### A PLASTIC-DAMAGE MODEL FOR CONCRETE LUBLINER PDF

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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The plastic hardening rate is generally defined by the equivalent plastic strain, so the sum of the principal damage values in three directions: The derivation of the detailed rate equation from 16 requires determining the evolution laws of the damage variables and plastic strains. Furthermore, this algorithm ensures that the plastic and damage consistent conditions are fulfilled at any stage of the loading process.

The arguments have been advanced both on physical grounds and on the basis of the mesh-sensitivity of numerical solutions obtained by means of the finite-element method.

To establish the constitutive law, a thermodynamic potential for the damaged elastoplastic material should be introduced as a function of the internal state variables. The numerical results suggest that the proposed model is able to describe concreete main features of the mechanical behavior for concrete under uniaxial, biaxial, and cyclic loadings.

The two parameters and characterizing the failure surface and the plastic hardening parameter can be determined by fitting both curves of stress-strain and stress-plastic strain obtained in the uniaxial tension test. At the given function of the plastic potential, the evolution law of the plastic strain is expressed as follows: Excellent agreement of numerical results for the u t: As Figure 5 shows, the numerical results obtained from the model are observed to be in good agreement with the experimental data.

A coupled plastic damage model with two damage scalars is proposed to describe the nonlinear features of concrete. All of the parameters can be identified from the uniaxial tension and compression tests. Based on the previous work of Yazdani and Karnawat [ 6 ], Ortiz [ 23 ], and Wu and Xu [ 25 ], the added compliance tensors are expressed in terms of response tensors and such that where the response tensors and determine the evolution directions of the added compliance tensors andrespectively.

It is assumed that damage can be represented effectively in the material compliance tensor. With the hofp of eqns 12 and I 3. The excellent agreement with experiment obtained in the solution of a difficult problem such as that of the notched beam shows that the potential of the present approach is great.

A new yield criterion of the form 2. The plasticity yield function widely used in effective stress space is modified to be applied in this study by considering a reduction in the plastic hardening rate.

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

A good agreement exists between the experimental data [ 33 ] and the numerical simulations obtained with the associated material parameters given in Table 1.

The specific reduction factor is defined as the sum of the principal values of a second-order damage tensor, which is deduced from the compliance tensor of the damaged material. The elastic trial stress is defined as follows: Based on this consideration, several researchers proposed an elastic degradation model in which the material stiffness or palstic-damage was adopted as the damage variable.

Ofiate Part I, pp. To couple the damage to the plasticity, the damage parameters are introduced into the plastic yield function by considering a reduction in the cor hardening rate. These responses observed in Figure 4 again indicate the coupled effect of damage and plasticity on the predicted behavior.

The plastic hardening functions and can be deduced by the derivative of the thermodynamic potential: They are identified as the end of the linear part of the stress-strain curves point in Figure 2.

## Mathematical Problems in Engineering

I I itrc shown. The model contains 12 parameters, which can be obtained by fitting both curves of the stress-strain and the stress-plastic strain in the uniaxial tension and compression tests.

The yield function determines under what conditions the concrete begins to yield and how the yielding of the material evolves as the irreversible deformation accumulates [ 26 ]. The numerical algorithm of the proposed constitutive model is implemented in a finite element code. In the present work, a coupled plastic damage model is formulated in the framework of thermodynamics.

The constitutive formulations are developed by considering an added flexibility due to microcrack growth. The total strain tensor is decomposed into an elastic part and plastic part: In the present work, is chosen as 0. Substituting 14 into 13 and calling for 5one obtains. Let us further assume that the areas under these curves arc finite and equal to.

I I are shown in Fig.