The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.
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Transcript of The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.
![Page 1: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/1.jpg)
The Mechanics of Crumpled Thin Sheets
Simon de Villiers , PGP, University of Oslo
![Page 2: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/2.jpg)
Why Crumpled Paper?
• Ubiquitous Phenomena
![Page 3: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/3.jpg)
Why Crumpled Paper?
• Ubiquitous Phenomena • Power law statistics
![Page 4: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/4.jpg)
Why Crumpled Paper?
• Ubiquitous Phenomena • Power law statistics• Self affine geometry
![Page 5: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/5.jpg)
Why Crumpled Paper?
• Ubiquitous Phenomena • Power law statistics• Self affine geometry• Contact area of rough surfaces
![Page 6: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/6.jpg)
Why Crumpled Paper?
• Ubiquitous Phenomena • Power law statistics• Self affine geometry• Contact area of rough surfaces• Convenient in the laboratory
![Page 7: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/7.jpg)
Balance
Crumpled film
Heavy stone table
Computer controlled micrometer screw gauge
Perspex plate
Experimental Setup
![Page 8: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/8.jpg)
Stress Relaxation
0 2000 4000 6000 8000 10000 12000 14000 160000
5
10
15
20
25
30
35
40
45Stress relaxation when 16cm diameter cirle of crumpled Aluminum foil was confined to 3mm
Bal
ance
rea
ding
in g
ram
s(st
ress
)
time in seconds
![Page 9: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/9.jpg)
Stress Relaxation
0 2000 4000 6000 8000 10000 12000 14000 160000
5
10
15
20
25
30
35
40
45Stress relaxation when 16cm diameter cirle of crumpled Aluminum foil was confined to 3mm
Bal
ance
rea
ding
in g
ram
s(st
ress
)
time in seconds10
010
110
210
310
410
50
5
10
15
20
25
30
35
40
45Stress relaxation when 16cm diameter cirle of crumpled Aluminum foil was confined to 3mm
Bal
ance
rea
ding
in g
ram
s(st
ress
)
time in seconds
![Page 10: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/10.jpg)
Stress Strain Relationship
0.5 1 1.5 2
x 104
0
500
1000
1500
2000
2500
3000
16cm circle of crumpled cellophane compressed 0 .1mm every minute
Time in seconds (incremental strain increase of 0.1mm per minute)
Bal
ance
read
ing
in g
ram
s(s
tress
)
![Page 11: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/11.jpg)
Stress Strain Relationship
0.5 1 1.5 2
x 104
0
500
1000
1500
2000
2500
3000
16cm circle of crumpled cellophane compressed 0 .1mm every minute
0.5 1 1.5 2
x 104
10-2
10-1
100
101
102
103
Time in seconds (incremental strain increase of 0.1mm per minute)
16cm circle of crumpled cellophane compressed 0 .1mm every minute
Time in seconds (incremental strain increase of 0.1mm per minute)
Bal
ance
read
ing
in g
ram
s(s
tress
)
![Page 12: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/12.jpg)
Regularly Folded Paper
5 10 15 20 25 300
100
200
300
400
500
600
700
800
time in seconds (constant strain rate 414µm/s)
Bal
ance
rea
ding
in g
ram
s(st
ress
)
Graph of elastic response with 1.5cm folded sheet against the empty response of the apparatus
1.5cm folded paperno paper
![Page 13: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/13.jpg)
Single Point Forcing Response
500 520 540 560 580 600 620 640 660
10
20
30
40
50
60
70
time in seconds (constant strain rate applied at a single point)
Bal
ance
rea
ding
in g
ram
s
Crumpled sheet pushed at a single point on its top surface
![Page 14: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/14.jpg)
Single Point Forcing Response
500 520 540 560 580 600 620 640 660
10
20
30
40
50
60
70
time in seconds (constant strain rate applied at a single point)
Bal
ance
rea
ding
in g
ram
s
Crumpled sheet pushed at a single point on its top surface
![Page 15: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/15.jpg)
3D Imaging
![Page 16: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/16.jpg)
Summary
• The importance of crumpled disorder in thin sheets.
• Logarithmic relaxation of stress.• Exponential increase of stress with strain.• Linear increase of stress with strain for
ordered/simple systems.
![Page 17: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/17.jpg)
Geological Relevance
• Frictional processes
• Thin elastic sheet dynamics in geological systems
• Rough surfaces
![Page 18: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/18.jpg)
Friction in the Experiment
0 50 100 150 200 2500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1 139131719
Amplitude normalized Graph of sizing with number of ridges being varied
norm
aliz
ed s
tres
s
time(s)
0 100 200 300 400 500 600 700 8000
200
400
600
800
1000
1200Positive and negative strainrate averaged Response
Bal
ance
rea
ding
in g
ram
s (s
tres
s)
Time in seconds (constant strain rate 41µm/s)
0 200 400 600 800 1000 1200 1400 16000
200
400
600
800
1000
1200
Time in seconds (constant strain rate 41µm/s)
Bal
ance
rea
ding
in g
ram
s (s
tres
s)
Compression and decompression of a regularly folded sheet
negative strain ratepositive strain rate
![Page 19: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/19.jpg)
Repetition of the Experiment
0 10 20 30 40 50 60 700
500
1000
1500
2000
2500
3000
3500
4000Graph of 8 compressions with a 10 second interval
Time in seconds (constant strain rate 414µm/s)
Bal
ance
rea
ding
in g
ram
s (s
tres
s)
0 5 10 15 20 25 30 350
500
1000
1500
2000
2500
3000
3500
4000
time in seconds (constant strain rate 414µm/s)
Bal
ance
rea
ding
in g
ram
s(st
ress
)
8 crumpled pieces of paper (15cm side square)
![Page 20: The Mechanics of Crumpled Thin Sheets Simon de Villiers, PGP, University of Oslo.](https://reader036.fdocuments.net/reader036/viewer/2022062504/5a4d1b687f8b9ab0599b1c6e/html5/thumbnails/20.jpg)