A coupled damage–plasticity model for concrete based on thermodynamic principles: Part I: model formulation and parameter identification (original) (raw)
Related papers
The paper presents an approach to constitutive modelling of concrete using damage mechanics and plasticity theory. The thermodynamic formulation, and parameter identification of a non-local coupled damage-plasticity model are presented in this study. The particular focus is the calibration of model parameters. It is shown that both the local parameters and the parameters governing the non-local interaction can be determined from experimental data reliably and consistently. A novel procedure is developed for parameter identification, using the separation of total dissipation energy into additive parts corresponding to different dissipation mechanisms. The relationship between the local and non-local parameters is also addressed, helping to obtain model responses consistent with the fracture energy of the material. The application of the model and the calibration procedure proposed in this study to the numerical failure analysis of concrete structures is illustrated through a series of real structural tests, showing both the performance of the model and the consistency of the proposed calibration procedure.
Elastic Plastic and Damage Model for Concrete Materials: Part I - Theoretical Formulation
A thermodynamically consistent macroscopic constitutive model for concrete that incorporates concrete effective stress space plasticity and fracture energy based - continuum damage mechanics is presented. A plasticity yield criterion, with multiple hardening functions and a non-associative plastic flow rule, is used simultaneously with two (tensile and compressive) isotropic damage criteria. The spectral decomposition of the stress tensor into tensile and compressive components is utilized in all criteria in order to simulate different responses of the material under various loading patterns. The damage criteria are based on the hydrostatic- deviatoric sensitive damage energy release rates in tension and compression derived from the Helmholtz free energy function. Three dissipation mechanisms are defined, one for plasticity and two for damage, to control the dissipation process in the material model. The consistent elastic-plastic-damage tangent operator is also derived, which concl...
A Tensile Plastic Damage Constitutive Model of Concrete Based on Energy
Based on the theory of damage mechanics, continuum mechanics and irreversible thermodynamics, considering the coupling relation of plastic stain and damage, the certain function relation is supposed between the plastic free energy and the elastic free energy, so the damage energy release rate is defined. According to the Weibull distribution curve, the relationship between the damage variable and the energy release rate is established, thus the concrete tensile damage evolution equation is deduced. Finally, based on the plastic characteristics of concrete under the action of tensile load, the empirical formula of plastic deformation is obtained. Therefore, the tensile plastic damage constitutive model of concrete is established. The uniaxial tension test results and engineering examples are used for verification of the effectiveness and applicability of this model. Analysis results show that the tensile plasticity constitutive model can more truly reflect the concrete tensile damage evolution process.
2009
A thermodynamically consistent macroscopic constitutive model for concrete that incorporates concrete effective stress space plasticity and fracture energy based-continuum damage mechanics is presented. A plasticity yield criterion, with multiple hardening functions and a non-associative plastic flow rule, is used simultaneously with two (tensile and compressive) isotropic damage criteria. The spectral decomposition of the stress tensor into tensile and compressive components is utilized in all criteria in order to simulate different responses of the material under various loading patterns. The damage criteria are based on the hydrostaticdeviatoric sensitive damage energy release rates in tension and compression derived from the Helmholtz free energy function. Three dissipation mechanisms are defined, one for plasticity and two for damage, to control the dissipation process in the material model. The consistent elastic-plastic-damage tangent operator is also derived, which concludes the theoretical formulation of the proposed model. Verification examples are provided in order to evaluate the ability of the proposed model to capture the behavior of concrete under different states of loading. The detailed scheme of numerical integration of the constitutive equations and the application of the proposed model to study concrete and reinforced concrete members are important issues discussed in part II of this work
A plasticity and anisotropic damage model for plain concrete
International Journal of Plasticity, 2007
A plastic-damage constitutive model for plain concrete is developed in this work. Anisotropic damage with a plasticity yield criterion and a damage criterion are introduced to be able to adequately describe the plastic and damage behavior of concrete. Moreover, in order to account for different effects under tensile and compressive loadings, two damage criteria are used: one for compression and a second for tension such that the total stress is decomposed into tensile and compressive components. Stiffness recovery caused by crack opening/closing is also incorporated. The strain equivalence hypothesis is used in deriving the constitutive equations such that the strains in the effective (undamaged) and damaged configurations are set equal. This leads to a decoupled algorithm for the effective stress computation and the damage evolution. It is also shown that the proposed constitutive relations comply with the laws of thermodynamics. A detailed numerical algorithm is coded using the user subroutine UMAT and then implemented in the advanced finite element program ABAQUS. The numerical simulations are shown for uniaxial and biaxial tension and compression. The results show very good correlation with the experimental data.
