Acta Mechanica Solida Sinica

, Volume 24, Issue 2, pp 153–165 | Cite as

Sectional finite element analysis of coupled deformation between elastoplastic sheet metal and visco-elastoplastic body

  • Zhongjin Wang
  • Jianguang Liu


The present paper is devoted to developing a new numerical simulation method for the analysis of viscous pressure forming (VPF), which is a sheet flexible-die forming (FDF) process. The pressure-carrying medium used in VPF is one kind of semisolid, flowable and viscous material and its deformation behavior can be described by the visco-elastoplastic constitutive model. A sectional finite element model for the coupled deformation analysis between the visco-elastoplastic pressure-carrying medium and the elastoplastic sheet metal is proposed. The resolution of the Updated Lagrangian (UL) formulation is based on a static explicit approach. The frictional contact between sheet metal and visco-elastoplastic pressure-carrying medium is treated by the penalty function method. Coupled deformation between sheet metal and visco-elastoplastic pressure-carrying medium with large slip is analyzed to validate the developed algorithm. Finally, the viscous pressure bulging (VPB) process of DC06 sheet metal is simulated. Good agreement between numerical simulation results and experimental measurements shows the validity of the developed algorithm.

Key words

viscous pressure forming(VPF) sheet forming sectional finite element analysis coupled deformation visco-elastoplastic pressure-carrying medium 



Young’s modulus


Poisson’s ratio


the slope of the equivalent stress/plastic strain


equivalent plastic strain


equivalent stress


initial yielding strain


material strength coefficient


work hardening index

A, B, h, α, β, ω

material parameters of visco-elastoplastic body


total time


time increment


plastic strain component


viscoelastic strain component


viscoplastic strain component


Kronecker delta tensor


Cauchy stress components


deviatoric stress components


Jaumman rate of Cauchy stress


velocity gradient in the local coordinate system


elastoplastic constitutive matrix


compliance matrix


elastic matrix


strain matrix


fluidity parameter


general yield criterion


second deviatoric stress invariant


shear yield strength


yield strength


integration parameter


tangential penalty factor


normal penalty factor


friction coefficient


time incremental parameter


elastic strain component

rate of traction


equivalent contact force virtual power rate


relative nodal velocity


shape function of contact segment


penetration (gap) rate


stiffness matrix of contact elements

n1e, n2e

total element number of sheet metal and visco-elastoplastic body


total number of contact point pair


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2011

Authors and Affiliations

  1. 1.School of Materials Science and EngineeringHarbin Institute of TechnologyHarbinChina

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