KSME Journal

, 6:6 | Cite as

A finite element program for simulating sheet-metal stretch forming processes

  • Y. T. Keum
  • R. H. Wagoner


A finite-element process modeling program, SHEET-3, was developed using triagnular elements for simulating the sheet-metal stretch forming operation of an arbitrarily-shaped punch and dies. The program employs an implicit, incremental algorithm based on a rigid-viscoplastic constitutive equation with corrections for material unloading. Contact and friction are introduced through a mesh-normal, which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivatives of the tool surfaces. The membrane approximation is adopted under the plane-stress assumption. In order to promote convergence, equilibrium and contact iterations are split. For describing an arbitrarily-shaped tool surface, a generalized tool description method is introduced. Simple shape of tools, such as the hemispherical punch and rounded flat-top punch can be analyzed. In addition, any tool described by equally-spaced digital data can be used, based on cubic B-spline or piecewise linear basis functions. The validity, accuracy and stability of the FEM formulation were numerically tested using simple stretch forming examples. Excellent agreement between measured and computed strains was obtained.

Key Words

Sheet-Metal Forming Simulation Rigid-Viscoplastic Hardening Press-Die Design Analysis Membrane Shell Theory Finite Element Method Tool Description 



Principal strain increment

\(\Delta \bar \varepsilon \)

Effective strain increment during †t


Principal stretch ratio


Time increment


Incremental displacement during Δt


Tangential incremental displacement


Trial incremental displacement


Correction displacement increment

\(\bar \varepsilon \)

Effective strain

\(\bar \varepsilon \)

Effective strain rate


Internal force vector


External force vector


Normal component ofF e


Tangential component ofF e


Contact force direction


External stiffness matrix


Internal stiffness matrix


Hill's non-quadratic yield function parameter


Strain rate sensitivity index


Coulomb friction coefficient


Mesh-based normal unit vector


Plastic anisotropy parameter


Tool surface function,z=S(x,y)


Principal Cauchy stress

\(\bar \sigma \)

Effective stress


Time variable; Length parameter


Mesh-based tangential unit vector


Reference time


Volume att=t 0


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Copyright information

© The Korean Society of Mechanical Engineers (KSME) 1992

Authors and Affiliations

  • Y. T. Keum
    • 1
  • R. H. Wagoner
    • 2
  1. 1.CAD/CAM Lab.Korea Institute of Science and TechnologySeoulKorea
  2. 2.Department of Materials Science and EngineeringThe Ohio State UniversityColumbusU.S.A.

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