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. 2022 Aug 26;15(17):5888. doi: 10.3390/ma15175888
a inner radius
b outer radius
h half-length
p dimensionless inner pressure
q dimensionless axial punch force
(r, θ, z) cylindrical coordinates
s dimensionless parameter introduced in Equation (23)
sr, sθ, sz deviatoric stress components
t time
ur radial velocity
uz axial velocity
H wall thickness
P inner pressure
R Lagrangian coordinate
Q axial punch force
U speed of expansion
V speed of elongation
α dimensionless inner radius
δ wall thinning
εeq equivalent strain
εr, εθ, εz strain components
η function of the polar radius introduced in Equation (23)
ξeq equivalent strain rate
ξr, ξθ, ξz strain rate components
ρ dimensionless radius
σ hydrostatic stress
σeq equivalent stress
σr, σθ, σz stress components
ω dimensionless axial feeding