Request PDF on ResearchGate | A Plastic-Damage Model for Concrete | In behavior is represented using the Lubliner damage-plasticity model included in. behavior of concrete using various proposed models. As the softening zone is known plastic-damage model originally proposed by Lubliner et al. and later on. Lubliner, J., Oliver, J., Oller, S. and Oñate, E. () A Plastic-Damage Model for Concrete. International Journal of Solids and Structures, 25,
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This finding corresponds to the expressions of the proposed damage energy release rate and the plastic yield criterion in which both the damage scalar and the plastic hardening rate are introduced.
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For example, considering that concrete is subjected to biaxial tension loading andthe reduction factor can be obtained Similarly,corresponding to compression loading, can be calculated In the special case concrwte uniaxial loadings or combined tension-compression loadingthe reduction factors can be expressed as 4. Damage variables are introduced all over the plastic yield function. Several authors applied this approach to develop the CPDM with a true stress space plastic yield function.
Cracking is the most important external mrmifestation of damage in a concrete struc- ture. lubljner
Good agrcemettt with the experimental results of Arrca and lngraffea It is not unreasonable to extend this rule to ali cases corresponding to compression meridians-that is. To couple the damage to the plasticity, the damage parameters are introduced into the plastic yield function by considering a plastiv-damage in the plastic hardening rate.
Excellent agreement of numerical results for the u t: The meridians thus described are therefore straight.
To receive news and publication updates for Mathematical Problems in Engineering, enter your email address in the box below. Also, displacements have been controlled using a standard spherical path technique Crisficld, The last expressions to be specified are the reduction factors.
Open Journal of Civil EngineeringVol. The parameter is a dimensionless constant given by Lubliner et al. To illustrate the effects of the model parameters, and on the behavior of the proposed model, the stress-strain curve, the stress-plastic strain curve, and the damage evolution under uniaxial compression are plotted in Figure 4 in which the results obtained from varying each parameter while vor the others fixed are also presented.
A Coupled Plastic Damage Model for Concrete considering the Effect of Damage on Plastic Flow
According to Shao et al. It is assumed that damage can be represented effectively in the material compliance tensor. This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This resuft will he xlopt4 as 3 working rule for the dctinition of f at the singuhtr points bcfonging to category h.
The plasticity part is based on the true stress using a concrrete function with tensile and compressive hardening functions. This result is in agreement with that described by the proposed damage energy release rate and the plastic yield criterion in which both the damage scalar and the plastic hardening rate are introduced. In general, the damage mechanics theories can be used to model the palstic-damage and growth of microcracks [ 1 — 3 ], whereas the plasticity theories can be used to model the plastic flow component of the deformation [ 4 ].
Considering, as previously, a reduction in the plastic hardening rate due to damage, the plastic energy is expressed as follows: From eqn f6 we obtain. Note that we are omitting any dependence of the yield criterion on the degradation variables.
In the special case of elastic damage loading without plastic flowthe damage multipliers and can be determined by calling for the damage consistency condition under static loading: The model parameters obtained from the experimental data [ 31 ] are listed in Table 1. The effective damage tensor is given by Differentiation of the elastic thermodynamic energy yields the strain-stress relations where is the component of the deviatoric tensor. An altcrnntivc definition of K, which reduces 8 in the uni: With an associated Row rule, this result gives the following value of the ratio of the transverse to the axial rofrrl strain rates: Triuxial stress strain relationship for concrete.
A plastic-damage model for concrete to Experimental bond Fig. As was also said. In biaxial tests on concrete and gromaterials it is usually found Kupfer et II. To couple the damage to the plasticity, the damage parameters are introduced into the plastic yield function by considering a reduction of the plastic hardening rate. Log In Sign Up.
The clfect of creep constitutive and damage relationships upon the rupture time of a solid circular torsion bar. Results obtained by different researchers for the same problem have been plotted in Fig. Irreversible plastic deformation will be formed during the deformation process of concrete. The plastic tensile and compressive hardening functions of the damaged material are then specified as It can be observed from 33 and 41 that the damage variables are introduced into the plastic yield function.
Instead, they have found that the bulk modulus depends primarily on the volume strain, and the shear modulus on the octahedral shear strain, n the elastic range. G, may be identified with the specific fracture energy Cc, defined as the energy required to form a unit area of crack.
In this section, the procedure for the determination of the model parameters is first presented. The framework of irreversible thermodynamics is adopted to describe the damage evolution and plasticity damage coupling.