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

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Abstract

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.

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Abbreviations

E :

Young’s modulus

ν :

Poisson’s ratio

H′ :

the slope of the equivalent stress/plastic strain

ε̅ p :

equivalent plastic strain

σ̅ :

equivalent stress

ε 0 :

initial yielding strain

K :

material strength coefficient

n :

work hardening index

A, B, h, α, β, ω:

material parameters of visco-elastoplastic body

t :

total time

Δt :

time increment

ε p :

plastic strain component

ε ve :

viscoelastic strain component

ε vp :

viscoplastic strain component

δ ij :

Kronecker delta tensor

σ ij :

Cauchy stress components

σ′ ij :

deviatoric stress components

σ ij :

Jaumman rate of Cauchy stress

l kl :

velocity gradient in the local coordinate system

D ijkl ep :

elastoplastic constitutive matrix

C :

compliance matrix

D :

elastic matrix

B L :

strain matrix

γ :

fluidity parameter

F :

general yield criterion

J′ 2 :

second deviatoric stress invariant

k :

shear yield strength

σ s :

yield strength

λ :

integration parameter

k T :

tangential penalty factor

k N :

normal penalty factor

μ :

friction coefficient

τ :

time incremental parameter

ε e :

elastic strain component

:

rate of traction

c :

equivalent contact force virtual power rate

δ c :

relative nodal velocity

N c :

shape function of contact segment

ġ :

penetration (gap) rate

K c :

stiffness matrix of contact elements

n1e, n2e:

total element number of sheet metal and visco-elastoplastic body

n c :

total number of contact point pair

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Correspondence to Jianguang Liu.

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Project supported by the National Natural Science Foundation of China (No. 50275035).

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Wang, Z., Liu, J. Sectional finite element analysis of coupled deformation between elastoplastic sheet metal and visco-elastoplastic body. Acta Mech. Solida Sin. 24, 153–165 (2011). https://doi.org/10.1016/S0894-9166(11)60017-7

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  • DOI: https://doi.org/10.1016/S0894-9166(11)60017-7

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