Application of the Nodal Integrated Finite Element Method to Cutting: a Preliminary Comparison with the “Traditional” FEM Approach

Abstract:

FEM implicit formulation shows specific limitations in processes such as cutting, where large deformation results in a heavy mesh distortion. Powerful rezoning-remeshing algorithms strongly reduce the effects of such a limitation but the computational times are significantly increased and additional errors are introduced. Nodal Integration is a recently introduced technique that allows finite element method to provide more reliable results when mesh becomes distorted in traditional FEMs. Furthermore, volumetric locking phenomenon seems to be avoided by using this integration technique instead of other methods, such as the coupled formulations. In this paper, a comparison between a “classical” FEM simulation and the Nodal Integration one is carried out taking into account a simple orthogonal cutting process.

• Periodical: Advanced Materials Research (Volume 223)
• Pages: 172-181
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.223.172
• Online since: April 2011
• Authors: Francesco Greco, Domenico Umbrello, Serena Di Renzo, Luigino Filice, I. Alfaro, Elías Cueto
• Keywords: Nodal Integration, Orthogonal Cutting

References

[1] Babuška I., Aziz A., 1976, On the angle condition in the Finite Element Method, SIAM Journal of Numerical Analysis, 13: 214-227.

DOI: 10.1137/0713021

[2] Strenkowski, J.S., Carroll, J.T., 1985, A finite element model of orthogonal metal cutting, ASME Journal of Engineering for Industry, 107: 346-354.

DOI: 10.1115/1.3186008

[3] Shih, A. J., 1995, Finite element simulation of orthogonal metal cutting, ASME Journal of Engineering for Industry, 117: 84-93.

DOI: 10.1115/1.2803283

[4] Strenkowski, J.S., Carroll, J.T., 1986, Finite element models of orthogonal cutting with application to single point diamond turning, International Journal of MechanicalScience, 30: 899-920.

DOI: 10.1016/0020-7403(88)90073-2

[5] Rakotomalala, R., Joyot, P., Touratier, M., 1993, Arbitrary Lagrangian-Eulerianthermomechanical finite element model of material cutting, Communications inNumerical Methods in Engineering, 9: 975-987.

DOI: 10.1002/cnm.1640091205

[6] Olovsson, L., Nilsson, L., Simonsson, K., 1999, An ALE Formulation for the Solution of Two-Dimensional Metal Cutting Problems, Computers and Structures, 72: 497–507.

DOI: 10.1016/s0045-7949(98)00332-0

[7] Belytschko, T., Krongauz, Y., Organ, D., Krysl, P., 1996, Meshless Methods: An Overview and recent developments, Computer Methods in Applied Mechanics and Engineering, 139(1-4): 3-47.

DOI: 10.1016/s0045-7825(96)01078-x

[8] Fried, I., 1973, Accuracy and condition of curved (isoparametric) finite elements. Journal of Sound and Vibration, 31: 345-355.

DOI: 10.1016/s0022-460x(73)80278-0

[9] Dohrmann, C.R., Heinstein, M.W., Jung, J., Key S.W., Witkowski W.R., 2000, Node-based uniform strain elements for three-node triangular and four-node tetrahedral meshes. International Journal for Numerical Methods in Engineering, 47: 1549–1568.

DOI: 10.1002/(sici)1097-0207(20000330)47:9<1549::aid-nme842>3.0.co;2-k

[10] Calamaz, M., Coupard, D. and Girot, F., A new material model for 2D numerical simulation of serrated chip formation when machining titanium alloy Ti–6Al–4V. International Journal of Machine Tools and Manufacture, 48: 275–288.

DOI: 10.1016/j.ijmachtools.2007.10.014

[11] Sima, M., Özel, T., 2010, Modified material constitutive models for serrated chip formation simulations and experimental validation in machining of titanium alloy Ti–6Al–4V. International Journal of Machine Tools and Manufacture, 50: 943-960.

DOI: 10.1016/j.ijmachtools.2010.08.004

[12] Kalpakjian, S., Schmid, S.R., 2003, Manufacturing processes for engineering materials. IV Ed. Pearson Education, Inc.

[13] Edelsbrunner, H., Kirkpatrick, D. G., Seidel, R, 1983, On the shape of a set of points in the plane, IEEE Transactions on Information Theory, IT-29(4): 551-559.

DOI: 10.1109/tit.1983.1056714