r7.02.11 Cohesive behavior laws: CZM_xxx_xxxet load control

Summary:

Cohesive laws of behavior:

• CZM_EXP_REG (Cohesive Zone Model EXPonentielle REGularisée)

• CZM_LIN_REG (Cohesive Zone Model LINéaire REGularisée)

• CZM_OUV_MIX (Cohesive Zone Model OUVerture based on a MIXte formulation)

• CZM_EXP_MIX (Cohesive Zone Model EXPonentielle based on a MIXte formulation)

• CZM_TAC_MIX (Cohesive Zone Model TAlon -Curnier based on a MIXte formulation)

• CZM_TRA_MIX (Cohesive Zone Model TRApèze based on a MIXte formulation)

• CZM_FAT_MIX (Cohesive Zone Model FATigue based on a MIXte formulation)

make it possible to model the opening of a crack taking into account a cohesive force between the lips of the crack. Surface energy makes it possible to take into account the energy cost of opening the crack. The latter is represented by finite joint elements for the first two and interface elements for the following ones.

The cohesive law CZM_ELAS_MIX is a simplified version of the previous models since the response remains elastic, with or without contact, and possibly with normal or tangential adherence. Among other things, it allows you to test a data layout before moving on to more advanced models.

The law of behavior CZM_LAB_MIX (Cohesive Zone Model Steel-Concrete Bonding based on a MIXte formulation) also makes it possible to model the sliding of steel reinforcements in relation to concrete within a structure.

Here we present the form of energy and the cohesive law that derives from it as a function of the displacement jump as well as the internal variables of the model. The existence of potential instabilities during the propagation of cracks may require control by elastic prediction, the elements of which are specific to these laws are presented.

• 1. Overview of cohesive laws
• 2. Definition of cohesive laws CZM_xxx_REG
  • 2.1. Surface energy
  • 2.2. Constraint vector
  • 2.3. Internal variables
• 3. Definition of cohesive laws CZM_xxx_MIX
  • 3.1. Elastic cohesive law CZM_ELAS_MIX
  • 3.2. Cohesive laws for fragile breakup CZM_OUV_MIX, CZM_TAC_MIX, and CZM_EXP_MIX
  • 3.3. Cohesive law for ductile rupture CZM_TRA_MIX
  • 3.4. Cohesive law for fatigue CZM_FAT_MIX
  • 3.5. Numeric parameters PENA_LAGR and RIGI_GLIS
  • 3.6. Internal variables
  • 3.7. Cohesive law for a steel-concrete bond CZM_LAB_MIX
• 4. Load management by elastic prediction
  • 4.1. Regularized laws
  • 4.2. Mixed-wording laws
• 5. Key words
  • 5.1. Laws CZM_xxx_REG
  • 5.2. Laws CZM_xxx_MIX
• 6. Bibliography
• 7. Description of document versions