The Stress Invariant Simulator (SISi)
Dr. André Haufe
DYNAmore Stress Invariant Simulator – A. Haufe
Dynamore GmbH
Industriestraße 2
70565 Stuttgart
http://www.dynamore.de
An engineering toy to visualize stress invariants
(downloadable from the www.dynamore.de)
Crafting instructions
page 1:
•
•
•
•
•
Download the PDF-file (this file!)
Print crafting sections on thick piece of paper
Cut out where indicated
Add four wooden sticks (approx.15cm of length)
Add some glue where necessary
(engineers should find out the locations without
further instructions from the pictures – all others
contact their local distributor please)
• Have fun!
DYNAmore Stress Invariant Simulator – A. Haufe
2
An engineering toy to visualize stress invariants
(downloadable from the www.dynamore.de)
Crafting instructions
page 2:
• Page 2 of the set may be added for further
clarification of the triaxiality variable.
Final shape of toy
DYNAmore Stress Invariant Simulator – A. Haufe
3
Stress Invariant Simulator (SISi)
Definition of stress invariants
I1   I   II   III   ii  3 p  3 m
J2 
1
sij sij
2
where
sij   ij 
I1
 ij
3
 vM  3J 2
  1
 0

tension
 1
 I   II   III
Tresca
  plane
DYNAmore Stress Invariant Simulator – A. Haufe
DYNAmore Stress Invariant Simulator (SISi)
von Mises

m
I
p

 1
 vM
 vM 3 vM

27 J 3
2  vM 3
where
J 3  det s
Haigh-Westergaard-coordinates
 III
 vM
p

 II
I
© by DYNAmore GmbH
4
Stress Invariant Simulator (SISi)
  0, 218
  0.3974
 I  0.125   II
 I  0.25   II

1
3
 I  0.5   II
 0
 I   II


  0,126
 I  2   II
1
3
2
3
 I   II
 I  2   II
  0, 218
 I  4   II
DYNAmore Stress Invariant Simulator – A. Haufe
  0.3974
1

3
 II  0
 I  8   II
5
FIN
DYNAmore Stress Invariant Simulator – A. Haufe
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