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.
Application of the Particle Finite Element Method in Machining Simulation Discussion of the Alpha-Shape Method in the Context of Strength of Materials
University of Kaiserslautern,
Kaiserslautern 67663, Germany
University of California, Berkeley,
Berkeley, CA 94720-1740
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.
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Sabel, M., Sator, C., Zohdi, T. I., and Müller, R. (November 7, 2016). "Application of the Particle Finite Element Method in Machining Simulation Discussion of the Alpha-Shape Method in the Context of Strength of Materials." ASME. J. Comput. Inf. Sci. Eng. March 2017; 17(1): 011002. https://doi.org/10.1115/1.4034434
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