r7.01.03 Behavioral law BETON_DOUBLE_DP with Drücker-Prager double criteria for concrete cracking and compression

Summary

The model presented in this document, behavior BETON_DOUBLE_DP, is a nonlinear law of behavior for concrete. It is based on the theory of plasticity, it is valid for three-dimensional stress states. The modeling hypotheses used are as follows:

• a field of reversibility of constraints delimited by two criteria of the Drücker Prager type,

• a work-hardening of each of the criteria,

• in compression, positive work hardening up to a peak, then negative work hardening,

• in traction, negative work hardening exclusively,

• a dependence of the shape of the post-peak curves in both cases (traction/compression) on the size of the finite element (the shape of this curve is linked to negative work hardening and to the cracking energy),

• normal plastic flow rules (associated plasticity) and an isotropic work hardening formulation,

• taking into account the dependence of the elasticity thresholds on temperature,

• taking into account the dependence of Young’s modulus on temperature.

Table of Contents

• 1. Ratings
• 2. Introduction
  • 2.1. Main characteristics of the model
  • 2.2. Why two Drücker Prager criteria
• 3. Reversibility domain and threshold functions
  • 3.1. Allure of the domain and the reversibility thresholds
  • 3.2. Mathematical expression of the reversibility domain
  • 3.3. Fracture criterion. choice of coefficients a, b, c and d
  • 3.4. Analysis of the selected reversibility domain
  • 3.5. Work hardening
• 4. Plastic drain
  • 4.1. General form of the rule of normality
  • 4.2. Expression of plastic flow in the current part
  • 4.3. Expression of plastic flow at the top of a cone
  • 4.4. Set of behavioral equations (summary)
• 5. Numerical integration of the law of behavior
  • 5.1. The global problem and the local problem: reminders
  • 5.2. Digital treatment of the regular case.
  • 5.3. Existence of a solution and condition of applicability
  • 5.4. Treatment of irregular cases
  • 5.5. Determining the tangent operator
  • 5.6. Internal variables of the model
  • 5.7. General resolution flow chart
• 6. Bibliography
• 7. Features and verification
• 8. Description of document versions