r5.03.20 Nonlinear elastic behavior relationship under large displacements

Summary:

It is proposed to describe here a non-linear elastic behavior relationship that coincides with the Hencky-vonMises elastoplastic law (isotropic work hardening) in the case of a load that induces a radial and monotonic evolution of the stresses at any point of the structure. This model is chosen in command STAT_NON_LINE using the keyword RELATION =” ELAS_VMIS_LINE “or” ELAS_VMIS_TRAC “under the keyword factor COMPORTEMENT.

This behavioral relationship is then extended to large displacements and rotations, insofar as it derives from a potential (hyperelastic law); this functionality is chosen through the keyword DEFORMATION =” GROT_GDEP “. It is available for all 2D and 3D isoparametric elements.

• 1. Nonlinear elastic behavior relationship: ELAS_VMIS_LINE and ELAS_VMIS_TRAC
  • 1.1. Objective
  • 1.2. Behavioral relationship
  • 1.3. Solving the equation in \(p\)
  • 1.4. Calculation of the behavioral relationship and tangent stiffness
  • 1.5. Taking into account thermal deformations
  • 1.6. Special treatment of plane stresses
• 2. Elasticity in large transformations
  • 2.1. Objective
  • 2.2. Virtual work of external efforts: dead load hypothesis
  • 2.3. Virtual work of inner efforts
  • 2.4. Variational formulation
• 3. Bibliography
• 4. Description of document versions