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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Determination of Specific Functions For Concrete Specific functions for concrete are proposed based on the general framework of the coupled plastic damage model given in the previous section.
The examples are taken from [ 7 ], with corresponding experimental data provided by Kupfer et al. Comparison between the experimental data and the numerical simulations shows that the proposed model is able to describe the main features of the mechanical performances observed in concrete material under uniaxial, biaxial, and cyclic loadings.
A coupled plastic damage model written in terms of the true stress has been proposed in this paper to describe the nonlinear features of concrete in uniaxial and biaxial loadings. In order that the value of K correspondins to the peak stress may be the same in the biaxial as in the uniaxial compression case. 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.
However, associated plasticity seems to match experimental results better after the stress peak in this case. The total strain tensor is decomposed into an elastic part and plastic part: In these models, the true stress appears in the plastic process, which clearly couples plasticity to damage [ 6101115 — 17 ].
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The plasticity part is based on the true stress using a yield function with two hardening variables, one for the tensile loading history and the other for the compressive loading history. Numerical results obtained in the finite-clement analysis of various concrctc structures using tbc framework of standard plasticity theory wcrc cncnuraging and motivated the present rcscarch. The tangent stiffness, as a piecewise linear operator, is symmetric if C, is symmetric crrrtlif C,g is proportional to Cff.
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 vector ecr is used as a measure of the opening and sliding of the crack.
For example, considering that concrete is subjected to biaxial tension loading andthe reduction factor can be obtained. According to the second principle of thermodynamics, any arbitrary irreversible process satisfies the Clausius-Duhem inequality as Substituting the time derivative of the thermodynamic potential into the inequality yields Because the inequality must hold for any value of,andthe constitutive equality can be obtained as follows: In attempting to extend the preceding definitions to multiaxial stress states.
Click here to sign up. The derivation of the detailed rate equation from 16 requires determining the evolution laws of the damage variables and plastic strains.
A Coupled Plastic Damage Model for Concrete considering the Effect of Damage on Plastic Flow
Quadrilateral finite elements under a uniaxial tension, b biaxial tension, c uniaxial compression, and d biaxial compression. Some of these models, developed by the use of two damage scalars and damage energy release rate-based damage criteria, show excellent performance in reproducing the typical nonlinear behavior of concrete materials under different monotonic and cyclic load conditions.
The experimental data of Kupfer et al. In the present work, a coupled plastic damage model is formulated in the mmodel of thermodynamics.
The practical significance of our results is that plasticity theory is a rather simple model in comparison with models based on fracture mechanics or the more sophisticated versions of continuum damage mechanics. Comparison of the model predictions with the experimental results in a cyclic uniaxial tension and b cyclic uniaxial compression. Excellent agreement of numerical results for the u t: With the hofp of eqns 12 and I 3.
I I itrc shown.
Several authors applied this approach to develop the CPDM with a true stress space plastic yield function. 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. IO b was controlled using a spherical path technique Crisfieid, I.
A cyclic multiaxial model for concrete. In general, the splitting mode is dominant in tension, whereas the compressive mode is dominant in compression.
One type of CPDMs is based on the concept of effective stress, which was initially proposed by Kachanov [ 14 ] for metal creep failure. Some of these limitations could bo avoided if a single constitutivc model could be used that governs the non-linear behnvior of concrete.
View at Google Scholar. 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.
The plastic yield function is usually expressed by a function of the stress tensor and plastic hardening function, so the damage parameters are included in the plastic yield function with the introduction of the reduction factor in the plastic hardening function. 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 in the true stress space.
Differentiation of the elastic thermodynamic energy yields the strain-stress relations where is the component of the deviatoric tensor.
Mathematical Problems in Engineering
The other set of singular points is of great importance because it includes biaxial and, as a special case. Mathematical Problems in Engineering. Good agrcemettt with the experimental results of Arrca and lngraffea Uniaxial compression is rcprcscntcd by: Specific functions for concrete are proposed based on the general framework of the coupled plastic damage model given in the previous section.
Such an cquntion mny bc JccIuccd from the more general equation.
According to Faria et al.