A comparison of meshless and finite element approaches to ductile damage in forming processes

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A comparison of meshless and finite element approaches to ductile damage in forming processes

Jose M. A. Cesar De Sa, Cai Zheng

IDMEC-Institute for Mechanical Engineering, Faculty of Engineering, University of Porto,Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal.

DOI:

https://doi.org/10.7494/cmms.2007.2.0153

Abstract:

In this work the ability and versatility of a meshless method, namely the Reproducing Kernel Particle Method, is assessed in the modelling of ductile damage in forming processes. The performance is compared with a traditional finite element approach. In particular the pathological behaviour associated with the size and orientation of the discretization, typical in finite elements, is investigated. The damage model is based on the Lemaitre model and includes an enhancement that distinguishes damage evolution for local tension and compression states. Damage is coupled with a plastic deformation model based on the “flow formulation”. Local and non-local damage models, of integral and gradient (explicit and implicit ) types, were implemented and compared.

Cite as:

Sa, J., Zheng, C., (2007). A comparison of meshless and finite element approaches to ductile damage in forming processes. Computer Methods in Materials Science, 7(2), 262 – 268. https://doi.org/10.7494/cmms.2007.2.0153

Article (PDF):

Keywords:

RKPM, Meshless method, Damage, Non-local models, Finite element method

References:

Andrade Pires, F. M., César de Sá, J. M. A., Costa Sousa, L., Natal Jorge, R. M., 2003, Numerical modelling of ductile plastic damage in bulk metal forming, Int. J. of Mech. Sci., 45, 273-294.

César de Sá, J. M A., Areias, P. M. A., Zheng, C., 2006, Damage modelling in metal forming problems using an implicit non-local gradient model, Comput. Methods Appl. Mech. Engrg., 195, 6646-6660.

Lemaitre, J., 1996, A course on damage mechanics, Berlin, Heidelberg, New York: Springer.

Liu, W. K., Jun, S., Zhang, Y. F., 1995, Reproducing kernel particle methods, Int. J. Numer. Meth. Fluids, 20, 1081-1106.

Peerlings, R.H.J., de Borst, R., Brekelmans, W.A.M., de Vree, J.H.P., 1996, Gradient enhanced damage for quasi-brittle materials, Int. J. Num. Meths in Engng, 39, 3391-3403.

Peerlings, R.H.J., Geers, M.G.D., de Borst, R., Brekelmans, W.A.M., 2001, A critical comparison of nonlocal and gradient-enhanced softening continua, Int. J. Solids and Structures, 38, 7732-7746.

Pijaudier-Cabot, G., Bazant, Z.P., 1987, Nonlocal damage theory, Journal of Engineering Mechanics, 113, 1512-1533.

Pijaudier-Cabot, G., Bazant, Z.P., Tabbara, M., 1988, Comparison of various models for strain-softening, Engineering Computations, 5, 141-150.

Zienkiewicz, O. C., Godbole, P. N., 1974, Flow of plastic and viscoplastic solids with special reference to extrusion and forming processes, Int. J. Numer. Meth. Eng., 8, 15-38.

Vaz Jr., M., de Santi Jr., N., Verran, G.O., de Souza Neto, E.A., 2005, Further studies on assessing ductile fracture using continuous damage coupled to an elasto-plastic material model. In D.R.J. Owen, E. Oñate, B. Suárez, eds, Computational Plasticity VIII – Fundamentals and Applications, 355-359. CIMNE.