A consistent penalty method for contact between a deforming viscoplastic workpiece and a rigid tool. (English) Zbl 0835.73072
Summary: A methodology is presented for enforcing a contact constraint between a viscoplastic workpiece and the tooling which deforms it. The algorithm is based on a consistent penalty approach wherein an elemental discretization permits elimination of contact tractions prior to solution for the velocity field. When written in rate form, the new algorithm allows contact constraints to be embedded in a viscoplastic formulation without altering the structure of the global matrix equation. Examples are presented to illustrate its use in metal forming simulations.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74A55 | Theories of friction (tribology) |
| 74M15 | Contact in solid mechanics |
| 74C10 | Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) |
References:
| [1] | Bathe, Int. j. numer. methods eng. 21 pp 65– (1985) |
| [2] | Lebon, Comput. Struct. 5 pp 925– (1992) |
| [3] | Oden, J. Appl. Mech. ASME 50 pp 67– (1983) |
| [4] | Simo, Int. j. numer. methods eng. 23 pp 779– (1986) |
| [5] | Parish, Int. j. numer. methods eng. 28 pp 1803– (1989) |
| [6] | Nour-Omid, Comm. Appl. Numer. Methods 3 pp 581– (1987) |
| [7] | Laursen, Int. j. numer. methods eng. 36 pp 3451– (1993) |
| [8] | Alart, Comput. Methods. Appl. Mech. Eng. 92 pp 353– (1991) |
| [9] | Heegaard, Int. j. numer. methods eng. 36 pp 569– (1993) |
| [10] | Simo, Comput. Methods Appl. Mech. Eng. 50 pp 163– (1985) |
| [11] | Nour-Omid, Comput. Methods Appl. Mech. Eng. 54 pp 131– (1986) |
| [12] | Papadopoulos, Int. j. numer. methods eng. 94 pp 373– (1992) |
| [13] | Engleman, Int. j. numer. methods fluids 2 pp 25– (1987) |
| [14] | Eggert, Int. J. Mech. Sci. 29 pp 95– (1987) |
| [15] | Mathur, Mech. Mat. 6 pp 179– (1987) |
| [16] | Lee, J. Appl. Mech. ASME 111 pp 318– (1989) |
| [17] | Eggert, Int. j. numer. methods eng. 31 pp 1031– (1991) |
| [18] | Sato, J. Comput. Phys. 22 pp 229– (1976) |
| [19] | Eggert, unpublished. |
| [20] | Wilson, J. Appl. Metalworking 6 pp 1– (1979) |
| [21] | Follansbee, Acta Metall. 36 pp 81– (1988) |
| [22] | Hart, J. Eng. Mater. Tech. 87 pp 76– (1976) |
| [23] | Brown, Int. J. Plasticity 5 pp 95– (1989) |
| [24] | and , ’Boundary friction measurements using a new sheet metal forming simulator’, Proc. NAMRC XIX (SME) 1991, pp. 37-42. |
| [25] | and , ’Frictional characteristics of 3014 aluminium sheet’, submitted. |
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