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 derivation of the plastic-damqge rate equation from 16 requires determining the evolution laws of the damage variables and plastic strains.
The meridians thus described are therefore straight.
In this algorithm, the damage and plastic corrector is along the normal at the elastic trial point, which avoids considering the intersection between the predicting increments of elastic stress and the damage surfaces. The plastic voncrete 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.
Many authors used this approach to couple damage to plasticity.
The parameter is a parameter expressed from the tensile and compressive plastic hardening functions: It is an essential feature of this model that the same function F a. Howcvcr, unlike the usual plasticity models with isotropic hardcniny, c is not nocsssarily taken simply as: Generally, the parameters and are the functions of the damage scalars, respectively.
Ofiate Part I, pp. Substituting 14 into 13 and calling for 5one obtains. This localization can also be clearly seen in Fig. The elastic trial stress is defined as follows: The model presented in this work is thermodynamically consistent and is developed using internal variables to represent the material damage state.
Considering, as previously, a reduction in the plastic hardening rate due to damage, the plastic energy is expressed as follows: To comply with the results of the studies [ 79 ], these numerical examples were analyzed using the single quadrilateral finite element shown in Figure 1. Subscribe to Table of Contents Alerts.
The plastic potential is also a function of the stress tensor, the scalar damage variables, and the internal hardening variables. I function of K.
In this model, the plasticity part is based on the true stress using a yield function with two hardening functions, one for the tensile loading history and the other for the compressive loading history. The singular points of the yield surfaccarc the following: The plastic tensile and compressive hardening functions of the damaged material are then specified as. Compressive failure may occur through several mechanisms-crushing, shearing. In general, the damage mechanics theories can be used to model the nucleation and ofr of microcracks [ 1 — 3 ], whereas the plasticity theories can be used to model the plastic flow component of the deformation [ 4 ].
A PLASTIC-DAMAGE MODEL FOR CONCRETE | ec pf –
The broitdcst arelt of success of pklsticity theory with conorctc is the treatment of reinforced concrete see Chcn, for 3 survey of the results und other situations in condrete the material acts primarily in compression.
General Framework of Coupled Plastic Damage Model The model presented in this work is thermodynamically consistent and is developed using internal variables to represent the material damage state. 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.
Also, displacements have been controlled using a standard spherical path technique Crisficld, In this section, the behavior of the proposed model in combined loadings biaxial compression and biaxial tension-compression is investigated.
Mathematical Problems in Engineering
Let TM and CM dcsignatc. The same result is nob found in triaxiai compression tests, at least at sufficiently large hydrostatic pressures; under these conditions it is found that the hardening goes on indefinitely.
To receive news and publication pplastic-damage for Mathematical Problems in Engineering, enter your email address in the box below. A maximum-dissipation principle in generalized plasticity.
To progress further, evolutionary relations are required for the added compliance tensors and. Material models for granular soils.
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The model parameters obtained for the concrete are listed in Table 2. Even if several types of expressions for the plastic yield function written in terms of the effective stress have been successfully applied to model some of the typical nonlinearities of concrete such as the volumetric dilation and strength increase under multidimensional compressionthey cannot be directly used mode the true stress space.
Based on this consideration, several researchers proposed an elastic degradation model in which the material stiffness or compliance was adopted as the damage variable.
The constitutive formulations are developed by considering an added flexibility due to microcrack growth.
It is assumed in 6 that the damage can be represented effectively in the material compliance tensor. Damage variables are introduced all over the plastic yield function. I I and ultimrtte toad point C of Fig. Lublindr new yield criterion of the form 2. Constitutive relations for concrete.