Statistical Damage Constitutive Model of Quasi-Brittle Materials

Recent studies have shown that statistical damage mechanics is one effective method to study the failure process of quasi-brittle materials. There are two key problems in setting up the statistical damage constitutive model of quasi-brittle materials, namely, determining the microunit strength and the parameters of statistical distribution that the microunit strength obeys. The four-parameter criterion is a failure criterion consisting of four unknown parameters. When the four parameters equal appropriate values, it may become the Drucker–Prager criterion (for rock), Mohr–Coulomb criterion (for rock), and Hsieh–Ting–Chen criterion (for concrete), so the four-parameter criterion may be used to simulate the elastoplastic behavior of rock and concrete quasi-brittle materials. In the paper, microunit strength is determined with the four-parameter criterion, thus the statistical damage constitutive model suits rock and concrete. The deficiencies of existing methods in determining the distribution parameters are investigated, and a new method for determining the distribution parameters is proposed. First, the theoretical relationships between the parameters and the strain and stress at the peak point of material failure curve are derived; second, the approximate relations between the strain and stress at the peak point of material failure curve and confining pressure are established through the curve fitting method; finally, the relations between the parameters and confining pressure are established. The proposed statistical damage softening constitutive model of quasi-brittle materials has universal meaning, the determination of distribution parameters has strict theoretical basis, and the distribution parameters can be conveniently obtained with general triaxial tests. Numerical examples are also presented to validate the model.     

Anisotropic Damage Model for Concrete

In this paper, a damage constitutive model accounting for induced anisotropy and bimodular elastic response is applied to two-dimensional analysis of reinforced concrete structures. Initially, a constitutive model for the concrete is presented, where the material is assumed as an initial elastic isotropic medium presenting anisotropy and bimodular response (distinct elastic responses, whether tension or compression stress states, prevail) induced by damage. Two damage tensors govern the stiffness under prevailing tension or compression stress states. Criteria are then proposed to characterize the dominant states. Finally, the proposed model is used in plane analysis of reinforced concrete beams to show its potential for use and to discuss its limitations.     

Coupled Environmental-Mechanical Damage Model of RC Structures

The evaluation of strength reduction of RC structures subjected to mechanical damage process and chemical attack is carried out, with regard to concrete deterioration and steel corrosion. A coupled environmental-mechanical damage model, developed as an extension of that previously published is presented. Two independent scalar mechanical damage parameters are introduced, each of them representing the degradation mechanisms occurring under tensile and compressive stress conditions. The stiffness recovery upon loading reversal, which is manifest when passing from tension into compression, is fully captured by the proposed model. The environmental damage is strongly related to the diffusion process, as well as to the evolution of the chemical reaction between pollutant and cementitious constituents. An enhanced local method is proposed to regularize the problem of nonobjectivity of the finite-element solution due to the strong strain softening behavior of concrete material. The splitting test of a concrete specimen and a static analysis of an RC frame subjected to mechanical loads and chemical attacks are carried out, and the damage evolution is analyzed in detail.     

Numerical Model for Time-Dependent Fracturing of Concrete

A finite-element formulation for the analysis of time-dependent failure of concrete is presented. The proposed formulation incorporates: (1) the viscoelastic behavior of uncracked concrete through a Maxwell chain model; and (2) the inelastic behavior of damaged concrete, characterized by a modified version of the microplane Model M4 which includes the rate dependence of fracturing. The proposed formulation is applied to the simulation of quasi-static concrete failure in the time domain. The different effects of creep and rate dependence of crack growth and their role in the lifetime of concrete structures are studied. The influence of different loading rates on the size effect is also analyzed with reference to single notched specimens, revealing the link between the size of the fracture process zone and the loading rate. The capability of the proposed numerical formulation is also verified for the case of sustained uniaxial compressive loads.     

