r7.01.09 Law of Behaviour ENDO_ORTH_BETON

Summary:

This documentation presents the theoretical writing and numerical integration of the law of behavior ENDO_ORTH_BETON developed by [bib1], which describes the anisotropy induced by damage in concrete, as well as unilateral effects (different behavior under tension and compression). The validation of the model in relation to experimental results is also proposed in this document.

Table of Contents

• 1. Introduction
  • 1.1. Characteristics of concrete damage
  • 1.2. Objectives of the ENDO_ORTH_BETON law
• 2. Expression of free energy
  • 2.1. Taking into account the closure of cracks
  • 2.2. Introduction of damage variables
  • 2.3. Terminals of damage
  • 2.4. Introduction of blocked energy
  • 2.5. Final expression of the free energy, stresses, and thermodynamic forces associated with damage variables
• 3. Law of evolution of damage variables
  • 3.1. Law of evolution
  • 3.2. Deformation-dependent threshold function
• 4. Parameter study
  • 4.1. Influence of parameter \(\alpha\)
  • 4.2. Influence of parameters \({\gamma }_{B}\) and \({\gamma }_{d}\)
  • 4.3. Influence of threshold function parameters
  • 4.4. Report on the study of parameters
• 5. Digital implementation
  • 5.1. Assessment of damage
  • 5.2. Calculation of the tangent matrix
• 6. Validation
  • 6.1. Identifying parameters
  • 6.2. Simple traction
  • 6.3. Simple compression
  • 6.4. Simple traction followed by simple compression
  • 6.5. Biaxial tests
• 7. Features and verification
• 8. Bibliography
• 9. Description of document versions