An elastic plastic damage formulation for concrete: Application to elementary tests and comparison with an isotropic damage model

Elastic damage models or elastic plastic constitutive laws are not totally satisfactory to describe the behaviour of concrete. They indeed fail to reproduce the unloading slopes during cyclic loading which define experimentally the value of the damage in the material. When coupled effects are considered, the capability of the numerical model to reproduce the unloading behaviour is essential, as an accurate value of the damage is needed. An elastic plastic damage formulation is so proposed to circumvent the disadvantages of both approaches. It is first tested on uniaxial tensile loading. It is then applied on one cyclic compression to highlight the improvements of the presented law (volumetric behaviour). Finally, a « passive » confinement test is proposed to underline the importance of using a plastic—damage approach for the simulation of a composite structure (steel tube with concrete).

The modeling of cyclic behavior in rock remains a challenge due to complex deformation characteristics. This paper studied the mechanical behaviors of granite samples under uniaxial cyclic loading and unloading through cyclic compression tests and acoustic emission (AE) monitoring. Then, a comprehensive body that consisted of an elastic element, plastic element, and friction element was proposed to describe the stress–strain relationship with respect to cyclic behavior, in which the friction element was connected in parallel with the serial combination of the elastic element and plastic element. Finally, the parameters of the proposed model were calibrated based on the mechanism analysis and backpropagation (BP) neural network. Results show that the behavior during unloading is primarily elastic and is accompanied by the obstruction of friction. During reloading, the behavior changes from elastic to elastic–plastic before and after the Kaiser point. The tangential modulus of the elastic element is dynamic in a linear positive correlation with elastic strain and a linear negative correlation with plastic strain; specifically, the elastic strain controls the variation process of the elastic modulus while the plastic strain determines the lower limit. The constitutive law of the plastic element is expressed by a logistic function, which means that the plastic strain increases in a trend of acceleration–deceleration. The friction element plays a major role in processing the massing effect, and the plastic element is prompted before the historical maximum stress, which reflects the ratcheting effect and Felicity effect. The reliability of the proposed constitutive model is confirmed by the comparison of the simulated stress–strain curves with the experimental curves.

Submarine and onshore pipelines transport enormous quantities of oil and gas vital to the economies of virtually all nations. Any failure to ensure safe and continuous operation of these pipelines can have serious economic implications, damage the environment and cause fatalities. A prerequisite to safe pipeline operation is to ensure their structural integrity to a high level of reliability throughout their operational lives. This integrity may be threatened by volumetric and shear ductile micro- and macro-fracture processes under long time loading or continuous operation. In this paper a mathematically consistent damage model for predicting the damage in pipeline structures under tensile and shear loading is considered. A detailed study of widely used damage models (e.g., Lemaitre’s and Gurson’s models) has been published in the literature. It has been shown that Gurson’s damage model is not able to adequately predict fracture propagation path under shear loading, whereas Lemaitre’s damage model (Lemaitre, 1985) shows good results in this case (e.g., Hambli 2001, Mkaddem et al. 2004). The opposite effect can be observed for some materials by using Gurson’s damage model in the case of tensile loading (e.g., Tvergaard and Needleman 1984; Zhang et al. 2000; Chen and Lambert 2003; Mashayekhi et al. 2007) and wiping die bending process (Mkaddem et al. 2004). Therefore, the mathematically consistent damage model which takes into account the advantages of both Lemaitre’s and Gurson’s models has been developed. The model is based on the assumption that the damage state of materials can be described by a damage tensor ωij. This allows for definition of two scalars that are ω = ωkk/3 (the volume damage) (Lukyanov, 2004) and α = ωij′ωij′ (a norm of the damage tensor deviator ωij′ = ωij −ωδij) (Lukyanov, 2004). The ω parameter describes the accumulation of micro-pore type damage (which may disappear under compression) and the parameter α describes the shear damage. The proposed damage model has been implemented into the finite element code ABAQUS by specifying the user material routine (UMAT). Based on experimental research which has been published by Lemaitre (1985), the proposed isotropic elastoplastic damage model is validated. The results for X-70 pipeline steel are also presented, discussed and future studies are outlined.

