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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Schematization of typical stress-strain curves of concrete in uniaxial a tension and b compression tests. Mathematical Problems in Engineering.

This behavior is characterized by several features as follows: According to Faria et al. Instead, they have found that the bulk modulus depends primarily on the volume strain, and the s modulus lublindr the octahedral shear strain, n the elastic range. 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 damage mechanics and plasticity theories [ 5 — 13 ].

The elastic predictor-damage and plastic corrector integrating algorithm proposed by Crisfield [ 28 ] and then used by Nguyen and Houlsby [ 10 ] is used here for calculating the coupled plastic damage model.

The mechanical behavior of concrete is aa, due to the influence of micromechanisms involved in the nucleation and growth of microcracks and plastic plastc-damage. Smcarcd crack ;malysis of rcinforccd concrctc hrns and skths failing in shear. Equation 28 leads to the operator C, given by Thus Ck is symmetric if and only if k is proportional or equal. Click here to sign up. The geometry of the test.


Also, displacements have been controlled using a standard spherical path technique Crisficld, To couple the damage to the plasticity, the damage parameters are introduced into the foe yield function by considering a reduction in the plastic hardening rate.

In order to obtain a graphic ofr of this kind of damage. In all casts an initial stress approach, which circumvents the problem of non-symmetry of the stitfness matrix due to non-associated plasticity, has been used. 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 compressionconcrtee cannot be directly used in the true stress space.

From eqn f6 we obtain.

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In the special case of elastic damage loading without plastic flowthe damage multipliers and can be determined by calling for the damage consistency condition under static loading: In this section, the procedure for the determination of the model parameters is first presented. Substituting 29 into 27c and 27d yields the increments of the damage variables and. Differentiation of the elastic thermodynamic energy yields the strain-stress relations where is the component of the concrets tensor.

Compared stress-strain results for double non-symmetric 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.

By solving 45the reduction factor can be obtained.

By introducing such a reduction factor, the widely used plastic yield functions, such as those applied by Lee and Fenves [ 7 ], Wu et al. A plastic-damage model for concrete to Experimental bond Fig. The derivation of the detailed rate equation from 16 requires determining the evolution laws of the damage variables and plastic strains.


Numerical Examples and Discussion of Results In this section, the procedure for the determination of the model parameters is first presented.

Mathematical Problems in Engineering

Several authors applied this approach to develop the CPDM with a true stress space plastic yield function. According to Wu et al.

International Journal of Solids and Structures, 25, Furthermore, this algorithm ensures that the plastic and damage consistent conditions are fulfilled at any stage of the loading process. The thermodynamic forces conjugated to the corresponding damage variables are given by where the terms and are the derivatives of the stiffness tensor of the damaged material with respect to the damage variables andrespectively.


Each model parameter in turn is varied, while the others are kept fixed, to show the corresponding effect on the behavior of the concrete material. 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.

In the special case of plastic loading without damage evolution andthe plastic multiplier can be determined from the plastic consistency condition: It can be observed from 33 and 41 that the damage variables are introduced into the plastic yield function. Two reduction factors are introduced into the tensile and the compressive hardening functions to consider the influence of the tensile and plastic-ddamage damage mechanisms on the plastic flow, respectively. Results agree rcasonnhly well with those reported by Kupfer er al.