The Constitutive Model And Numerical Analysis Of The Steel Fiber Reinforcement Concrete Based On The Smear Crack Model

Steel fiber reinforced concrete(SFRC)not only with the advantages of high compressive strength of concrete but also the low tensile strength,low toughness are effectively improved by the steel fiber.SFRC has been better applicability and widely in engineering.This paper explores the fiber reinforcement effect on cracks,and establishs the new constitutive model of SFRC.In the elastic stage,the steel fiber is regarded as additive with high performance.Based on the two-phase composite law,the elastic modulus and shear modulus of SFRC is modified by considering the excellent mechanical properties of steel fiber.In the tensile stage,to fully consider the steel fiber pull-out process,the relationship between the fiber reinforcement stress and crack width is established.Based on the smeared crack constitutive model of the plain concrete and the bond-slip model,the constitutive model of SFRC is established by considering the effect of matrix and steel fiber on crack.The established constitutive model of SFRC is achieved by FORTRAN programming and introduced into the finite element software ABAQUS through the secondary development of user-defined subroutine interface UMAT.The constitutive model of SFRC is used and the corresponding finite element models are established in ABAQUS for tensile,compression and bending tests.By comparing the simulation and experimental results,the accuracy of the proposed constitutive model is verified.Moreover,based on the finite element models of SFRC under tensile and compressive loading,the influence of fiber volume fraction,length,and diameter on the mechanical properties is explored,the prediction formulas of compressive strength,tensile strength,and peak strain are established.Long and short steel fibers have different reinforcing effects on cracks.The reinforcing effects of hybrid fibers are calculated,and the constitutive model of the hybrid steel fiber reinforced concrete(Hy SFRC)is established under uniaxial tension.The proposed constitutive model is adopted in the finite element software ABAQUS,the finite element model of Hy SFRC is established and numerical simulation analysis is performed.The accuracy of the proposed constitutive model is verified by comparing the simulation and experimental results.Moreover,parametric analysis of the steel fiber is carried out to explore the influence of the fiber content and aspect ratio.Taking into account the enhancement coefficient and matrix spalling coefficient of inclined fiber pull-out process,the inclined coefficient is established,and the range of the effective inclination angle and the optimal inclination angle are determined.The coefficient of fiber spacing is calculated by the fiber spacing and fiber influence distance,the fiber critical volume fraction is proposed by the fiber spacing coefficient.To accurately simulate SFRC with the high fiber content,the proposed constitutive model is further modified by considering the coefficient of inclined enhancement and spacing coefficient.Based on tensile tests of SFRC with high volume fraction,the finite element models are established for verifing the modified constitutive model.Based on the softening modulus of concrete after cracking and the reinforcement effect of steel fiber,the strengthening/softening modulus of SFRC after cracking is proposed.The modulus is used as the criterion of whether the tensile stress of SFRC appears the second peak,and the three states of tensile strength of SFRC have been proposed by the modulus.While the influence of volume fraction,length,and diameter of fiber on the peak stress of SFRC is explored under tension.The addition of steel fiber improves the tensile strength,compressive strength,residual strength,and toughness of the plain concrete.Focusing on the reinforcing effect of steel fiber in multiple states,the suitable constitutive model of SFRC is proposed.The proposed model can accurately and efficiently simulate mechanical properties of SFRC under the various status.Therefore,it would provide theoretical support for the wide application in engineering.