README.md



Finite Strain Viscoelastic - Viscoplastic (VEVP) ¹ Constitutive Law


Description
Quantity


Material parameters
51


Internal variables
108


Material Parameters Description
The UMAT implementation uses the material parameters in the following order:


No
Description
Parameter
Unit


1
Power Series Strain Approximation
order
-


2
Bulk Modulus
K_{\infty}
Pa


3
Shear Modulus
G_{\infty}
Pa


4
Yield Exponent
\alpha
-


5
Plastic Poisson Ratio
\nu_p
-


6
Viscoplastic coefficient
\eta
Pas


7
Viscoplasic exponent
p
-


8
Initial Yield Limit - Compression
\sigma_{c0}
Pa


9
Isotropic Hardening - Compression H_c=c_0+H_{c}^{0}exp(-h_c\gamma)

c_0
-


10
Isotropic Hardening - Compression
H_{c}^{0}
-


11
Isotropic Hardening - Compression
h_{c}
-


12
Initial Yield Limit - Tension
\sigma_{t0}
Pa


13
Isotropic Hardening - Tension H_t=t_{0}+H_{t}^{0}exp(-h_{t}\gamma)

t_{0}
-


14
Isotropic Hardening - Tension
H_{t}^{0}
-


15
Isotropic Hardening - Tension
h_{t}
-


16
Kinematic Hardening Parameter H_b = h_{b0}+h_{b1}\gamma+h_{b2}\gamma^2

h_{b0}
-


17
Kinematic Hardening Parameter
h_{b1}
-


18
Kinematic Hardening Parameter
h_{b2}
-


19
Bulk Modulus - Maxwell branch 1 ²

K_1
Pa


20
Bulk Modulus - Maxwell branch 2
K_2
Pa


21
Bulk Modulus - Maxwell branch 3
K_3
Pa


22
Bulk Modulus - Maxwell branch 4
K_4
Pa


23
Bulk Modulus - Maxwell branch 5
K_5
Pa


24
Bulk Modulus - Maxwell branch 6
K_6
Pa


25
Bulk Modulus - Maxwell branch 7
K_7
Pa


26
Bulk Modulus - Maxwell branch 8
K_8
Pa


27
Retardation Time Volumetric - Maxwell Branch 1
k_1
s


28
Retardation Time Volumetric - Maxwell Branch 2
k_2
s


29
Retardation Time Volumetric - Maxwell Branch 3
k_3
s


30
Retardation Time Volumetric - Maxwell Branch 4
k_4
s


31
Retardation Time Volumetric - Maxwell Branch 5
k_5
s


32
Retardation Time Volumetric - Maxwell Branch 6
k_6
s


33
Retardation Time Volumetric - Maxwell Branch 7
k_7
s


34
Retardation Time Volumetric - Maxwell Branch 8
k_8
s


35
Shear Modulus- Maxwell branch 1 ²

G_1
Pa


36
Shear Modulus- Maxwell branch 2
G_2
Pa


37
Shear Modulus- Maxwell branch 3
G_3
Pa


38
Shear Modulus- Maxwell branch 4
G_4
Pa


39
Shear Modulus- Maxwell branch 5
G_5
Pa


40
Shear Modulus- Maxwell branch 6
G_6
Pa


41
Shear Modulus- Maxwell branch 7
G_7
Pa


42
Shear Modulus- Maxwell branch 8
G_8
Pa


43
Retardation Time Deviatoric - Maxwell Branch 1
g_1
s


44
Retardation Time Deviatoric - Maxwell Branch 2
g_2
s


45
Retardation Time Deviatoric - Maxwell Branch 3
g_3
s


46
Retardation Time Deviatoric - Maxwell Branch 4
g_4
s


47
Retardation Time Deviatoric - Maxwell Branch 5
g_5
s


48
Retardation Time Deviatoric - Maxwell Branch 6
g_6
s


49
Retardation Time Deviatoric - Maxwell Branch 7
g_7
s


50
Retardation Time Deviatoric - Maxwell Branch 8
g_8
s


Remark
Lines 164-168 have to be uncommented for use in FFTMAD but have to be commented for ABAQUS or cm3Libraries.
If you comment out, then in ABAQUS, use the inp file to set initial values for F_vp.

Disclaimer
Code related to MOAMMM project
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 862015.
Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union. Neither
the European Union nor the granting authority can be held responsible for them.


The finite-strain visco-elastic visco-plastic model follows: "Nguyen, V. D., Lani, F., Pardoen, T., Morelle, X., & Noels, L. (01 October 2016). A large strain hyperelastic viscoelastic-viscoplastic-damage constitutive model based on a multi-mechanism non-local damage continuum for amorphous glassy polymers. International Journal of Solids and Structures, 96, 192-216.  doi:10.1016/j.ijsolstr.2016.06.008" which can be downloaded here.

we would be grateful if you could cite this publication in case you use the files ↩


The UMAT is hardcoded for 8 Maxwell VE Branches. If you feel the need for more branches send me an email at mohibmustafa@gmail.com. ↩ ↩²