George Popescu's page for :

Physics for Information Technology Class


Prof. Neil Gershenfeld

George Popescu's Project : Experiemental and theoretical study of press fit structures and joints

Introduction and background  
What is GIK ?

You can find out more about GIK parts over here :

GIK is mass-produced two-dimensional components contruction kit that allows for three-dimensional assembly . This significantly enlarges the available material set, allows reversible disassembly, and imposes constraints that reduce the accumulation of local positioning errors in constructing a global shape.
One of it's advantages is that it can work at any scale :
It can also work in many different materials :

What is the project exactly?

The project has 4 parts :

  • First part is to model using a finite element methode the material behavior ( strain field, displacement, histeresis cycle... ) of GIK parts.
  • Second is to experimentally measure the histeresis cycle as a function of different variable ( GIK size , materials, surface roughness... ) and maybe infer from that a good guess on how does the friction fit mechanism work.
  • Third is to compare the material behavior of single GIK parts and 1D, 2D and 3D GIK structures.
  • And forth : compare the "error" or "freedom" ( which is to be defined ) of GIK parts when they are assembled in a 2GIK 0D parts structure, a 1D GIK structure, 2D GIK structure and of course 3D GIK structure.
Why is the project useful ?

So far , there is very little literature on press fit and/or friction fit constructions. Press fit/friction fit allow for simple cheap and srtaighforward assembly of error free structures because they are alignment free.There are 4 questions we would like to answer to ( see previous point).

  1. The first point will give us a scientific method to study a press-fit construction made out of discrete additively assembled parts.
  2. Second will allow us to make material behavior prediction and put numbers on material aging.
  3. Third part is an open question : will a GIK-crystal material behave differently from a real atomic material ? How much influence has a GIK atom on a material ?
  4. Forth : this will actually give a good suggestion if the idea of digital construction is true or not.
What are we looking for , which results do we expect ?

May 10th :

1.For the first part we expect to demonstrate experimentally expected facts , plus to have some concrete numbers for stress and deformation as a function of the material.
2.For the second part we expect to measure the hysteresis cycle without too much trouble, and to measure the GIK assembly energy as a function of the GIK gap. If we have a f=-kx graph we can assimilate it to a spring. If we have an other graph we can get an other model... A measurement of the surface roughness will also help. On the way , as we have to measure the GIK gap width , we will also get statistics of these GAPs (with error bars).
3. For the 3rd point we expect to demonstrate that the material behaves similarly if it's bulk or GIK-shaped ( same Yound modulus for bulk plywood , and GIK assemble plywood ? )
4. For the 4th point we expect to demonstrate that a 3D GIK structure has less freedom ( each degree of freedom has a smaller allowed interval to vary in) than a 2D GIK structure.


Project steps  

Make a plan of : what is to be done, make a time schedule.

There are a couple of things to be done before everything :

  1. Decide which software to use for modelisation : Femlab or Ansys : 2 days
  2. Learn how to use the Instron : 2 days
  3. Learn how to use the scanner for measurements : 1 day
  4. Decide which GIK geometry/parts to use : 1/2 day
  5. Decide which experiments to do.

Do a literature search, learn how to use the tools, install and learn the software ( Ansys).

Here are some references obtained from Prof. Sass :

  • R. Messler, Joining of Advanced Materials, Butterworth-Heinemann, 1993
  • S. Genc, R. Messler, G. Gabriele, A Systematic Approach to Integral Snap-Fit Attachment Design, Research in Engineering Design, 1998, Vol. 10, Issue 2, pp. 84-93
  • P. Bonenberger, in: ANTEC '95 Conference--Society of Plastic Engineers Annual Technical Conference and Exhibit, New design methodology for integral attachments. Vol3, 7-11 May, Boston, MA, pp. 3788-3792. 1995
  • K. Knapp, in: ANTEC '97 Conference--Society of Plastic Engineers Annual Technical Conference and Exhibit, Stress-Strain Response of Polymers for Predicting the Behavior of Integral Fasteners. Vol3, 7-11 May, Boston, MA, pp. 3766-3770. 199
  • L. Wang, G. Gabriele, A. Luscher in: ANTEC '95 Conference-Society of Plastic Engineers Annual Technical Conference and Exhibit, Failure Analysis of a Bayonet-Finger Snap-Fit. Vol3, 7-11 May, Boston, MA, pp. 3799-3803. 1995
  • A. Kilian, in: K. Klinger (Ed.), Fabrication of partially double-curved surfaces out of flat sheet materials through a 3d puzzle approach,: ACADIA 2003, Connecting Crossroads of Digital Discourse, Muncie Indiana, pp. 74-81
  • Industrial Origami
  • Lamina Design
  • : A review of Friciton Models and Friction compensation

Decide which experiments are necessary, think of the protocols.

