(
Single axisymmetric Blatz-Ko element test
Blatz-Ko hyperelastic material harden in compression, and soften slightly in tension.
foamlike rubber.
Applicability: Strech ratio <= 2.0
R0=1  inital radius
L0=1  inital length
G=1., nu=0.46, beta = 14.
Cauchy stress = G*lambda^[1+2*nu]*[1-lambda^[-2*[1+nu]]]
where lambda is = L/L0 [strech ratio].
for lambda = 2  true stress = 3.18.
R/R0=[L/L0]^[-nu]
R/R0=0.73 for L/L0=2
Refs.  
  1.  R.A. Brockman, "On the Use of the Blatz-Ko Constitutive Model in Nonlinear
      Finite Element Analysis", Computers&Structers Vol 24, No 4, pp 607-611[1986]

  2.  P.J.Blatz, W.L. Ko, "Application of Finite Elastic Theory to the Deformation
      of Rubbery Materials", Trans. Soc. Rheol. 6,223-251[1962].

Test supplied by: Osman F Buyukisik, osman@fuse.net
)

echo -no
number_of_space_dimensions 2
materi_velocity
materi_displacement
materi_stress
materi_strain_elasti
materi_strain_total
end_initia

node 1  0. 0.
node 2  1. 0.
node 3  0. 1.
node 4  1. 1.
element 1  -quad4 1 2 3 4

group_type 0  -materi
group_materi_elasti_young     0  3.0
group_materi_elasti_poisson   0  0.46
( Blatz-Ko paramaters mu, beta  mu is the linear shear modulus, beta=2*nu/[1-2*nu] )
group_materi_hyper_blatz_ko   0  1. 14.0
group_materi_memory 0  -total
group_axisymmetric 0 -yes

(centerline)
geometry_line  1  0. 0. 0. 1. 1.e-1
(lower edge)
geometry_line  2  0. 0. 1. 0. 1.e-1
(upper edge)
geometry_line  3  0. 1. 1. 1. 1.e-1

bounda_unknown 1  -geometry_line 2 -vely 
bounda_time    1  0. 0. 100. 0.
bounda_unknown 2  -geometry_line 1 -velx 
bounda_time    2  0. 0. 100. 0.
bounda_unknown 3  -geometry_line 3 -vely 
bounda_time    3  0. 0. 1. 1

control_timestep  10  0.1 1.0
control_timestep_iterations  10 10
(
control_print    10 -time_current
control_print_history 10 -node_dof 4 -sigyy
)

target_item 1  -node_dof 4 -sigyy
target_value 1  3.18021  0.01
target_item 2  -node_dof 4 -velx
target_value 2  -0.27 0.04

end_data
