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 OĆ±ate, E. () A Plastic-Damage Model for Concrete. International Journal of Solids and Structures, 25,

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It is assumed that damage can be represented effectively in the material compliance tensor. These responses observed in Figure 3 show the coupled effect of damage and plasticity on the predicted response.

Because the associative flow rule is adopted in the present model, the plastic yield function is also used as the plastic potential to obtain the plastic strain.

The excellent agreement with experiment obtained in the solution of a concrehe problem such as that of the notched beam shows that the potential of the present approach is great.

The framework of irreversible thermodynamics is adopted to describe the damage evolution and plasticity damage coupling. The following notational convention is used in this section: The form taken by tho proposed yitld surface on ditrcrcnt planes of the stress space is shown in Fig.

Their mathematical expressions can be logarithmic, power, or exponential functions. Furthermore, this algorithm ensures that the plastic and damage consistent conditions are fulfilled at any stage of the loading process. In order to obtain a graphic representation of this kind of damage. The mechanical behavior of concrete is unique, due to the influence of micromechanisms involved in the nucleation and growth of microcracks and plastic flow.

The derivation of the fir rate equation from 16 requires determining the evolution laws of the damage variables and plastic strains. Once r is known.

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By solving 1617and 21 in terms of the trial stress, the increments of the equivalent plastic strains andplastic strainand damage variables and can be obtained: The model presented in this work is thermodynamically consistent and is developed using internal variables to represent the material damage state.

On the creep rupture of structures. Substituting 29 into 27c and 27d yields the increments of the damage variables and. In order words, while the yield surface however defined is closed. Damage variables are introduced all over the plastic yield function. By using these parameters, simulations of biaxial compression-compression and compression-tension tests with different stress ratios have been performed.

The plasticity part is developed without using the effective stress concept. The special cuscs of pure tension and compression follow obviously from cqn According to the second principle of thermodynamics, any arbitrary irreversible process satisfies the Clausius-Duhem inequality as.

The plasticity yield function widely used in effective stress space is modified to be applied in this study by considering a fir in the plastic hardening rate. These coupled plastic damage models CPDMs could be formulated in the irreversible thermodynamics framework and can be easily applied to describe the essential nonlinear performances of concrete including the strain softening and the stiffness degradation.

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. To comply with the results of cnocrete studies [ 79 ], these numerical examples were analyzed using the single quadrilateral finite element shown in Figure 1. MLchanics of distributed cracking.

## Mathematical Problems in Engineering

Effect of the parameters on the model response in tension: With an associated Row rule, this result gives the following value of the ratio of the transverse to the axial rofrrl strain rates: The parameter is a dimensionless constant given by Lubliner et al.

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: Based on the experimental results, the ratio lies between 1. A possible form is [ 44 k t7. Back substituting the increments of the damage variables into 29 results in the stress increment. It can be observed in Figure 4 that the numerical predictions, including not only the hardening and softening regimes of the stress-strain curve but also the stress-plastic strain curve, are in good agreement with the experimental data [ 31 ].

The clfect of creep constitutive and damage relationships upon the rupture time of a solid circular torsion bar.

### A PLASTIC-DAMAGE MODEL FOR CONCRETE | ec pf –

Two reduction factors are introduced into the tensile and the compressive hardening functions to consider the influence of the tensile and compressive damage mechanisms on the plastic flow, respectively. These responses observed in Figure 4 again indicate the coupled effect of damage and plasticity on the predicted behavior.

It can be shown that these functions can be obtained, in monotonic radial loading, from the following forms of 6, and A first attempt of the authors to obtain suitable yield criteria for concrete in the form of eqn 2 was to modify the Mohr- Coulomb criterion to tit enpcrimsntal data.