Capsules, composed of a liquid core protected by a thin deformable membrane, offer high-potential applications in many fields of industry such as bioengineering. One of their limitations comes from the absence of models of capsule damage and/or rupture when they are subjected to an external flow. To assess when rupture is initiated, we develop a fluid-structure interaction (FSI) numerical model of a capsule in Stokes flow that accounts for potential damage of the capsule membrane. We consider the framework of Continuum Damage Mechanics and model the membrane with an isotropic brittle damage model, in which the membrane damage state depends on the history of loading. The FSI problem is solved by coupling the finite element method, to solve for the membrane deformation, with the boundary integral method, to solve for the inner and outer fluid flows. The model is applied to an initially spherical capsule subjected to a simple shear flow. Damage initiates at a critical value of the capillary number, ratio of the fluid viscous forces to the membrane elastic forces, and rupture at a higher capillary number, when it reaches a threshold value. The material parameters introduced in the damage model do not influence the mode of damage but only the values of the critical and threshold capillary numbers. When the capillary number is larger than the critical value, damage develops in the two symmetric central regions containing the vorticity axis. It is indeed in these regions that the internal tensions are the highest on the membrane.

Analysis of stresses and displacements around underground openings is necessary in a wide variety of civil, petroleum and mining engineering problems. In addition, an excavation damaged zone (EDZ) is generally formed around underground openings as a result of high stress magnitudes even in the absence of blasting effects. The rock materials surrounding the underground excavations typically demonstrate nonlinear and irreversible mechanical response in particular under high in situ stress states. The dominant cause of irreversible deformations in brittle rocks is damage process. One of the most widely used methods in tunnel design is the convergence-confinement method (CCM) for its practical application. The elastic-plastic models are usually used in the convergence-confinement method as a constitutive model for rock behavior. The plastic models used to simulate the rock behavior, do not consider the important issues such as stiffness degradation and softening. Therefore, the use of damage constitutive models in the convergence-confinement method is essential in the design process of rock structures. In this paper, the basic concepts of continuum damage mechanics are outlined. Then a numerical stepwise procedure for a circular tunnel under hydrostatic stress field, with consideration of a damage model for rock mass has been implemented. The ground response curve and radius of excavation damage zone were calculated based on an isotropic damage model. The convergence-confinement method based on damage model can consider the effects of post-peak rock behavior on the ground response curve and excavation damage zone. The analysis of results show the important effect of brittleness parameter on the tunnel wall convergence, ground response curve and excavation damage radius.

In this paper, the probabilistic behavior of plain concrete beams subjected to flexure is studied using a continuous mesoscale model. The model is two-dimensional where aggregate and mortar are treated as separate constituents having their own characteristic properties. The aggregate is represented as ellipses and generated under prescribed grading curves. Ellipses are randomly placed so it requires probabilistic analysis for model using the Monte Carlo simulation with 20 realizations to represent geometry uncertainty. The nonlinear behavior is simulated with an isotropic damage model for the mortar, while the aggregate is assumed to be elastic. The isotropic damage model softening behavior is defined in terms of fracture mechanics parameters. This damage model is compared with the fixed crack model in macroscale study before using it in the mesoscale model. Then, it is used in the mesoscale model to simulate flexure test and compared to experimental data and shows a good agreement. The probabilistic behavior of the model response is presented through the standard deviation, moment parameters and cumulative probability density functions in different loading stages. It shows variation of the probabilistic characteristics between pre-peak and post-peak behaviour of load-CMOD curves.

This paper reports on the non‐linear static analysis of 2D concrete structures using an hybrid‐mixed stress formulation and continuum damage mechanics. The finite element model adopted is based on the direct and independent approximation of three fields: the effective stress and displacement fields in the domain of each element and the displacement field on the static boundary. The non‐linear behaviour of the material is modelled with a non‐local isotropic damage model. A set of numerical examples are presented to illustrate and validate the use of such numerical technique. The performance of the model is assessed by comparison with results obtained using other numerical schemes presented in the literature and also with experimental results. Copyright © 2005 John Wiley & Sons, Ltd.

