In particle finite element simulations, a continuous body is represented by a set of particles that carry all physical information of the body, such as the deformation. In order to form this body, the boundary of the particle set needs to be determined. This is accomplished by the α-shape method, where the crucial parameter α controls the level of detail of the detected shape. However, in solid mechanics, it can be observed that α has an influence on the structural integrity as well. In this paper, we study a single boundary segment of a body during a deformation and it is shown that α can be interpreted as the maximum stretch of this segment. On the continuum level, a relation between α and the eigenvalues of the right Cauchy–Green tensor is presented.

References

References
1.
Oñate
,
E.
,
Idelsohn
,
S. R.
,
Del Pin
,
F.
, and
Aubry
,
R.
,
2004
, “
The Particle Finite Element Method—An Overview
,”
Int. J. Comput. Methods
,
1
(
2
), pp.
267
307
.
2.
Carbonell
,
J. M.
,
Oñate
,
E.
, and
Suárez
,
B.
,
2013
, “
Modelling of Tunnelling Processes and Rock Cutting Tool Wear With the Particle Finite Element Method
,”
Comput. Mech.
,
52
(
3
), pp.
607
629
.
3.
Sabel
,
M.
,
Sator
,
C.
, and
Müller
,
R.
,
2014
, “
A Particle Finite Element Method for Machining Simulations
,”
Comput. Mech.
,
54
(
1
), pp.
123
131
.
4.
Idelsohn
,
S. R.
,
Oñate
,
E.
,
Del Pin
,
F.
, and
Calvo
,
N.
,
2006
, “
Fluid-Structure Interaction Using the Particle Finite Element Method
,”
Comput. Methods Appl. Mech. Eng.
,
195
(
17–18
), pp.
2100
2123
.
5.
Edelsbrunner
,
H.
, and
Mücke
,
E. P.
,
1994
, “
Three-Dimensional Alpha Shapes
,”
ACM Trans. Graphics
,
13
(
1
), pp.
43
72
.
6.
Fischer
,
K.
,
2000
, “
Introduction to Alpha Shapes
,” Department of Information and Computing Sciences, Faculty of Science, Utrecht University, Utrecht, The Netherlands.
7.
Taylor
,
R. L.
,
2009
, “
FEAP—A Finite Element Analysis Program: User Manual
,” Department of Civil and Environmental Engineering, University of California, Berkley, CA.
8.
Holzapfel
,
G.
,
2000
,
Nonlinear Solid Mechanics
,
Wiley
,
Graz, Austria
.
9.
Bathe
,
K. J.
,
1996
,
Finite Element Procedures
,
Prentice Hall
,
Cambridge, UK
.
10.
Wriggers
,
P.
,
2001
,
Nichtlineare Finite-Element-Methoden
,
Springer Verlag
,
Hannover, Germany
.
11.
Greve
,
R.
,
2003
,
Kontinuumsmechanik
,
Springer Verlag
,
Darmstadt, Germany
.
12.
Lee
,
E. H.
,
1969
, “
Elastic-Plastic Deformation at Finite Strains
,”
ASME J. Appl. Mech.
,
36
(
1
), pp.
1
6
.
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