We need a way to measure accurately GIK parts. I am going to use the scanner with 1600 DPI resolution to measure GIK distances.

May 5th : Actually this doesn't work. The scanner we have is only 300DPI. I ordered a new scanner which should be able to do 9600 DPI ( or 2.6 micrometers precision ) but it's not here yet. Also we will be able to measure only x,y , no z and no angles.

May10th : I now have a new Canon scanner and I can scan up to an incredible 19200 DPI. However the file is too big and nowbody can open it. I've been using 9200 DPI , and opening the files with Corel Draw ( who is measuring for me , very practicle) in grayscale ( only 300 Mo files :D ). I didn't saved the files.

We need a way to measure forces : I am going to use the instron with a PC to aquire the results.

May 5th : I am struggling to talk to the instron. We have a GPIB-ENET 100T card/box but it doesn't seem to work at all. Once this will be working I HOPE there alread is a VI for the Instron, otherwise I will be in trouble (time wise)!

May10th: A ENET-GPIB is on it's way from NI. I learned , thanks to Neil's example, how to use sockets to send and receive UDP packets. I also read the Instron manual and it seams preatty simple to communicate with it. I just hope the GPIB-ENET will transform my command to the INSTRON and I won't have to worry about that. The last piece is to figure out how to exploit the numbers I will get back : if I should use Python ( do I have enough time to learn it ?) or back to old Matlab...

We need GIK parts : I am going to make those on the laser cutter. The materiall is still to be decided. We where thinking of using cardboard BUT cardboard is anysotropic. But , we expect if we make the GIK parts large enough, to be relatively homogenous.

May 5th : I made cardboard GIK parts ( 2mm thick ECT 44 ) (see figure lower on this page ). Only tried one version. I did measured also the REAL dimension ( see figure lower too)/

Today I also learned how to use the Instron. I measured for this the load/extension curve for plywood and calculated the longitudinal spring constant for Plywood : 721 N/m

Start modeling GIK parts using FEMLAB or Ansys


So far I didn't decided yet if I am going to use FEMLAB or Ansys. Here is the first results with Femlab on a connection between 2 GIK parts.

In order to simulate the cardboard in FEMLAB we will need to know the following materials parameters :

  • E Young's modulus
  • nu Poisson's ratio
  • rho Density
  • thickness Thickness of the structure

And for Plane stress and plane strain simulation we will also need :

  • dM Mass damping parameter
  • dK Stiffness damping parameter

I believe we can measure the first 2 properties with the Instron , rho and thickness with a scale and the scanner. However I don't know yet hot do measure dM and dK ...

April 20 th.

I decided I am going to use Femlab. So I developped the model a little bit farther and learned a little bit more about how to use Femlab well. So far the time dependent solver doesn't seem to work very well. Also if the parts are a little complicated (complete GIK parts) direct solving runs out of memory. However it seams that indirect solvers produce asymetric solution for highly symetric parts... Here are the first results.


May 5th :

According to Comsol Tech support : "As you can see only one solid is represented, the other is considered to be rigid (and so the deformations are negligible). The current version does not support contact between two elastic solid but this feature will be available in the next version of the structure mechanics module." I did got an example of elastic model against solid model and will work on it Monday ( or before).

Ara says : "George, I've been thinking we should get the structural mechanics module... Ara " :)

Also Tushar Mahale did this very good analysis :

May10th : I am going to build my own model based on the paper :

May 22nd : And also based on this webpage


In parallel , make different material GIK parts for the experiments.

Before making different material GIK I had to choose a geometry/design. So far here is the first design I think I will use for GIK parts. This is just the first try. Maybe I will end up changing the parts after the first experiments. Tushar Mahale, who is also working on related topics, did ended up changing the parts geometry to increase the contact surface between 2 parts. The numbers are in mils and are the measurement of the GIK slot width ( and the parts are scaled accordingly).The 4 extra parts are a try to make more tolerant GIK parts because so far GIK dimensions have to be adjusted very well to the material thickness or the parts won't fit together well.

Follow #3 protocols.



Present the results

Finite element simulations 1.0
With Femlab I obtained the following results :

I am not happy with the results because :

  1. I can't really measure on the Instron the stress strain fields I am obtaining here. I would like to find a way in Femlab to calculate the necessary force to put 2 parts in contact.
  2. The only material properties I have are for some RED HARD WOOD (not cardboard)
  3. The parts don't seem to move during the simulation even if I am doing a dynamic simulation (not static !)

But here are the results. The first picture is the drawing with the mesh. The dimensions are meters. The 2nd picture is the von Misses strain field isosurfaces and the arrows the displacement..
I applied 1000 N on each GIK parts standing in free air.

