Elastoplastic Damage Constitutive Model Of Ultra-High Performance Concrete

As a sustainable and high performance concrete material,UHPC exhibits excellent durability and composite performance,and has less energy consumpution,less damage and pollution to the environment.Since its inception,UHPC has received widespresd attention and has been succssfully applied in bridge engineering,construction engineering,structural maintenance and reinforcement and other fields.In engineering applications,the shape and stress state of various structures are more complex.Hence,it is urgent to conduct the nonlinear analysis of structures.Nevertheless,the reliability and accuracy of analysis results mainly depend on the accuracy and rationality of nonlinear constitutive relations of materials.Meanwhile,the nonlinear behavior of concrete material and structures is mainly caused by plastic deformation and damage evolution.Therefore,the establishment of elastoplastic damage constitutive model of UHPC,which is the key for the nonlinear analysis of sturctures,has become an important research direction of UHPC structuers,and is crucial to promote the application of UHPC material and guide the design of UHPC structures.Supported by the key project of National Natural Science Foundation of China "Research on the Mechanical Properties and Design Calculation Theory of Ultra-high Performance Concrete filled Steel Tube under Complex Load"(Grant NO.51738011),the present work is carried out by means of experimental research,theoretical analysis and numerical realization.The cyclic stress-strain relationship of uniaxial tension/compression,triaxial stress-strain relationship and elastic-plastic damage constitutive relationship of UHPC are systematically and deeply studied.The main research content and result of this paper are as follows:(1)Considering the influence of steel fiber volume fraction,steel fiber aspect ratio and polypropylene fiber volume fraction,16 groups of 96 prisms were designed.Through uniaxial cyclic compressive test and acoustic emission technology,failure mode of UHPC was investiged,the stress-strain relationship was obtained.The mechanical properties with respect to plastic strain,stiffness degradation and damage evlolution of UHPC were analyzed.The damage mechanism and hybrid fiber reinforcing mechanism of UHPC were revealed.The damage constutitive model of UHPC under uniaxial cyclic compression was established.The results showed: UHPC with hybrid fiber shows obvious ductile failure mode,and the specimen can remain good integrity.The peak stress,peak strain,limit strain and toughness of UHPC under uniaxial compression increase with the increase of volume fraction and aspect ratio of steel fiber(SF),while the increase of polypropylene(PF)fiber volume fraction can enhance the peak stress.Hybrid fibers can alleviate the stiffness degradation and stress softening and increase the residual stress.The plastic strain increases linearly with unloading strain.Steel fiber can effectively alleviate the accumulation of plastic strain,while PF fiber has insignificant effect.An equation related to fiber reinforcing indexes is proposed to characterize the damage evolution of UHPC under uniaxial compression.The internal damage mechanisms of UHPC under uniaxial compression include closure of initial micro-crack and collapse of micro-hole inside UHPC,cracking of UHPC matrix,friction of fracture surface,debonding and pullout of SF as well as elongation and fracture of PF fiber,etc.Tensile cracks and shear cracks exist in all UHPC specimens.The failure of UHPC with PF fiber alone is mainly dominated by tensile cracks,while the failure of UHPC with only SF or hybrid fiber is mainly controlled by shear cracks.(2)Considering the influence of steel fiber volume fraction,steel fiber aspect ratio and polypropylene fiber volume fraction,16 groups of 96 cylindrical specimens were prepared.Through uniaxial cyclic tensile test,AE and SEM test results,failure mode of UHPC was studied,the stress-strain curve was obtained.The mechanical properties in terms of plastic strain,stiffness degradation and damage evolution of UHPC were analyzed.The damage mechanism and reinforcing mechanism of hybrid fibers were elucidated.The damage constutitive model of UHPC under uniaxial cyclic tension was established.The results showed: UHPC with hybrid fibers exhibits ductile failure mode.The peak stress,peak strain and tensile toughness of UHPC under uniaxial tension are improved with the increase of olume fraction and aspect ratio of steel fiber.PF helps further improves the tensile toughness in the post-peak response.Elastic stiffness degradation can be moderated due to the inclusion of hybrid fibers,especially the steel fibers.Plastic strain accumulation has a linear relationship with envelope unloading strain,which is not affected by hybird fiber characteristic parameters.An equation is proposed to represent the damage evolution law of UHPC under uniaxial tension.The internal damage mechanisms of UHPC under uniaxial tension include cracking of UHPC matrix,friction of fracture surface,debonding and pullout of steel fibers as well as elongation and fracture of polypropylene fiber,etc.The dense microstructure of UHPC matrix is hepful to improve the whole tensile properties.Steel fibers can bridge force,change the direction of crack development,make the stress redistribution through debonding,sliding and pullout.Polypropylene fibers can absorb energy and increase ductility by tension,delamination,fracture.Steel fiber and polypropylene fiber form a mesh structure together to inhibit damage evolution synergistically.(3)In consideration of the influence of confining pressure,steel fiber volume fraction,steel fiber aspect ratio and polypropylene fiber volume fraction and other factors,13 groups of 39 cylinder samples were cast to explore the stress-stain relationship of UHPC under triaxial compression.The failure mode was summarized.The triaxial mechanical properties,stress-strain curve and volume strain-stain curve were analyzed.The mathematical expressions of peak stress and peak strain under different confining pressures and a triaxial constitutive model were proposed.The strength criterion of UHPC was established.The results showed that UHPC specimen exhibits shear failure.Besides,the specimen after test remains good integrity.The confining pressure and steel fiber can obviously improve the triaxial mechanical properties of UHPC,and the polypropylene fiber contributes to deformation ability.Considering the effect of hybrid fibers,the tensile and compression meridian function of UHPC are established.Based on the William-Warnke model,the multi-axial strength criterion of UHPC is established,which can accurately predict the strength of UHPC with different fiber characteristic parameters under complex stress states.Besides,compared with yield surface shape of fiber reinforced concrete,the yield surface shape of UHPC is sharper.(4)Based on irreversible thermodynamics,elastoplastic mechanics and continuum damage mechanics,considering the influence of damage development on plastic deformation development,in the effective stress space,the yield criterion is established based on the William-Warnke model,the non-associated flow rule is developed based on improved Drucker-Prager form plastic potential function,and the plastic hardening criterion is proposed according to test results,combined with consistency condition,UHPC elastoplastic constitutive model was established.In the nominal stress space,the damage criterion is determined based on damage energy release rate,the damage flow law is calibrated based on test results.The elastoplastic damage constitutive model of UHPC is constructed.With definite physical meaning,the established constitutive model can truly reflect the nonlinear behavior and damage evolution of UHPC under different stress states.(5)Two parallel integration algorithms were used to calculate the development of plasticity and damage,respectively.Based on the user-definded material condtitutive relationship interface provided by finite element software ABAQUS,the corresponding subroutine was programmed and implemented numercially.Then the unmerical algorithm was validated by the experimental results under different stress states and different loading paths from independent research.It is proved that the proposed constitutive model can effectively simulate the mechanical performance of UHPC under different load conditions.Therefore,the UHPC elastoplastic damage constitutive model is suitable for subsequent numerical simulation of UHPC members and structures.Finally,based on summary of the research results in this paper,some suggestions are put forward for future research of this task.