A smoothed radial point interpolation method (S-RPIM) for large-deformation elasto-visco-plastic analysis occurring in sheet metal blanking processes
Abderrachid Hamrani  1, *@  , Idir Belaidi  2, *@  , Fatma Zohra Bouarab  3, *@  
1 : Département de Génie Mécanique, Faculté des Sciences de l'Ingénieur, Université de Boumerdes  (DGM, FSI, UMBB)  -  Site web
Faculté des sciences de l'ingénieur, Cité Frantz. Fanon, 35000 Boumerdès -  Algérie
2 : Laboratoire Energétique Mécanique & Ingénierie  (LEMI)
Avenue de l'Indépendance 35000 BOUMERDES -  Algérie
3 : Materiaux, Pro cedes et Environnement  (Université M'hamed Bougara Boumerdes)
* : Auteur correspondant

In this paper, a meshfree cell-based smoothed radial point interpolation method (CS-RPIM) is extended to large-deformation elasto-visco-plasticity analysis for simulation of high speed sheet metal blanking processes. For this purpose, two techniques included in large-deformation analysis formulation are employed: a Johnson–Cook flow stress model and an updated Lagrangian scheme to integrate the constitutive relations. The volumetric locking due to the nearly incompressible behavior of elastic-visco-plastic deformations is remedied by relaxing the volumetric strain through the mean value computed by the strain smoothing approach coupled with the meshfree radial point interpolation method (RPIM) (based on the radial basis functions interpolation). The next step concern the description of ductile fracture initiation and propagation, which is essential to predict final product shapes in the blanking process. A hybrid approach is elaborated combining a damage model, based on a failure criterion for the brittle mode initiation; assumed to initiate when the maximum tensile principal stress at a node reaches a critical value, and a stress intensity factor model, to handle the crack propagation calculations once the crack opening is already created. The proposed algorithm duplicates cutting nodes that meet specific conditions and avoid the global remeshing procedure. Validity of the CS-RPIM for large-deformation metal forming problem is proved by benchmarks, and numerical example of sheet metal blanking process. Obtained results demonstrates that, the proposed method possess (1) superior accuracy and convergence properties for strain energy solutions comparing to the standard FEM, (2) the combination of the strain smoothing approach with the powerfull RPIM technique can easily simulate problems with severe element distortion, and solve volumetric locking problem in large-deformation analysis. 


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