Here is the stress field of a single GIK part when pressed against a flat surface :

May 22nd : Now that I know how to use Femlab I simulated precisely my experiment (2 GIKs in contact, a little bit too large for each other ) and here are the results :

Also here are the first results with the Instron (it's working ! ) (Comment on May 15th : results obtained by hand , by writing down the values indicated on the screen and moving the Extensiometer by discrete macro steps ):

In order to get meaningfull measurements with the Instron we need to be able to measure well a GIK part dimensions. I've been trying to use the scanner which should go to 1600DPI but I couldn't find out how to use it at higher resolution that 300DPI. 300DPI is not enough, but here is what we get with it : This is a cardboard GIK part made out of 110 mils thick ECT44 cardboard. The slot's width should have been 120 mils ( as indicated by the writing on the part). The measurement was done with Corel based on the resolution of DPI and counting the number of pixels.

And the STATIC ( = at equilibrium) Load vs Extension hysteresis graph for 2 95 mils (at drawing) GIK parts made out of cardboard ECT44 110mils thick (or about) :

We can see the hysteresis cycle. However this diagram was made by hand and computer control is necessary. The next step will be to use the computer to control the Instron.

Measuring GIK slot sizes :

Measuring the error angles of 2D vs 3D structures for GIK 125 and GIK 105 :


Conclusion : building 3D is reducing the GIK freedom of move (also called structure looseness) !

May 15th :

It took me 2 weeks to be able to talk to the Instron. I gave up using Ethernet to that purpose ( I just can't find a way to make it work and my project was about GIKs not
learning how to program low level Ethernet). Once I got the GPIB talking ( using an old PCI-GPIB card next to the Instron) , taking all these results took 2 days.

So here are the results ( the pictures a well organised because I am also giving a talk today at noon and I made nice slides :) )

First the material behavior :

Comparing bulk plywood with GIK structure :

Load extension curve for 2 GIK parts :


Max load before breaking as a function of GIK width :

And now error correction.

There is angular error correction ( showed with cardboard Lego GIKs)

And linear error correction : showed with plywood white birch GIKs :


Now if we do the same think with Delrin and plot error VS size of the structure this is what we get :

May 15th : Last thing to be done is to make a model of the friction and paste it to the measurements, if necessary with parameter identification. DONE

The model is by Bilam and Sorine ( see this link : . I implemented the model in Matlab and fitted the model to the experimental data. This is the Matlab code :

"function F = frictionmodel(param,x)
%Bliman and Sorine

%change the sign of V for the way you go around the cycle
v=1*1e-3/60; %1mm/min to m/s
d=2e-3; %in m
T=d/v; % in s


%not used in the fitting model
%x=[0:dx:2e-3]; % position in m


%constantes experimentales :
%fs=0.7 %N
%fk=0.45 %N
%se=0.02e-3 %m
%sp=0.03e-3 %m

fs=param(1); %N
fk=param(2); %N
se=param(3); %m
sp=param(4); %m


%p= solution de :
% (m1*m2+2)/(m1*m2)*log(p)-(p-1)*log(m2)==0
%we found p!



A=[-1/eta/epsilonf 0 ; 0 -1/epsilonf];
B=[f1/eta/epsilonf ; -f2/epsilonf];
C=[1 1];

for n=1:(length(F)-1)






May 22nd : Using 2 polarizing lenses from here ( ) and by making a set-up ( with a lot of scotch tape, a hacked and prepared microscope lamp and a soldering vice :) ) under the Instron I recorded stress patterns ( using my camera Nikon 995 with a tripod ! ) . The sampels where 1/2 inch thick Acrylic GIK parts

Compare results to existing literature

May 15th :

The Hysteresis cycles correspond exactly to what is found in literature ( see :

May 22nd Fianl Results :

1. I made a finite element simulation of stress/strain in a GIK part, and in 2 GIK parts assembled.Here are the results :

2. I recorded an hysteresis cycle with the instron and simulated it's behavavior (see up here for the model), here are the results :

3. The material behaves like a bulk materials :

4. Error prevention :



  1. Introduction GIKs and bricks

    Why digital ? ( Error correction, self replication )
    Can one machine reproduce itself given itís own accuracy due to itís own parts ? YES by construction
    Why additive ? ( Multi materials )
    Why small : resolution

  2. Material Properties

    Compression : still the same material
    Extension : friction fit works
    Shear Ö TO DO

  3. Virtues

    Error correction : demonstrated
    Active/ Multi material : demonstrated
    Multiscale : demonstrated

  4. Problems

    Surfaces : hinges ?
    Evil Snowman (sacrificial parts)

Which conclusion can we have based on the results ?

I would conclude that GIK material is exactly as expected !

Is press fit structures an interessting enough object to be studied independently ?

Press fit structures seam to work as bulk structures. More work is necessary about shear forces but I think it definetevely is on the reasearch map.

Impact on the assembler ?

So far, all experiments tend to show that we will be able to assemble GIK parts without any problem and with error prevention.