Creep Damage Assessment and Lifetime Predictions for Metallic Materials under Variable Loading Conditions in Elevated Temperature Applications

In this paper the problem of creep damage assessing as well as of creep life prediction of metallic materials under variable loading conditions is considered. A non‐linear model for creep damage accumulation which is based on a more general physical‐phenomenological model describing the mechanical behaviour of metallic materials under creep conditions, is presented. The model is suitable for the prediction of the creep damage accumulation under variable load and/or temperature. The proposed model takes into account the previous damage history and, definitely, the loading order. In any case the creep strain accumulation is taken into account as this is directly associated with the creep damage accumulation. Theoretical results agree well with the experiments.     

Identification and Validation of a Discrete Element Model for Concrete

The use of a three-dimensional discrete element method (DEM) is proposed to study concrete structures submitted to dynamic loading. The aim of this paper is to validate the model first in the quasistatic domain, and second in dynamic compression, at the sample scale. A particular growing technique is used to set a densely packed assembly of arbitrarily sized spherical particles interacting together, representing concrete. An important difference from classical DEMs where only contact interactions are considered, is the use of an interaction range. First, the correct identification of parameters of the DEM model to simulate elastic and nonlinear deformation including damage and rupture is made through quasistatic uniaxial compression and tension tests. The influence of the packing is shown. The model produces a quantitative match of strength and deformation characteristics of concrete in terms of Young’s modulus, Poisson’s coefficient, and compressive and tensile strengths. Then, its validity is extended through dynamic tests. The simulations exhibit complex macroscopic behaviors of concrete, such as strain softening, fractures that arise from extensive microcracking throughout the assembly, and strain rate dependency.     

TB-EPUDC-015复合材料层压板的疲劳损伤模型

This paper develops a mathematical model for fatigue damage evolution in composite materials. The characteristics of damage growth in composite materials are studied and compared with those of damage growth in homogeneous materials. Continuum damage mechanics concepts are used to evaluate the degradation of composite materials under cyclic loading. A new damage accumulation model is proposed to capture the unique characteristics of composite materials. The proposed model is found to be more accurate than existing models, both in modelling the rapid damage growth at the early stages of life and near the end of fatigue life. The parameters of the proposed model are obtained from experimental data. A example is implemented to illustrate that the proposed model is able to accurately fit several different sets of experimental data.     

Microplane Model M5f for Multiaxial Behavior and Fracture of Fiber-Reinforced Concrete

Despite impressive advances, the existing constitutive and fracture models for fiber-reinforced concrete (FRC) are essentially limited to uniaxial loading. The microplane modeling approach, which has already been successful for concrete, rock, clay, sand, and foam, is shown capable of describing the nonlinear hardening–softening behavior and fracturing of FRC under not only uniaxial but also general multiaxial loading. The present work generalizes model M5 for concrete without fibers, the distinguishing feature of which is a series coupling of kinematically and statically constrained microplane systems. This feature allows simulating the evolution of dense narrow cracks of many orientations into wide cracks of one distinct orientation. The crack opening on a statically constrained microplane is used to determine the resistance of fibers normal to the microplane. An effective iterative algorithm suitable for each loading step of finite element analysis is developed, and a simple sequential procedure for identifying the model parameters from test data is formulated. The model allows a close match of published test data on uniaxial and multiaxial stress–strain curves, and on multiaxial failure envelopes.     

Performance Simulation of Nuclear Containments for Security

Under blast loading, nuclear containment structures are subjected to cyclic flexural, axial, and shear forces. Less attention has been paid to modeling the cyclic behavior of reinforced concrete elements in which shear deformations are significant, such as in nuclear containments. Research has demonstrated that the strength of concrete in the principal compression direction is softened by tension in the lateral direction. This interaction has been considered for monotonic loading for many years. To consider this interaction for cyclic loading, the material laws recently derived by Mansour et al. in 2001 for the cyclic softened membrane model (CSMM) can be used. Both fire and explosion effects resulting from blast loading can also be incorporated into the constitutive models of concrete and reinforcing bars. This paper presents a method to implement the CSMM model, so that it can be used to simulate the performance of nuclear containments for security by the design communities.     

