Research Of Self-Repairing Performance For Sma Concrete Beam Based On The Bidirectional B-Spline QR Method

Shape memory alloy (SMA) can made concrete structures possessing functions such as self-monitoring, self-diagnosis, self-healing and autofrettage by its shape memory effect and pseudoelastic effect. It has been gradually applied in the civil engineering. In practical engineering, the concrete member usually works with cracks, the stiffness and bearing capacity of concrete will be weaken by cracks, even the damage of the member will be accelerated. At present, the research of crack self-healing for shape memory alloy smart concrete were mostly based on experiments, further research in theorv still needs. In this paper, the self-repairing performance for cracks in concrete beamwas studied based on the limited response characteristics of shape memory alloy, the main research contents as follows: Firstly, the recovery force of shape memory alloy was studied byperformance experiment. The stress-strain relationship of SMA under uniaxial tensile was analyzed. The effects of constant current, terraced current, initial strain and current intensity on recovery stress of SMA were studied. The curves of relationship between recovery stress and temperature of SMA wire under different initial strain was obtained. Secondly, the spline node displacement of the structure was used to express the unit node displacement based on the principle of bidirectional B-spline QR method. With the aid of element stiffness matrix of the finite element method, the elastoplastic stiffness equation of bidirectional B-spline QR method was derived. Based on elastoplastic incremental theory, the yield condition, flow rule, strengthening model and damage condition of the concrete was defined. The stress-strain nonlinear relationships of the concrete under the stress states such as bidirectional compressive, bidirectional tensile and tension-compression were given. The detailed solving process of the nonlinear analysis by bidirectional B-spline QR method was derivated based on the incremental initial stress iterative method. The correctness and efficiency of elastic-plastic analysis model for the concrete beam based on bidirectional spline QR method was verified by numerical examples.Thirdly, based on the elastic-plastic analysis of bidirectional spline QR method, the recovery force of SMA wire was equivalent to eccentric force, and introduced into the stiffness equation as spline node loads, the crack self-healing equation of SMA smart concrete beam was derivated, a new model for crack analysis of concrete beam was established. The nonlinear analysis program of bidirectional spline QR method was compiled with MATLAB, and the validity and effectiveness of the proposed new model was demonstrated by numerical examples. Finally, the effects of depth-span ratio, reinforcement ratio, eccentric distance and initial strain of SMA on the repair properties were discussed by parametric analysis. The results show that, SMA has good repair performance for cracks in concrete beam, the deflection can be reduced, the stress distribution of steel can be improved and the bearing capacity of concrete beam will increase. The depth-span ratio and initial strain of SMA have significant impact on the repair properties, the reinforcement ratio of the beam and the eccentric distance of SMA have a certain degree of influence.In this paper, the analysis model of crack self-healing performance for SMA smart concrete beam based on bidirectional spline QR method, which has the advantage of easy to deal with crack problem and high computation efficiency, proposes a new thought for crack analysis of the concrete beam. The studies of this paper will provide some useful theoretical basis for the practical engineering.