Plastic-damage Uniaxial Constitutive Model For Confined And Rate-dependent Concrete

In the nonlinear analysis of complex concrete structure, the constitutive ofthe material takes an important role. Under the loads, plastic strain happens inthe material, with damage happening in the same time. In order to improve theprecision of nonlinear analysis, the plastic-damage model was improvedaccounting the coupling relation between damage and plastic strain. Then it wasextended to the confined concrete and the rate-dependent concrete by studyingthe influence to the damage evolution process from the confining effect anddifferent strain rates. The contents are as following.Firstly, the fundamental equation of plastic-damage concrete constitutivewas deduced, based on the Irreversible Thermo Theory and continuum damagemechnics. Plastic Helmholtz free energy of material was confirmed by anfunction of inner variables. Accounting the coupling relation between damageand plastic strain, the damage evolution equation was deduced by establishingthe relation between damage energy dissipation rate and damage variable. Themodel was verified, by the comparison with the monotonous and cyclic tests, toreflect the nonlinear behavior and damage evolution process of uniaxial concrete.Secondly, based on the plastic-damage model established, the confine effectof the stirrup and steel tube to the damage evolution of concrete was studiedrespectively. A factor, named damage confine factor, was induced to reflect theinfluence to the damage evolution pattern from different physical quantities.Then the damage evolution equation of stirrup confining and steel tube confiningconcrete respectively was established. And the function of plastic deformationwas given. The model was verified, by comparison with confined concrete tests,to reflect the constitutive of confined concrete well.Lastly, the model established above was extended to the rate-dependentconcrete, accounting the effect of different strain rate. For uniaxial compressionconcrete, the rate effect to the damage evolution was ignored but reflected by therefined elastic modulus. As for uniaxial tension concrete, the damage rate factorwas induced to fix the damage evolution equation influenced by different strainrates. The model was verified, by comparison with concrete tests on different strain rates, to reflect the constitutive of rate-dependent concrete well.