Elasto-plastic zero-length element

[miwilhel]

I am trying to model an elasto-plastic zero-length element. After the load factor is beyond the yielding point, opensees does not converge anymore.

Here the input file
**************
# EPZeroLength.tcl - wil October 17th, 2005
# Zero Length element with EP material
#
# Units: N, mm, s
# ------------------------------
# Start of model generation
# ------------------------------

# Create ModelBuilder (with two-dimensions and 2 DOF/node)

model BasicBuilder -ndm 2 -ndf 2

# Create nodes & add to Domain - command: node nodeId xCrd yCrd

node 1 0.0 0.0

node 2 0 0.0

# Set the boundary conditions - command: fix nodeID xResrnt? yRestrnt?

fix 1 1 1

fix 2 0 1

# Define materials for truss elements

# -----------------------------------

# Create Elastic material prototype - command: uniaxialMaterial Elastic matID E

#uniaxialMaterial Hysteretic 1 50000 5 51000 10 51001 50 -50000 -5 -51000 -10 -51001 -50 1 1 1 1
#uniaxialMaterial Hysteretic 1 50000 5 50000 10 -50000 -5 -50000 -10 1 1 1 1
uniaxialMaterial ElasticPP 1 10000 5

# Define elements

# ---------------

# Create truss elements - command: element truss trussID node1 node2 A matID

element zeroLength 1 1 2 -mat 1 1 -dir 1 2

# Define loads

# ------------

# Create a Plain load pattern with a linear TimeSeries

pattern Plain 1 "Linear" {

# Create the nodal load - command: load nodeID xForce yForce

load 2 10000 0

}

# ------------------------------
# End of model generation
# ------------------------------

# ------------------------------
# Start of analysis generation
# ------------------------------

# Create the system of equation, a SPD using a band storage scheme

system BandSPD

# Create the DOF numberer, the reverse Cuthill-McKee algorithm

numberer RCM

# Create the constraint handler, a Plain handler is used as homo constraints

constraints Plain

# Create the integration scheme, the LoadControl scheme using steps of 1.0

integrator DisplacementControl 2 1 0.01

# Create convergence criteria

test NormDispIncr 0.001 50

# Create the solution algorithm, a Linear algorithm is created

algorithm Newton

# create the analysis object

analysis Static

# ------------------------------
# End of analysis generation
# ------------------------------

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

# create a Recorder object for the nodal displacements at node 4

recorder Node -file EPZeroLength.out -time -node 2 -dof 1 disp

# --------------------------------
# End of recorder generation
# ---------------------------------

# ------------------------------
# Finally perform the analysis
# ------------------------------

# Perform the analysis

analyze 600

# Print the current state at node 4 and at all elements

print node 2

print ele

Actually I wanted to model a zerolength element with a trilinear hysteretic model where the last linear segment models the softening. For the interator I choose arc length, which didn't work. Then I simplified my problem to elasto-plastic and tried with the displacement controlled integrator. Here are my questions:

1. Can someone find the mistake in my tcl script and why opensees is not able to solve this problem?
2. Is someone familiar with the arc length integrator for softening problems (e.g. trilinear hysteretic model).

[fmk]

It is not a convergence issue. The problem is that the ElasticPP results in zero stiffness once
material has yielded. DisplacementControl tries to predict an initial trial disp at each iteration by solving a matrix equation which uses the current tangent matrix (in your case the matrix is a 1x1 with 0.0 as the only coefficient, once the material has yielded) .. hence the error message about the solver failing.

Before anybody goes mentioning trying to use ModifiedNewton with the initial stiffness. Initial Stiffness iterations will only help for the step where the initial stifness at the start of the load step is not zero.

The ArcLength and MinUnbalance methods also use the current stiffness at the start of each iteration to predict an initial trial step and hence will also fail.

[SophieMTL]

I found the same problem!
I would like to use ElasticPPGap and because of zero stiffness at the start it doesn't work.
What could be the solution to go through this issue ?
Thank you.