ABSTRACTBecause of their simplicity, many isotropic damage models have been used to approximately predict the fatigue life of metallic engineering components. However, experimental observations confirm that the anisotropic damage evolves at probable failure sites even for isotropic materials. In this study, a model of microstructure of boom–panel is constructed to simulate a representative volume element (RVE), and the anisotropic damage of the RVE is described by the independent isotropic damage of boom and panel. Firstly, the constitutive equation of the RVE in terms of stiffness of boom–panel is deduced by the principle of deformation and static consistency. Then the expressions of damage‐driving force for boom and panel based on the principle of thermodynamics are introduced, and the damage evolution equations are constructed. The parameters of boom and panel are identified from fatigue test data of uniaxial tension and pure torsion, respectively. Finally, the aforementioned method is applied to predict the fatigue life of two structures: one is Pitch‐Change‐Link, which is a kind of structure in helicopter, and the other is a specimen under tension–torsion. The prediction results all fit well with the experimental data.

: In present investigation, analyses for the damage evolution behavior of particulate composite materials by using the finite element method (FEM) and the s-version finite element method (s-FEM) were carried out. The analyses were carried out in particular interest in the phenomenon of crack propagation. Prior to crack propagation, material damage develops in the material. The material damage may be in the forms of microviod and/or microcracks in the binder (matrix) and in the form of binder (matrix)/particle separation that is known to be dewetting. In a macroscopic sense, the reinforcing particles distribute evenly in matrix. However, at microscopic level, the density of the distributed particles varies. This means that the stiffness and strength of the material also have some spatial variations. Material damages initiate at the weak material locations and then propagate the surroundings. When cracks are present in the material, the cracks interact with the surroundings and the material To simulate such scenarios, we adopted two kinds of damage constitutive models. One is isotropic damage model and the other is ?separate dilatational/deviatoric damage constitutive model? in which the contributions of hydrostatic and of deviatoric stresses are accounted for independently. A parameter in the separate dilatational/ deviatoric damage model can characterize which, hydrostatic or deviatoric stress component, has dominant influence to the damage behavior of the material. A series of analyses on uncracked and cracked specimen with statistically varying material stiffness at a microscopic level were carried out. The results revealed that the damage behavior is highly influenced by the damage mode.

The roller compacted concrete gravity dam is poured by thin layers and there are many horizontal layer surfaces and joint surfaces in the dam. The shear strength of these surfaces is obviously lower than that of the RCC concrete. These horizontal layer surfaces and joint surface are the key positions affecting the strength, stability and seepage of the dam. The height of the most RCC gravity dams is about 100m. The height is relatively low and the horizontal thrust is relatively small. So anti-sliding stability issue along the layer surfaces has not attracted enough attention. But for the dams 200m high, this problem is very prominent. In this study, using an isotropic damage model, based on the effective stress principle of porous media, taking the stress-seepage-damage coupling effect into account, the failure mechanism of Huangdeng RCC gravity dam is discussed. The results show that the failure mechanism of RCC gravity dam is the shear slipping along the layer surfaces and the foundation surface.

Analytical solution to the 1D Lemaitre's isotropic damage model and plane stress projected implicit integration procedure

This work focuses on the concurrent effects of stress and temperature changes on the opening and closure of cracks in porous rocks. A phenomenological approach is used to express the damaged tangent properties of rock. The model couples an anisotropic mechanical damage model initially designed for solids to an isotropic thermal damage model developed for salt rock. The solid mechanics damage model is improved according to the poro-mechanical thermodynamic framework. Deformation is decomposed into purely elastic, mechanically damaged, and thermally damaged strains. Thermal damage is defined so as to account both for crack opening and crack closure. Preliminary numerical results illustrate the importance of thermo-mechanical couplings on cracking. This research work is expected to bring new insights in thermo-hydromechanical damage modeling in unsaturated rocks, for possible applications on nuclear waste management.

On the possibility of using damaged plasticity models in the assessment of structural response of gravity beams

Evaluation of fiber-reinforced and cement-stabilized rammed-earth composite under cyclic loading

A novel constitutive model with plastic internal and damage variables for brittle rocks