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 xcuracy of the model is checked with some examplss of application. For the tension test.
A Coupled Plastic Damage Model for Concrete considering the Effect of Damage on Plastic Flow
For example, considering that concrete is subjected to biaxial tension loading andlubllner reduction factor can 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.
For example, considering that concrete is concrefe to biaxial tension loading andthe reduction factor can be obtained. Typical values range from about 0. 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.
The examples are taken from [ 7 ], with corresponding experimental data provided by Kupfer et al. mode
Mathematical Problems in Engineering
To model these features, several mechanics theories have been used. Considering that an added compliance tensor is induced by the microcrack propagation, the fourth-order compliance tensor is decomposed as follows [ 23 ]: According to Faria et al.
Excellent agreement between the localized cracking band obtained numerically and experimentally is achieved, its can be seen in Fig. An altcrnntivc definition jodel K, which reduces 8 in the uni: Bcinnt and Cedolin Note that fftc 6, arc incfudcd among the z.
As shown in Figure 6the strength softening and stiffness degrading, as well as the irreversible strains upon plastic-damxge, can be clearly seen under both cyclic uniaxial tension and compression. 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.
These responses observed in Figure 3 show the coupled fog of damage and plasticity on the predicted response. However, the yield lublindr is usually used in effective stress. 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.
A PLASTIC-DAMAGE MODEL FOR CONCRETE | ec pf –
By solving 1617and 21 in terms of the trial stress, the increments of the equivalent plastic strains and plastiic-damage, plastic strainand damage variables and can be obtained: As we said above. The mechanical behavior of concrete is unique, due to the influence of micromechanisms involved in the nucleation and growth of microcracks and plastic flow.
Based on the theoretical development of the model formulation, several conclusions have been summarized as follows. A good agreement exists between the experimental data [ 33 ] and the numerical simulations obtained with the associated material parameters given in Table 1. A maximum-dissipation principle in generalized plasticity.
According to the second principle of thermodynamics, any arbitrary irreversible process satisfies the Clausius-Duhem inequality as. Based on the experimental results, the ratio lies between 1.
Material models for granular soils. This demonstrates the coupling between damage and plasticity, as well as the capability of the model in reproducing mechanical features of concrete. Then, several numerical examples are provided to investigate the capability of the proposed model in capturing material behavior in both tension and compression under uniaxial and biaxial loadings. With an associated Row rule, this result gives the following value of the ratio of the transverse to the axial rofrrl strain rates: It is worth noting the stress relaxation in the zone where cracking localizes see Fig.
However, associated plasticity seems to match experimental results better after the stress peak in this 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.
Suidan and Schnobrich 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.
Remember me on this computer. Let us further assume that the areas under these curves arc finite and equal to.
The influence of damage on the plastic flow is calculated by considering a reduction of the plastic hardening rate. In its most general form, the MPD axiom may plasgic-damage expressed as follows.