndm 3 -ndf 3

# create the materials node 1 0.00000000 0.00000000 0.00000000 node 2 0.00000000 1.00000000 0.00000000 node 3 1.00000000 1.00000000 0.00000000 node 4 1.00000000 0.00000000 0.00000000 node 5 0.00000000 0.00000000 1.00000000 node 6 0.00000000 1.00000000 1.00000000 node 7 1.00000000 1.00000000 1.00000000 node 8 1.00000000 0.00000000 1.00000000

# create the materials

set E 20000.0 set nu 0.499 set G [expr $E / 2.0 / (1 + $nu)] set K [expr $E / 3.0 / (1 - 2.0 * $nu)]

set R [expr 100.0] set su [expr sqrt(3.0 / 8.0) * $R] # nDMaterial ElasticIsotropic 1 100000 0.3 # nDMaterial J2CyclicBoundingSurface tag? G? K? su? rho? h? m? k_in? chi? beta? in kpa nDMaterial J2CyclicBoundingSurface 1 $G $K $su 1.7 $G 1.0 0.0 0.0 0.5

# create the elements element SSPbrick 1 1 4 3 2 5 8 7 6 1

# create the fixities fix 1 1 1 1 fix 2 1 0 1 fix 3 0 0 1 fix 4 0 1 1 fix 5 1 1 0 fix 6 1 0 0 fix 7 0 0 0 fix 8 0 1 0

# recorders recorder Node -file "displacement.out" -nodeRange 1 8 -dof 1 2 3 disp recorder Node -file "velocity.out" -nodeRange 1 8 -dof 1 2 3 vel recorder Node -file "reactions.out" -nodeRange 1 8 -dof 1 2 3 reaction recorder Element -file "stress.out" -ele 1 stress recorder Element -file "strain.out" -ele 1 strain

# load pattern pattern Plain 1 {Series -time {0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0} -values {0.0 1.0 0.0 -1.0 0.0 1.0 0.0 -1.0 0.0} -factor -1.0} { sp 5 3 [lindex $strains $ii] sp 6 3 [lindex $strains $ii] sp 7 3 [lindex $strains $ii] sp 8 3 [lindex $strains $ii] }

# analysis constraints Transformation test NormDispIncr 1e-9 50 1 algorithm Newton numberer Plain system SparseSPD integrator LoadControl 0.004 analysis Static

analyze 2000

wipe

[edit] References

Borja R., Amies A., "Multiaxial Cyclic Plasticity Model for Clays". Journal of Geotech. Engrg., 1994, 120(6):1051-1070