J2CyclicBoundingSurface Material

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J2CyclicBoundingSurface $matTag $G $K $Su $Den $h $m $ho $k_in $beta

$matTag	integer tag identifying material
$G	shear modulus
$K	bulk modulus
$su	undrained shear strength
$Den	mass density of the material
$h	hardening parameter
$m	hardening exponent
$h0	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"

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Code Developed by: Alborz Ghofrani, Pedro Arduino, U Washington

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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

Example

This example, provides an conventional triaxial compression test using one 8-node SSPBrick element and J2CyclicBOundingSurface material model.

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

References

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