Mapping of the invariants K2 and K3 of the Hencky's tensor.

Mapping of the invariants K2 and K3 of the Hencky's tensor for the AE2 and the perfect cylinder geometries described by different 8-chains models.

The different documents are :
- Invariants_Hencky_UVARM.f : UVARM fortran script that compute the invariants K1, K2 and K3 of the Hencky's tensor without any assumption about the incompressibility.
- Map_AE2_Li_Mj.csv : raw data of the vertical displacement, torsion angle, K2, and K3 for the AE2 geometry associated with the parameters lambda_m=i and mu=j of the 8-chains model.
- ArrudaBoyce_L1_M01_K3_1.csv : raw data of the simulation associated with the path K3=1 (8-chains parameters : lambda_m=1 & mu=0.1).
- ArrudaBoyce_L1_M01_K3_0.csv : raw data of the simulation associated with the path K3=0 (8-chains parameters : lambda_m=1 & mu=0.1).
- Arruda_Boyce_materials_mapping.py : Python script that allows to plot the K2 and K3 maps for the differents 8-chains models.
- Perfect_cylinder_kinematic_and_maps.py : Python script that allows to compute and plot the K2 and K3 maps for the perfect cylinder.
- Simulation_script_Abaqus.py : Python script that allows to do all the required Abaqus simulations to get the map.
- AE2_AB_L1_M01.cae : CAE file of the AE2 geometry (this example is associated witht the 8-chains parameters lambda_m=1 & mu=0.1)
- AE2_AB_L1_M01.jnl : JNL file associated to the AE2_AB_L1_M01.cae file.

The scripts have to be completed by te user to adapt the different path but no other modifications are required.

As reference the paper of Criscione et al. is given to get the description of the invariants.