J2Plasticity material

[alfonsogdr]

Good afternoon to all the OpenSees Community.

I have a doubt about J2Plasticity nDMaterial. I have running simulations using this material with shell elements and I have problems when I reach plastic behaviour. I have not this problems with others nDMaterial like Drucker-Prager. I have seen the source code of J2Plasticity material and the equation of Saturation Isotropic Hardening with linear term is: q(xi) = simga_infty + (sigma_0 - sigma_infty)*exp(-delta*xi) + H*xi while in OpenSees documentation is q(xi) = simga_0 + (sigma_0 - sigma_infty)*exp(-delta*xi) + H*xi. I don't know if the problem has to do with this and there is an error in the source code of this material. Any suggestions?

Thank you very much in advance.

[mhscott]

Please explain the problem in more detail and provide inputs/outputs.

[alfonsogdr]

Good morning. The model is a rectangular simply suported plate in its four edges with a central load applied in positive z direction. I have done the same model with ANSYS using a von Mises yield criterium because I wanted to compare it with J2Plasticity model. I want a Bi-Linear material law so I have erased exponential hardening. Linear hardening parameter is E/1000. I have used LoadControl integrator despite lack of convergence at first because I wanted to compare the displacement of central node with ANSYS model. When I run the model with Drucker-Prager yield criterium I obtain similar results in Linear range and the begining of plastic range it is produced at the same load, the behaviour in plastic range is a little bit different but I think this is due to the differences between drucker-prager and von mises yield criteria.

Image comparing results: https://ibb.co/X7KxFbn

When I run the model with J2Plasticity material model I get results that are not consistent. It is like it doesnt reach plastic range and behaves like a linear material model. I don't know if this could happen due to the discrepancies between the equations in OpenSees documentation
(q(xi) = simga_0 + (sigma_0 - sigma_infty)*exp(-delta*xi) + H*xi) and the one of the source code of J2Plasticity nDMaterial (q(xi) = simga_infty + (sigma_0 - sigma_infty)*exp(-delta*xi) + H*xi).

Thank you very much in advance. Kind Regards.


# ------------------------------
# Start of model generation
# ------------------------------

# Remove existing model
wipe

# Create ModelBuilder (with three-dimensions and 6 DOF/node)
model BasicBuilder -ndm 3 -ndf 6

# ------------
# ----Units&Constants.tcl---------------------------------------------------------
# define basic units

# Define parameters

# Plate dimensions (240mm; 200mm; 10mm)
set width 0.2
set h 0.24
set th 0.01

# Element size
set minmesh 0.01

# Nodes and Elements plate
set nx [expr {int([expr {round($width/$minmesh)}])}]
set ny [expr {int([expr {round($h/$minmesh)}])}]


# Steel S275: Young Modulus E=210000 MPa; Linear hardening H=E/1000; Shear modulus G=81000 MPa; Bulk modulus K; Yield strength fy=275 MPa; Ultimate strength fu=430 MPa
set E 210000000000
set H [expr $E/1000]
set G 81000000000
set v 0.3
set K [expr $E*$G/(3*(3*$G-$E))]
set fy 275000000
set fu 430000000

# Element ShellMITC4
set Plate ShellMITC4

# ------------
# Create the material
# ------------

# J2plasticity Bi-linear material

#nDMaterial J2Plasticity 1 $K $G $fy $fu 0 $H

# Drucker-Prager Bi-linear material

nDMaterial DruckerPrager 1 $K $G $fy 0.0 0.0 0.0 0.0 0.0 0.0 $H 1.0 7850

nDMaterial PlateFiber 2 1


# Plate section

section PlateFiber 1 2 $th
set platesection "1"

# ------------
# Define elements
# ---------------

block2D $nx $ny 1 1 $Plate $platesection {
1 0 0 0
2 0.2 0 0
3 0.2 0.240 0
4 0 0.240 0
}

# ------------
# Define Boundary conditions
# ---------------

# Four edges simply supported Uz=0
for {set i 1} {$i <= [expr ($nx-1)]} {incr i 1} {
fix [expr int(($nx+1)*($ny+1)-$i)] 0 0 1 0 0 0
fix [expr int(($nx+1)-$i)] 0 0 1 0 0 0
}

for {set i 1} {$i <= [expr ($ny-1)]} {incr i 1} {
fix [expr int(($nx+1)*(($ny-$i)+1)-$nx)] 0 0 1 0 0 0
fix [expr int(($nx+1)*(($ny-$i)+1))] 0 0 1 0 0 0
}

# Rigid body conditions four corners supported (Ux=Uy=Uz=0)
fix 1 1 1 1 0 0 0
fix [expr $nx+1] 1 1 1 0 0 0
fix [expr ($nx+1)*($ny+1)] 1 1 1 0 0 0
fix [expr ($nx+1)*($ny+1)-$nx] 1 1 1 0 0 0


# ------------
# Define loads
# ------------

timeSeries Linear 1

# Applied a punctual central load in positive Z direction
pattern Plain 1 1 {
load [expr (($nx+1)*($ny+1)+1)/2] 0 0 40000 0 0 0
}

# ------------------------------
# Start of recorder generation
# ------------------------------

# Displacement central node
recorder Node -file dz.out -time -node [expr (($nx+1)*($ny+1)+1)/2] -dof 3 disp

# ------------------------------
# Analysis
# ------------------------------

constraints Plain

numberer RCM

system BandGeneral

test EnergyIncr 1E-6 10 0

algorithm Newton

set s 1
integrator LoadControl $s
#integrator ArcLength $s 1.0
analysis Static
set num_analysis 1
set ok [analyze $num_analysis]

if {$ok == 0} {
puts "Analysis done at First iteration"
} else {
while {$ok != 0} {
reset
set s [expr $s*0.5]
set num_analysis [expr $num_analysis*2]
integrator LoadControl $s
# integrator ArcLength $s 1.0
analysis Static
set ok [analyze $num_analysis]
}
}

# ------------------------------
# Print
# ------------------------------

print node [expr (($nx+1)*($ny+1)+1)/2]