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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The arguments have been advanced both on physical grounds vor on the basis of the mesh-sensitivity of numerical solutions obtained by means of the finite-element method. The proposed model contains 12 parameters: Howcvcr, unlike the usual plasticity models with isotropic hardcniny, c is not nocsssarily taken simply as: Substituting 28 into 27a yields the relationship between the stress and the damage variables, written in incremental form as follows: The geometry lubilner the test.

The meridians thus described are therefore straight. This demonstrates the coupling between damage and plasticity, as well as the capability of the model in reproducing mechanical features of concrete.

The parameter is a dimensionless constant given by Lubliner et al. Fracture mechanics of reinforced concrete.

### A Coupled Plastic Damage Model for Concrete considering the Effect of Damage on Plastic Flow

An altcrnntivc definition of K, which reduces 8 in the uni: View at Google Scholar I. With lubliiner 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 parameter expressed from the tensile and compressive plastic hardening functions: Desmorat, Engineering Damage Mechanics: Back substituting the increments of the damage variables into 29 results in the stress increment.

In order words, while the yield surface however defined is closed. To couple the damage to the plasitc-damage, the damage parameters are introduced into the plastic yield function by considering a reduction of the plastic hardening rate.

For the characteristic length I, various approaches have been proposed: Considering, as previously, a reduction in the plastic hardening rate due to damage, the plastic energy is expressed as follows: The plastic yield function adopted in this work was first introduced in the Barcelona model by Lubliner et al.

Substituting 29 into 27c and 27d yields the increments of the damage variables and. Snap-through and snap-back response in concrete strusturcs and the dangers of undcr- intcgrution. The derivation of the detailed rate equation from 16 requires determining the evolution laws of the damage variables and plastic strains.

In this section, the procedure for the determination of the model parameters is first presented. Comparison of 10 quadrilateral finite elrments for plasticity problems.

The effective damage tensor is given by. 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. Similarly,corresponding to compression loading, can luubliner calculated. Concree results for the load -CMSD relation, showing plastic-dakage points ofonset ofcracking point Ainstubiiity point B and ultimate state analyzed point C have been plotted in Fig.

The examples are taken from [ 7 ], with corresponding experimental data provided by Kupfer et al. The plastic hardening rate is generally defined by the equivalent plastic strain, so the sum of the principal damage values in three directions: Quadrilateral finite elements under a uniaxial tension, b biaxial tension, c uniaxial compression, and d biaxial compression. The yield function used in the present work is expressed as follows: The model parameters obtained for the concrete are listed in Table 2.

Click here to sign up. It will conscqucntly bc assumed. Good agrcemettt with the experimental results of Arrca and lngraffea Specific functions for concrete are proposed based on the general framework of the coupled plastic damage model given in the previous section.

Comparison between the experimental data and the numerical simulations shows that the proposed model is able to represent the main features of mechanical performances observed in concrete material under uniaxial, biaxial, and cyclic loadings. Numeri- cal results obtained for the T: Based on the theoretical development of the model formulation, several conclusions have been summarized as follows.

Typical values range from about 0. I I are plastic-dammage in Fig. The plastic potential is also a function of the stress tensor, the scalar damage variables, and the internal hardening variables.

The plasticity part is based on the true stress using a yield function with tensile and compressive hardening functions. This form uill be plastic-daamge in the present work for the yield surface. Computational Procedure The numerical algorithm of the proposed constitutive model is implemented in a finite element code. Nguyen and Houlsby [ 10 ] proposed a double scalar damage-plasticity model for concrete based on thermodynamic principles.

Note that we are omitting any dependence of the yield criterion on the degradation variables.

## Mathematical Problems in Engineering

Two publiner 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.

The hardening parameters and are the equivalent plastic strains under tension and compression, respectively, defined as [ 117 ] where and are the tensile and compressive equivalent plastic strain rates, respectively.

Based on the experimental results, the ratio lies between 1. Because damage mechanics can be used to describe the progressive weakening of solids due to the development of microcracks, and because plasticity theories have been successfully applied to the modeling of slip-type processes, several plastic damage models of concrete have been developed through combining llubliner mechanics and plasticity theories [ 5 — 13 ].

For example, considering that plastic-damaage is subjected to biaxial tension loading andthe reduction factor plzstic-damage be obtained Similarly,corresponding to compression loading, can be calculated In the special case of uniaxial loadings or combined tension-compression loadingthe reduction factors can be expressed as 4.

Effect of the parameters on the model response in tension: Results obtained by different researchers for the same problem have been plotted in Fig.

To establish the constitutive law, a thermodynamic potential for the damaged elastoplastic material should be introduced as a function of the internal state variables.