An Improved Particle Finite Element Method for the Simulation of Machining Processes

Authors Xialong Ye, Juan Manuel Rodríguez Prieto, Ralf Müller

Thumbnail PDF


  • Filesize: 1.91 MB
  • 9 pages

Document Identifiers

Author Details

Xialong Ye
  • Applied Mechanics, Technische Universität Kaiserslautern, Germany
Juan Manuel Rodríguez Prieto
  • Mechanical Engineering Department, Universidad EAFIT, Medellín, Colombia
Ralf Müller
  • Applied Mechanics, Technische Universität Kaiserslautern, Germany

Cite AsGet BibTex

Xialong Ye, Juan Manuel Rodríguez Prieto, and Ralf Müller. An Improved Particle Finite Element Method for the Simulation of Machining Processes. In 2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020). Open Access Series in Informatics (OASIcs), Volume 89, pp. 13:1-13:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Machining is one of the most common and versatile manufacturing processes in industry, e.g. automotive industry and aerospace industry. But classical numerical methods such as the Finite Element Method (FEM) have difficulties to simulate it, because the material undergoes large deformations, large strain, large strain rates and high temperatures in this process. One option to simulate such kind of problems is the Particle Finite Element Method (PFEM) which combines the advantages of continuum mechanics and discrete modeling techniques. In this study we develop the PFEM further and call it the Adaptive Particle Finite Element Method (A-PFEM). Compared to the PFEM the A-PFEM enables insertion of particles and improves significantly the mesh quality along the numerical simulation. The A-PFEM improves accuracy and precision, while it decreases computing time and resolves the phenomena that take place in machining. Because metal cutting involves plastic deformation we resort to the J₂ flow theory with isotropic hardening. At last some numerical examples are presented to compare the performance of the PFEM and A-PFEM.

Subject Classification

ACM Subject Classification
  • Applied computing → Physical sciences and engineering
  • Particle Finite Element Method
  • Alpha Shape Method
  • Metal Cutting


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. H. K. Toenshoff B. Denkena. Spanen. Springer-Verlag, 2011. Google Scholar
  2. K. Fischer. Introduction to alpha shapes. Department of Information and Computing Sciences,Faculty of Science, Utrecht University, 2000. Google Scholar
  3. E. P. Mücke H. Edelsbrunner. Three-dimensional alpha shapes. ACM Transactions on Graphics, 13(1):43-72, 1994. Google Scholar
  4. G. Holzapfel. Nonlinear Solid Mechanics. John Wiley & Sons, 2001. Google Scholar
  5. S. R. Idelsohn, E. Oñate, F. Del Pin, and N. Calvo. The particle finite element method. an overview. International Journal of Computational Methods, 1(2):267-307, 2004. Google Scholar
  6. T.J.R. Hughes J. C. Simo. Computational Inelasticity, volume 7. Springer Science & Business Media, 2006. Google Scholar
  7. A. Svoboda J. M. Rodriguez, P. Jonsén. A particle finite element method for machining simulations. VII European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, Greece, 5–10 June 05/06/2016-10/06/2016, 1:539-553, 2016. Google Scholar
  8. A. Svoboda J.M. Rodríguez, P. Jonsén. Simulation of metal cutting using the particle finite-element method and a physically based plasticity model. Computational Particle Mechanics, 4:35-51, 2017. Google Scholar
  9. E. H. Lee. Elastic-plastic deformation at finite strains. Journal of Applied Mechanics, 36(1):1-6, 1969. Google Scholar
  10. A. Frangi M. Cremonesi and U. Perego. A lagrangian finite element approach for the analysis of fluid–structure interaction problems. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 84:610-630, 2010. Google Scholar
  11. R. Müller M. Sabel and C. Sator. Simulation of cutting processes by the particle finite element method. GAMM‐Mitteilungen, 40(1):51-70, 2017. Google Scholar
  12. J. Oliver, J.C. Cante, R. Weyler, C. González, and J. Hernández. Particle finite element methods in solid mechanics problems. Computational plasticity, pages 87-103, 2007. Google Scholar
  13. J. R. Shewchuk. Triangle: Engineering a 2d quality mesh generator and delaunay triangulator. Applied Computational Geometry: Towards Geometric Engineering, pages 203-222, 1996. Google Scholar
  14. R. L. Taylor. Feap - a finite element analysis program: User manual. Department of Civil and Environmental Engineering, University of California, Berkley, 2009. Google Scholar
  15. P. Wriggers. Nonlinear finite element methods. Springer Science & Business Media, 2008. Google Scholar