Study On Constitutive Model Of Ultra-High Performance Concrete Based On Continuum-Meso-Damage Mechanics

Ultra-high performance concrete(UHPC)has outstanding mechanical properties such as high tensile strength,high toughness and strain hardening,which has broad engineering application prospects.Its constitutive model is an important base for engineering structure design,finite element calculation and structural health monitoring.At present,the research results on the constitutive model of UHPC are limited,and there is no unified specification.Most of the research methods stay at the level of experimental phenomena,and there are few methods focusing on the mechanical mechanism.It should be noted that there are many initial micro-defects in UHPC,including micro-voids and micro-cracks.Under external force,a series of irreversible changes such as void growth and coalescence will occur in the initial micro-defects,which makes the material stress show nonlinear characteristics such as stiffness degradation and strength softening in the process of strain development,resulting in the deterioration of the macro-mechanical properties of the structure and ultimate failure.Therefore,the constitutive model of UHPC based on damage mechanics theory can more accurately grasp the essential law of material deformation in accordance with such deformation and failure mechanism.The main work and innovations of this paper are as follows:(1)A constitutive model framework for micro-void damage of UHPC is proposed.Based on the meso-damage mechanics method,a spherical void model in a finite volume sphere is established.According to the boundary conditions of the model,the displacement function is constructed and the constraint condition of the principle of minimum potential energy is satisfied.The constitutive model framework for micro-void damage of UHPC is derived through displacement method,volume averaging method and Lagrange multiplier method.The figurative damage factor is introduced into the constitutive model,which opens a breakthrough for the research of damage factor evolution law.(2)A constitutive model framework for decoupling damage of UHPC is proposed.Based on the principle of irreversible thermodynamics in continuous media,the free energy state function of the material is introduced,and the abstract damage variable reflecting the degradation degree of the free energy is defined.The decoupling damage constitutive model with simple mathematical form and higher computational efficiency is derived by mathematical transformation.In order to adapt to the finite element incremental calculation mode,it is expressed as an incremental form.(3)The evolution equation of damage factor in the micro-void damage constitutive model of UHPC is established.Based on the experimental stress-strain data of UHPC with different mix proportions,the damage factor corresponding to any experimental strain point is calculated in combination with the theoretical framework of the micro-void damage constitutive model.Through a large amount of data analysis,simulation,error correction,etc.,the damage factor evolution equations of UHPC under uniaxial tension and compression are proposed.(4)The evolution equation of damage variable in the decoupling damage constitutive model of UHPC is established,and the mode of establishing the damage evolution equation of UHPC under complex stress states is clarified.Based on the equivalence principle that the calculation results of different constitutive models reflect the same objective physical deformation law of materials,the functional relationship between damage variable and damage factor is obtained by numerical experiments,and the evolution equation of damage variable is indirectly obtained by combining with the evolution equation of damage factor.Based on the damage energy release rate,the damage factor evolution equation is established in the generalized stress space,and the damage evolution equation of UHPC under complex stress states can be established.(5)The stiffness degradation effect,strength softening effect and flow hardening phenomenon of UHPC under uniaxial stress state are predicted by using a complete decoupling damage constitutive model.On this basis,the calculation method of flexural capacity of normal section of reinforced UHPC beam is explored,and the calculation formula of flexural capacity considering the contribution of UHPC in tension area of section is established.The theoretical formula and numerical strip method are used to calculate the normal section flexural capacity of beams with different reinforcement ratios and the contribution rate of UHPC in tensile zone to flexural capacity.The difference between the calculation results of flexural capacity and the experimentation results is within the allowable error range,and the contribution rate of UHPC to the capacity of the beam decreases with the increase of the reinforcement ratio.The contribution rate of UHPC in tension zone to normal section flexural capacity is generally about 10% for the beams with moderate reinforcement ratio.