1. A New XFEM Modeling Technique For The Pinching Effect in RC Columns Subjected To Lateral Cyclic Loads
Jiangtao Yu,
Associate Professor, Research Institute of Structural Engineering and Disaster Reduction, College of Civil Engineering, Tongji University, Shanghai, China. Corresponding author.
Wanli Xu
M.S., Candidate, Research Institute of Structural Engineering and Disaster Reduction, College of Civil Engineering, Tongji University, Shanghai, China.
2015/05/06

2. The seismic performance of RC members
第四届全国抗震加固改造技术学术研讨会

3. Cracking propagation by XFEM

4. Principles and Methods in Simulation
1. Concrete is a typical quasi-brittle, discontinuous material, not an elastic-plastic, continuous material;
2. The crack opening and closing of concrete is mechanical based behavior, instead of material property;
3. Artificial simplifications, such as plane section assumption and the coupling between steel bar and concrete, should be avoided as far as possible.
Methods:
1. Discontinuous algorithm for discontinuous materials. Extended Finite Element Method is adopted to simulate the initiation and propagation of crack;
2. Traction–separation law, together with fracture energy dissipation rate, is used to judge the concrete behavior in post-cracking period;
3. Contact algorithm is used to simulate the crack closure;
4. Multi-cracking in concrete structure is exhibited by considering the interaction between concrete and bar.

5. Inputs for ABAQUS and XFEM
Constitutive of the material
1. Concrete behavior before cracking: modulus and maximum circumferential tensile strength (maximum tensile circumferential stress intensity factor criterion);
2. Concrete behavior after cracking: BK mixed mode, fracture energy dissipation rate;
3. Compressive behavior of concrete: elastic-plastic model based on isotropic hardening law;
4. Crack closure: Use phantom nodes (XFEM) to compute surface contact;
5. Tensile and compressive behavior of steel: classic bilinear elastic-plastic model, identical for compression and tension. Bauschinger effect is taken into consideration by kinematic hardening law. Buckling of bar is considered in certain circumstances.
6.Bond-slip relationship: CEB-FIP bond-slip model
Member select in ABAQUS:
Concrete: CPS4R; Steel bar: Truss Member T2D2; Bond-slip relationship: CONNECTOR。

6. Validation in macroscopic level

7. Validation in macroscopic level
Loading diagram of displacement history

8. Validation in macroscopic level
Crack initiating
Comparison of hysteretic loops

9. Validation in macroscopic level
Comparison of skeleton curves
Single loop of load-displacement

10. Further discussion Three Mechanisms, Five Keywords
The formation mechanism of the pseudo-constitutive relationship of concrete;
The formation mechanism of multi-crack in reinforced concrete;
The formation mechanism of pinching effect in reinforced concrete;
Keywords: Mesoscopic; discontinuous; fluctuation; mismatch; counteraction;

11. Formation mechanism of the constitutive relationship of concrete
Artificially defined
(most FEM modle)
Computed
(XFEM model)

12. Formation mechanism of the constitutive relationship of concrete
（a） （b）

13. The formation mechanism of multi-crack in reinforced concrete
Deformation fluctuation for concrete and steel
Slips between concrete and steel
Keyword: fluctuation

14. Macroscopic phenomenon
One explanation of pinching effect : delayed crack closure.
Following characteristics could be inferred at the circumstance of low axial compressive ratio:
Accumulated unrecovered concrete deformation under compression;
Accumulated unrecovered steel deformation under tension;
Member tends to elongate
Keyword: mismatch
Explanation

15. Analyze of pinching effect——Concrete
Steel
Concrete
Bauschinger effect
Steel
Concrete

16. Keyword: counteraction
Bending contribution of rebar and concrete
Concrete: Quadrant one and three
Steel rebar: all four quadrants

17. Analyze of pinching effect——Rebar
Tensile zone undergoes more slippage in comparison with that of the compressive zone
Compressive zone
Tensile zone
Keyword: mismatch; counteract

18. Thank you for your attention
Reporter: Wanli Xu
2015/05/06