Hysteretic Material

[civilengineering]

Hi everyone

How can I change a Hysteretic material model to a bilinear material model such that lead to same analysis results?

In this regard, firstly, I conducted time history analysis with the below material model (Elastic-Perfectly Plastic):

uniaxialMaterial ElasticPP 1 $k 0.01789755

secondly, I conducted the same analysis again but with hysteretic material model:

uniaxialMaterial Hysteretic 1 [expr $k*0.01789755] 0.01789755 [expr $k*0.01789755] [expr 2.0*0.01789755] [expr -1*$k*0.01789755] -0.01789755 [expr -1*$k*0.01789755] [expr -1*2.0*0.01789755] 1. 1. 0. 0. 0.

but the results of two analyses are not identical. What should I do?

[armkam]

It sounds to me the problem is you limited plastic strain of your defined hysteretic material to a small one [expr 2.0*0.01789755]. On the other hand, the EPP material does not have any limitation in plastic strain. Hence, I suggest to try a big strain such as [expr 1000*0.01789755] and then see how close the results are.

[civilengineering]

Dear armkam

Thank you for your consideration. I did it but the results did not change by applying factor 1000. I need to solve this problem. I would be grateful if someone could solve that.

[armkam]

Could you try steel01 material with a small value (say b=0.0000001) for hardening ratio to see if you get the same results?
Also for hysteretic material it may worth the try to set the factor 10000000.
Are the results completely different or have an error? What analysis are you using? I suggest first use simple static analysis then pushover and then transient.

[civilengineering]

Dear Armkam

I used steel01 material with a small value (b=0.0000001) for hardening ratio and also I used hysteretic material with the factor 10000000, but the results did not change. The difference between the results is much and I conducted time history analysis.

[civilengineering]

Is there anyone who can please help me?

[fmk]

post a simple 2 node, 1 zero length example that demonstrates the different answers.

[civilengineering]

Thank you so much Dr. fmk
A simple 2 node, 1 zero length example (a time history analysis subjected to ground motion) is posted below with two material models, firstly the ElasticPP material is activated, then the analysis is performed with the Hysteretic material.

#####################################################
wipe
model basic -ndm 1 -ndf 1
node 1 0.
node 2 0.
set dt 0.01
fix 1 1
set m 1.0
set pi 3.14
set k 1.0
mass 2 $m

uniaxialMaterial ElasticPP 1 $k 0.01789755 #firstly with ElasticPP material

#uniaxialMaterial Hysteretic 1 [expr $k*0.01789755] 0.01789755 [expr $k*0.01789755] [expr 10000000.0*0.01789755] [expr -1*$k*0.01789755] -0.01789755 [expr -1*$k*0.01789755] [expr -1*10000000.0*0.01789755] 1. 1. 0. 0. 1. #secondly with Hysteretic material


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



# ------------ define & apply damping
set lambda [eigen -fullGenLapack 1]
set T [expr (2*$pi)/sqrt($lambda)]
puts "T = $T"
set freq [expr sqrt($lambda)]
set dampRatio 0.05
rayleigh 0. 0. 0. [expr 2*$dampRatio/$freq]


set accel "Series -dt 0.01 -filePath ARSMF.txt -factor [expr 9.81]"

pattern UniformExcitation 3 1 -accel $accel


recorder Node -file node1reac.out -time -node 1 -dof 1 reaction

recorder Node -file node2disp.out -time -node 2 -dof 1 disp


constraints Transformation
numberer RCM
system SparseGeneral
test RelativeNormDispIncr 1.0e-4 10
algorithm ModifiedNewton
integrator Newmark 0.5 0.25
analysis Transient
analyze [expr int(20.0/$dt)] $dt

When two analyses are done, the output entitled "node2disp.out", is different with two material models.

[civilengineering]

Dear Dr fmk

You said that "post a simple 2 node, 1 zero length example that demonstrates the different answers."

I posted a simple example above. please guide me for solving the problem.