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.
Abstract. The formation of chips in cutting processes is characterised by large deformations and large configurational changes and therefore challenges established modeling techniques. To overcome these difficulties, the particle finite element method (PFEM) combines the benefits of discrete modeling techniques with methods based on continuum mechanics. In this work an outline of the PFEM, as well as an explanation of the finite element formulation are provided. The impact of the boundary detection on the structural integrity is studied. The numerical examples include a tensile test as well as cutting simulations. The paper is concluded by a comparison of cutting forces with analytical results.
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