r7.01.37 Dissipative Homogenised Reinforced Concrete (DHRC) constitutive model devoted to reinforced concrete plates

Abstract:

This documentation presents the theoretical formulation and numerical integration of the DHRCconstitutive law, acronym for « dissipative homogenised reinforced concrete » used with modelling DKTG plates. It is one of models called « global » used to thin structures (beams, plates and shells). Nonlinear phenomena such as plasticity or damage, are directly related to the generalized strains (extension, curvature, distortion) and generalized stresses (membrane forces, bending and cutting edges). So, this constitutive law is applied with a finite element plate or shell. Compared to a multi-layered approach, CPU time and memory are saved. The advantage over multi-layer shells is even more important when the constituents of the plate behaves in a quasi-brittle manner (concrete, for example), as the global model avoids localization issues.

The DHRCconstitutive law idealizes both damage and irreversible deformation under combined membrane stress resulting and bending of reinforced concrete plates using « homogenized » parameters. This constitutive law represents an evolution of the GLRC_DMconstitutive model which idealises only damage in membrane and bending situations. Unlike GLRC_DM, the DHRCconstitutive model has a complete theoretical justification by using the theory of periodic homogenization: it idealises the effects of steel-concrete slip in addition to the degradation of stiffness from the concrete diffuse cracking, the bending-membrane coupling in a consistent way and accounts for the orthotropy and possible asymmetries coming from steel reinforcement grids. The DHRCmacroscopic constitutive law is not softening: this avoids solving problems throughout the structural analysis.

The parameter setting of this constitutive law results of the particular characteristics of concrete and steel materials used, and the geometrical characteristics of the section, the thickness ratio of steel rebar, positions and directions, which are input data of an identification procedure from the responses of representative elementary volumes of the section of the reinforced concrete plate. The total user parameter number is \(21\): \(11\) geometrical parameters and \(10\) material parameters.

• 1. Introduction
  • 1.1. Global modelling
  • 1.2. Objectives of the DHRCconstitutive model
  • 1.3. Ratings
• 2. Formulation of the constitutive law
  • 2.1. Actual Problem and Modelling Assumptions
• 3. Weak Form of the Auxiliary Problems and Homogenised Model
  • 3.1. Local Auxiliary Problems
  • 3.2. Macroscopic homogenised model
• 4. Finite Element implementation
  • 4.1. Parameter identification procedure
  • 4.2. Identification approach
  • 4.3. Microscopic material parameters in RVE \(\Omega\)
  • 4.4. Macroscopic material parameters to be determined
  • 4.5. Automated procedure
  • 4.6. Analytical trivial example
  • 4.7. Comparison of parameters with other constitutive models
  • 4.8. Internal Variables of the DHRC Model
• 5. Verification
• 6. Validation
• 7. References
• 8. Appendix
  • 8.1. Auxiliary problems table
  • 8.2. Convexity of the strain energy density function with discontinuity in damage function
  • 8.3. Proof of the zero-valued tensor \(B\) if microscopic damage field is homogeneous in the RVE