Safe Scaled Distance for Masonry Infilled RC Frame Structures Subjected to Airblast Loads

Terrorist bombing and accidental explosion may generate extreme loading conditions on nearby structures, resulting in damage and even collapse of structures. The degree of damage to a structure depends on the capacity of the detonation and its location as well as structural conditions. Some guidelines are available to assess the safety of unstrengthened buildings to airblast loads. These guidelines are usually given in terms of the safe scaled distance between explosion center and structure, whereas the structure conditions, which also affect its performance, are not explicitly defined. The safe scaled distance is obtained primarily from field blasting tests and experiences of structure damage to blast loads. These guidelines can be used for a quick safety assessment of structures, but do not provide clear damage scenarios of the structures. In a previous paper, damages of low-rise masonry infilled reinforced concrete (RC) structures to surface explosion of different scaled distances are numerically simulated. It was found that RC frame would collapse when the scaled distance was less than 1.82?m/kg1/3; and the front masonry wall would suffer excessive damage when the scaled distance was less than about 4.5?m/kg1/3. The present paper is an extension of the latter work. It employs a more detailed RC model with distinctive definitions of concrete and reinforcement material performance. More thorough analyses are carried out to find the correlation between the scaled distance and the damage level of low-rise and medium-rise masonry infilled RC frames. The different failure mechanisms between the low-rise and medium-rise structures to blast loads are also observed and discussed. The computer program LS-DYNA3D with user defined RC and homogenized masonry material models is used in numerical calculations. The numerical results are also compared with the safe scaled distance recommended in the United Stated Department of Defense’s regulations, ASCE guidelines, and those derived in the previous paper.     

New Approach for Modeling the Contribution of NSM FRP Strips for Shear Strengthening of RC Beams

This paper presents the main features of an analytical model recently developed to predict the near-surface mounted (NSM) fiber-reinforced polymer (FRP) strips shear strength contribution to a reinforced concrete (RC) beam throughout the beam’s loading process. It assumes that the possible failure modes that can affect the ultimate behavior of an NSM FRP strip comprise: loss of bond (debonding); concrete semiconical tensile fracture; mixed shallow-semicone-plus-debonding; and strip tensile fracture. That model was developed by fulfilling equilibrium, kinematic compatibility, and constitutive law of both the adhered materials and the bond between them. The debonding process of an NSM FRP strip to concrete was interpreted and closed-form equations were derived after proposing a new local bond stress-slip relationship. The model proposed also addressed complex phenomena such as the interaction between the force transferred to the surrounding concrete through bond stresses and concrete fracture as well as the interaction among adjacent strips. The main features of the proposed modeling strategy are shown along with the main underlying physical-mechanical concepts and assumptions. Using recent experimental data, the predictive performance of the model is assessed. The model is also applied to single out the influence of relevant parameters on the NSM technique effectiveness for the shear strengthening of RC beams.     

Techniques for Numerical Simulations of Concrete Slabs for Demolishing by Blasting

The subject of this article is the numerical simulation of concrete under explosive loading using a meshbased and a meshfree discretization technique. The presented techniques are verified by experimental data. Experimental evidence suggests that the complete stress–strain history relation must be considered as a basis for constitutive modeling if concrete is subjected to high loading rates. These dynamic phenomena cause a retardation of damage activation which must be taken into account when constitutive modeling is pursued on mesolevel instead of microlevel. By including a dynamic relaxation formulation within the framework of a general three-dimensional coupled continuum damage-plasticity law, it is shown that the solution of the wave propagation problem in materials with strain-softening becomes independent of mesh size. As the simulation of concrete under contact detonation causes severe numerical problems because of the large deformations, special numerical spatial discretization techniques have to be used. In this article we compare the results of a concrete slab under contact detonation using the finite element method code LS-DYNA with an arbitrary Lagrangian Eulerian coupling and the results obtained by a MLSPH code developed at our institute with experimental data. The same constitutive model for concrete and the same equation of state for the explosive is implemented in the two codes. The results of the different numerical simulations and the experimental data agree with each other well.     

