r5.03.28 Gradient damage law ENDO_FISS_EXP

Summary:

This document describes the fragile elastic behavior model ENDO_FISS_EXP, available in non-local modeling with damage gradient GRAD_VARI. The damage is modelled isotropically, which preferably involves modeling the cracks individually and not by homogenization: the discretization scale must be adapted to this choice. From a phenomenological point of view, the damage criterion is adapted to the modeling of concrete, in particular by distinguishing between the states of tension and compression. In addition, a compression stiffness restoration is introduced to reflect the closure of the cracks. On the other hand, the model is in principle not suitable for modeling the damage of concrete under compression. Finally, it should be noted that the response of the model tends towards that of a cohesive law when the characteristic length becomes small compared to the size of the structure. As a result, the question of identifying this characteristic length does not arise as long as it is sufficiently small. And the model can provide access to the quantities of interest of cohesive laws, such as crack opening.

• 1. Field of application
  • 1.1. Purposes
  • 1.2. Material parameters
  • 1.3. Internal variables
• 2. Continuous model
  • 2.1. Stress-deformations relationship
  • 2.2. Evolution of damage
• 3. Digital integration
  • 3.1. Discretized equations
  • 3.2. Solving the algorithmic evolution equation
  • 3.3. Effective calculation of the gamma function
  • 3.4. Tangent matrix
• 4. Description of document versions
• 5. Bibliography