Non-local regularization is applied to a new coupled damage–plasticity model (Int. J. Numer. Anal. Meth. Geomech. 2007; DOI: 10.1002/nag.627), turning it into a non-local model. This procedure resolves softening-related problems encountered in local constitutive models when dealing with softening materials. The parameter identification of the new non-local coupled damage–plasticity model is addressed, with all parameters being shown to be obtainable from the experimental data on concrete. Because of the appearance of non-local spatial integrals in the constitutive equations, a new implementation scheme is developed for the integration of the non-local incremental constitutive equations in nonlinear finite element analysis. The performance of the non-local model is assessed against a range of two-dimensional structural tests on concrete, illustrating the stability of the stress update procedure and the lack of mesh dependency of the model.
A thermodynamic approach to non-local damage modelling of concrete
This paper focuses on the development of a thermodynamic approach to constitutive modelling of concrete materials, with emphasis on the use of non-local damage models. Effort is put on the construction of a consistent and rigorous thermodynamic framework, which readily allows the incorporation of non-local features into the constitutive modelling. This is an important feature in developing non-local constitutive models based on thermodynamics. Examples of non-local constitutive models derived from this framework and numerical examples are given to demonstrate the promising features of the proposed approach
Engineering Fracture Mechanics, 2010
A coupled plasticity-damage model for plain concrete is presented in this paper. Based on continuum damage mechanics (CDM), an isotropic and anisotropic damage model coupled with a plasticity model is proposed in order to effectively predict and simulate plain concrete fracture. Two different damage evolution laws for both tension and compression are formulated for a more accurate prediction of the plain concrete behavior. In order to derive the constitutive equations and for the easiness in the numerical implementation, in the CDM framework the strain equivalence hypothesis is adopted such that the strain in the effective (undamaged) configuration is equivalent to the strain in the nominal (damaged) configuration. The proposed constitutive model has been shown to satisfy the thermodynamics requirements. Detailed numerical algorithms are developed for the finite element implementation of the proposed coupled plasticity-damage model. The numerical algorithm is coded using the user subroutine UMAT and then implemented in the commercial finite element analysis program Abaqus. Special emphasis is placed on identifying the plasticity and damage model material parameters from loading–unloading uniaxial test results. The overall performance of the proposed model is verified by comparing the model predictions to various experimental data, such as monotonic uniaxial tension and compression tests, monotonic biaxial compression test, loading–unloading uniaxial tensile and compressive tests, and mixed-mode fracture tests.
A plastic-damage model for concrete under compression
International Journal of Mechanical Sciences, 2019
A phenomenological model for plain concrete under compression is formulated within the framework of the coupled elastoplastic-damage theory. Phenomenological elastoplastic-damage models have been widely used for concrete because of their capability of representing both the permanent inelastic deformations and the degradation of material moduli beyond the elastic range. The essential contribution introduced in this paper is the proposed partitioning of the strain tensor within the coupled elastoplasticdamage framework which simplifies the selection of the failure surface and the potential function. Proposed partitioning permits the use of single failure criterion and single potential surface that are effective for both damage and plasticity models during inelastic deformations. Therefore, the coupled elastoplastic-damage model can be easily calibrated to fit the observed concrete behaviour based on well-established non-associated plasticity rules for concrete. The proposed approach also simplifies the numerical procedure by eliminating iterations that is required to equilibrate the stresses in plastic and damage components of the model. The numerical implementation is explained, and the results predicted by the model are compared with experimental data provided in the literature.
VALIDATION OF A DAMAGE PLASTICITY MODEL FOR CONCRETE IN TENSION AND IN COMPRESSION
A benchmark for the validation of an elastic plastic damage constitutive law in tension and in compression is presented. The aim is to propose, on a concrete example, an entire validation process including elementary (compression test), structural (reinforced bending beams) and pre-industrial tests that could be reused for further studies.