侧向冲击荷载下钢筋混凝土墩柱的性能

采用数值仿真技术建立了足尺钢筋混凝土墩柱精细有限元模型, 分析了侧向冲击荷载下墩柱的动态响应和抗冲击性能, 提出了一种基于截面损伤因子的损伤评估方法, 讨论了不同碰撞参数对钢筋混凝土墩柱破坏模式和损伤机理的影响.结果表明: 冲击荷载下钢筋混凝土墩柱的耗能主要分为接触区域局部耗能和构件整体耗能; 当冲击体的初始动能恒定时, 冲击质量和冲击速度的不同组合会导致钢筋混凝土墩柱损伤破坏机理的显著差异; 基于截面损伤因子的损伤评估方法可以比较准确地描述墩柱的破坏状态.轴压力对墩柱抗撞能力的有利贡献比较有限, 且墩柱随着轴力的增大更易发生剪切破坏; 冲头刚度对碰撞力和墩柱动态响应的影响十分显著.      

Pressure-Level Dependency and Densification Behavior of Sand Through Generalized Plasticity Model

Natural soil deposits and man-made earth structures exhibit complicated engineering behavior that is influenced by factors such as the stress level and drainage conditions. The stress conditions within a soil structure vary greatly, ranging from very low to very high values, due to the dead weight, loading and boundary conditions. Saturated sand deposits that exhibit drained conditions under static loading become undrained when subject to earthquake excitations. The Pastor–Zienkiewicz–Chan model has demonstrated considerable success in describing the inelastic behavior of soils under isotropic monotonic and cyclic loadings, including liquefaction and cyclic mobility. This study proposed modifications to the Pastor–Zienkiewicz–Chan model so that effects of stress level and densification behavior are simulated. The proposed model suggested that the angle of internal friction, elastic and plastic moduli are dependent on the pressure levels. Relevant modifications were made to incorporate a power term of mean effective stress on the loading plastic modulus so that a stress-level dependent volume change is obtained in combination with the stress-dilatancy relationship. To better simulate cyclic loading with reference to densification behavior, an exponential term of plastic volumetric strain is included for the unloading and reloading plastic moduli. A total of 11 parameters are needed for monotonic loading, whereas 15 parameters are needed in describing the cyclic behavior. The model simulations were compared with undrained and drained triaxial test results of several kinds of sand under dense and loose states. The predictive capability for monotonic and cyclic loading conditions was also demonstrated.     

Active Confinement of Reinforced Concrete Bridge Columns Using Shape Memory Alloys

This paper presents experimental and analytical work conducted to explore the feasibility of using an innovative technique for seismic retrofitting of RC bridge columns using shape memory alloys (SMAs) spirals. The high recovery stress associated with the shape recovery of SMAs is being sought in this study as an easy and reliable method to apply external active confining pressure on RC bridge columns to improve their ductility. Uniaxial compression tests of concrete cylinders confined with SMA spirals show a significant improvement in the concrete strength and ductility even under small confining pressure. The experimental results are used to calibrate the concrete constitutive model used in the analytical study. Analytical models of bridge columns retrofitted with SMA spirals and carbon fiber-reinforced polymer (CFRP) sheets are studied under displacement-controlled cyclic loading and a suite of strong earthquake records. The analytical results proves the superiority of the proposed technique using SMA spirals to CFRP sheets in terms of enhancing the strength and effective stiffness and reducing the concrete damage and residual drifts of retrofitted columns.     

