r5.03.19 Hyperelastic and visco-hyper-elastic laws of behavior: almost incompressible material

Summary:

Two laws of hyper-elastic and visco-hyper-elastic behavior adopted for elastomers are described here. The parameters characterizing the two materials are defined in [DEFI_MATERIAU] with the keywords ELAS_HYPER and ELAS_HYPER_VISC.

The hyper-elastic part is the same for both models, of the Signorin type, which is a generalized version of the Mooney-Rivlin laws. It is implemented « natively » for ELAS_HYPER and under MFront for ELAS_HYPER_VISC. The viscous part of the latter is modelled by a generalized Maxwell type viscoelastic branch, placed in parallel.

These models are chosen in the [STAT_NON_LINE] or [DYNA_NON_LINE] command using the keywords RELATION =” ELAS_HYPER “and RELATION =” ELAS_HYPER_VISC “and under the keyword [COMPORTEMENT]. This relationship extends to large transformations; this feature is chosen using the keyword DEFORMATION =” GREEN_LAGRANGE “. It is available for 3D, 3D_SI, C_ PLAN, and D_ PLAN elements.

• 1. Hyper-elastic formulation
  • 1.1. Cinematics
  • 1.2. Deformation potential — compressible case
  • 1.3. Deformation potential — incompressible case
• 2. Viscous formulation
  • 2.1. Piola-Kirchhoff stress tensor 2
  • 2.2. Lagrangian elasticity tensor
• 3. Analytical expressions
  • 3.1. Piola-Kirchhoff 2 stress tensor of the visco_hyper_elastic law
• 4. Bibliographical references