# J2CyclicBoundingSurface Material ```tcl J2CyclicBoundingSurface $matTag $G $K $Su $Den $h $m $h0 $chi $beta ```
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integer tag identifying material |
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shear modulus |
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bulk modulus |
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undrained shear strength |
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mass density of the material |
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hardening parameter |
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hardening exponent |
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initial hardening parameter |
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initial damping (viscous). chi = 2*dr_o/omega (dr_o = damping ratio at zero strain, omega = angular frequency) |
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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
e.g. recorder Element -eleRange 1 $numElem -time -file stress.out stress
|Elastic: ||updateMaterialStage -material $matTag -stage 0 |- |Elastoplastic: ||updateMaterialStage -material $matTag -stage 1 |}
This example, provides an conventional triaxial compression test using one 8-node SSPBrick element and J2CyclicBOundingSurface material model.
```tcl
set strains {0.05}
for {set ii 0} {$ii < [llength $strains]} {incr ii} {
wipe
model BasicBuilder -ndm 3 -ndf 3
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
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 J2CyclicBoundingSurface 1 $G $K $su 1.7 $G 1.0 0.2 0.0 0.005 0.5
element SSPbrick 1 1 4 3 2 5 8 7 6 1
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
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
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] }
constraints Transformation test NormDispIncr 1e-9 50 1 algorithm Newton numberer Plain system SparseSPD integrator LoadControl 0.004 analysis Static
analyze 2000
wipe ```
Borja R., Amies A., "Multiaxial Cyclic Plasticity Model for Clays". Journal of Geotech. Engrg., 1994, 120(6):1051-1070