Damage Identification on the Tilff Bridge by Vibration Monitoring Using Optical Fiber Strain Sensors

Vibration testing is a well-known practice for damage identification of civil engineering structures. The real modal parameters of a structure can be determined from the data obtained by tests using system identification methods. By comparing these measured modal parameters with the modal parameters of a numerical model of the same structure in undamaged condition, damage detection, localization, and quantification is possible. This paper presents a real-life application of this technique to assess the structural health of the 50-year old bridge of Tilff, a prestressed three-cell box-girder concrete bridge with variable height. A complete ambient vibration survey comprising both vertical accelerations and axial strains has been carried out. The in situ use of optical fiber strain sensors for the direct measurement of modal strains is an original contribution of this work. It is a big step forward in the exploration of modal curvatures for damage identification because the accuracy in calculating the modal curvatures is substantially improved by directly measuring modal strains rather than deriving the modal curvatures from acceleration measurements. From the ambient vibrations, natural frequencies, damping factors, modal displacements and modal curvatures are extracted by the stochastic subspace identification method. These modal parameters are used for damage identification which is performed by the updating of a finite element model of the intact structure. The obtained results are then compared to the inspections performed on the bridge.     

Numerical Modeling of Concrete-FRP Debonding Using a Crack Band Approach

In this study, numerical procedures are proposed to predict the structural behavior of concrete members strengthened with fiber-reinforced polymeric (FRP) sheets or plates. The concept of damage band or crack band is introduced and used for predicting the debonding failure of the concrete-epoxy interface formed when FRP sheets or plates are externally bonded to a concrete substrate. In the crack band approach, all the processes taking place during the failure of a concrete-epoxy interface are smeared in a band of fixed width. This makes the approach attractive from a modeling point of view since continuum theories, along with softening relations, can be used to model the damage which causes debonding of the interface. In order to validate this approach, numerical predictions, using the concept of crack band, are compared against experimental results obtained from tests of concrete blocks and reinforced concrete beams strengthened with FRP. In particular, the capability of the proposed numerical approach to predict the load-displacement response, strain distributions, failure sequences, damage distribution, and failure mechanisms experimentally observed is verified. Results presented in this study indicate that the concept of crack band is appropriate when modeling concrete-epoxy interfaces under general states of stresses.     

Structural Health Monitoring by Piezo–Impedance Transducers. II: Applications

This paper, the second in a two-part series, presents a new methodology for structural identification and nondestructive evaluation by piezo–impedance transducers. The theoretical development and experimental validation of the underlying lead–zirconium–titanate (PZT)–structure interaction model was presented in the first part. In our newly proposed method, the damage in evaluated on the basis of the equivalent system parameters “identified” by the surface-bonded piezo–impedance transducer. As proof of concept, the proposed method is applied to perform structural identification and damage diagnosis on a representative lab-sized aerospace structural component. It is then extended to identify and monitor a prototype reinforced concrete bridge during a destructive load test. The proposed method was found to be able to successfully identify as well as evaluate damages in both the structures.     

Multicomponent Model of Reinforced Concrete Joints for Cyclic Loading

Efficient simplified models are available for reinforced concrete beams and columns, with the assumption of a perfectly rigid connection. However, interior beam∕column joints have been shown to be the area of strong deformation and degradation mechanisms, involving mainly the cyclic behaviors of concrete under shear and of bond under push-pull loading. In this paper, a global component-based model is proposed for the beam∕column connections of reinforced concrete frame structures that can be directly connected to beam elements. This model incorporates explicitly the modeling of concrete, steel, and steel∕concrete bond. Thus, the key mechanisms of deformation and degradation of the connection, as well as various interactions can be taken into account naturally. In particular, the effect of push-pull-type loading on the flexural steels can be captured. On the basis of a local finite-element modeling of the connection, simplifying assumptions are proposed and implemented leading to the component-based model. Both approaches (local and component-based) are compared on an application example.