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. E-mail: yujiangtao@tongji.edu.cn Wanli Xu M.S., Candidate, Research Institute of Structural Engineering and Disaster Reduction, College of Civil Engineering, Tongji University, Shanghai, China. Email: 1_vanie@tongji.edu.cn 2015/05/06

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

Cracking propagation by XFEM

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.

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。

Validation in macroscopic level http://www.collapseprevention.net/list.asp?adID=1

Validation in macroscopic level Loading diagram of displacement history

Validation in macroscopic level Crack initiating Comparison of hysteretic loops

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

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;

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

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

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

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

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

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

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

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