J2CyclicBoundingSurface Material: Difference between revisions

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This command is used to construct a multi-dimensional J2CyclicBoundingSurface material.
{{CommandManualMenu}}
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 


{|
| style="background:yellow; color:black; width:800px" | '''J2CyclicBoundingSurface $matTag $G $K $Su $Den $h $m $ho $k_in $beta'''
|} 
{|
|  style="width:150px" | '''$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"
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
Code Developed by: <span style="color:blue">Alborz Ghofrani, [http://www.ce.washington.edu/people/faculty/bios/arduino_p.html  Pedro Arduino, U Washington]</span>


    Valid Element Recorder queries are
----
        stress, strain


e.g.
==Notes==
recorder Element -eleRange 1 $numElem -time -file stress.out  stress
* 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 or Elastoplastic response could be enforced by
:::{|
|Elastic:      ||updateMaterialStage -material $matTag -stage 0
|-
|Elastoplastic: ||updateMaterialStage -material $matTag -stage 1
|}


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


==Theory==


[edit] Theory


[edit] Example
==Example==


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




<source lang="tcl">
# HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH #
# HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH #
# 3D Conventional Triaxial Compression Test Using One Element              #
# 3D Conventional Triaxial Compression Test Using One Element              #
Line 130: Line 140:


wipe
wipe
</source>


[edit] References
==References==


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

Revision as of 02:22, 18 July 2019



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"

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

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


Theory

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

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