Research Papers

Application of the Particle Finite Element Method in Machining Simulation Discussion of the Alpha-Shape Method in the Context of Strength of Materials

[+] Author and Article Information
Matthias Sabel

Institute of Applied Mechanics,
University of Kaiserslautern,
Kaiserslautern 67663, Germany
e-mail: msabel@rhrk.uni-kl.de

Christian Sator

Institute of Applied Mechanics,
University of Kaiserslautern,
Kaiserslautern 67663, Germany

Tarek I. Zohdi

Computational Mechanics Research Laboratory,
University of California, Berkeley,
Berkeley, CA 94720-1740

Ralf Müller

Institute of Applied Mechanics,
University of Kaiserslautern,
Kaiserslautern 67663, Germany
e-mail: ram@rhrk.uni-kl.de

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received September 23, 2015; final manuscript received August 4, 2016; published online November 7, 2016. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 17(1), 011002 (Nov 07, 2016) (7 pages) Paper No: JCISE-15-1299; doi: 10.1115/1.4034434 History: Received September 23, 2015; Revised August 04, 2016

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.

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Fig. 1

PFEM algorithm in pseudocode

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Fig. 2

Detecting segments between particles

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Fig. 3

Result of boundary detection for α = 1.0 and α = 2.0

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Fig. 4

Line element in reference- and spatial-configuration

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Fig. 5

Punched strip and critical boundary segment

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Fig. 6

Maximum eigenvalue compared to α-limit for α = 1.0

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Fig. 7

Dimensions and displacements for uniaxial tension and simple shear simulations

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Fig. 8

Specimen under uniaxial tension

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Fig. 9

Maximum eigenvalue in simple shear simulation

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Fig. 10

Punched strip in undeformed setting

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Fig. 11

Maximum eigenvalue plotted on deformed configuration

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Fig. 12

Stretch of boundary segments h/H and critical stretch α = 0.9

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Fig. 13

Stretch of boundary segments h/H and critical stretch α = 1.0

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Fig. 14

Stretch of boundary segments h/H and critical stretch α = 1.1

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Fig. 15

Boundary segments and α-circles before and after separation

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Fig. 16

Maximum eigenvalues in workpiece for α = 0.8

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Fig. 17

Turning simulation for α = 1.0

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Fig. 18

Maximum eigenvalues and corresponding eigenvectors

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Fig. 19

Stretch of boundary segment compared to α



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