Plastic-damage Constitutive Model Research Articles

Seismic capacity assessment of cracked lining tunnel based on the pseudo-static method

Crack is one of the most common lining deteriorations, which is generally regarded as an indicator of tunnel safety. The present study investigated the lining cracks of 11 tunnels which are 200 km away from the Longmenshan fault zone. In order to evaluate the seismic capacity of these tunnels with longitudinal cracks in the permanent lining, a modified deformation-based pseudo-static assessment method was developed. The propagation of lining cracks was simulated by a reconstructed damaged plasticity constitutive model of reinforced concrete. The analyses adopted a two-dimensional finite element model and took tunnel depth, initial crack position, and the interaction between soil and lining structures into account. The analysis results showed that the modified evaluation method could simulate the damage process of lining structures under the action of seismic shear wave well. The results also showed that the failure modes of tunnels with cracked permanent lining were different with different burial depth in an earthquake. The cracks in the spandrel had the greatest impact on the seismic capacity of tunnels and should be reinforced in time before the earthquake. In addition, the interaction between the temporary support and permanent lining had little effect on the damage process of linings but had an impact on the damage speed. This study can provide a reference for the safety assessment of cracked lining tunnels in seismically active areas and help to determine the reinforcement measures and time more reasonably.

A spherical smart aggregate sensor based electro-mechanical impedance method for quantitative damage evaluation of concrete

In this study, the concrete damage induced by compression is evaluated quantitatively using spherical smart aggregate sensor based on electro-mechanical impedance method. The sensitivity of the spherical smart aggregate sensor embedded in concrete cubes is investigated by comparing the electrical signals recorded during the compressive process with those of the smart aggregate sensor embedded in concrete cubes. Furthermore, the finite element model of concrete cube with an embedded spherical smart aggregate sensor is developed to simulate the concrete compressive tests. The concrete damaged plasticity constitutive model is utilized to simulate the concrete damage process. The numerical model is verified with the experimentally measured compressive test results. Finally, the damage volume ratio is presented to quantify the damage level of concrete based on the numerical model. The relationship between the root mean square deviation index of the conductance signatures obtained from experiments and the damage volume ratio computed by numerical simulation is established to quantify the concrete damage level. The results show that the spherical smart aggregate sensor is more sensitive than the smart aggregate sensor in monitoring the three-dimensional concrete structures. The proposed empirical fitting curve can effectively evaluate the concrete damage level quantitatively.

Numerical and experimental study on flexural behavior of reinforced concrete beams: Digital image correlation approach

Understanding the realistic behavior of concrete up to failure under different loading conditions within the framework of damage mechanics and plasticity would lead to an enhanced design of concrete structures. In the present investigation, QR (Quick Response) code based random speckle pattern is used as a non-contact sensor, which is an innovative approach in the field of digital image correlation (DIC). A four-point bending test was performed on RC beams of size 1800 mm x 150 mm x 200 mm. Image processing was done using an open source Ncorr algorithm for the results obtained using random speckle pattern and QR code based random speckle pattern. Load-deflection curves of RC beams were plotted for the results obtained using both contact and non-contact (DIC) sensors, and further, Moment (M)-Curvature (k) relationship of RC beams was developed. The loading curves obtained were used as input data for material model parameters in finite element analysis. In finite element method (FEM) based software, concrete damage plasticity (CDP) constitutive model is used to predict the realistic nonlinear quasi-static flexural behavior of RC beams for monotonic loading condition. The results obtained using QR code based DIC are observed to be on par with conventional results and FEM results.

Damage Detection in Reinforced Concrete Berthing Jetty Using a Plasticity Model Approach

A conventional method of damage modeling by a reduction in stiffness is insufficient to model the complex non-linear damage characteristics of concrete material accurately. In this research, the concrete damage plasticity constitutive model is used to develop the numerical model of a deck beam on a berthing jetty in the Abaqus finite element package. The model constitutes a solid section of 3D hexahedral brick elements for concrete material embedded with 2D quadrilateral surface elements as reinforcements. The model was validated against experimental results of a beam of comparable dimensions in a cited literature. The validated beam model is then used in a three-point load test configuration to demonstrate its applicability for preliminary numerical evaluation of damage detection strategy in marine concrete structural health monitoring. The natural frequency was identified to detect the presence of damage and mode shape curvature was found sensitive to the location of damage.

A New 3D Empirical Plastic and Damage Model for Simulating the Failure of Concrete Structure

A new plastic–damage constitutive model based on the combination of damage mechanics and classical plastic theory was developed to simulate the failure of concrete. In order to explain different material behaviors of concrete under tensile and compressive loadings, the plastic yield criterion, the different kinematic hardening rule for tension and compressive and the isotropic flow rule were established in the effective stress space. Meanwhile, two different empirical damage evolution equations were adopted: one for compression and the other for tension. A multi-axial damage influence factor was also introduced to fully describe the anisotropic damage of concrete. Finally, the model response was compared with a wide range of experiment results. The results showed that the model could well describe the nonlinear behavior of concrete in a complex stress state.

Experimental assessment and damage modelling of hybrid timber beam-to-steel column connections under cyclic loads

This paper presents an experimental and numerical study on the behaviour of timber beam-to-steel column connections under cyclic loads. Special attention is given to the accumulation of damage in the timber components and to its simulation. To this end, the fundamental nonlinear cyclic response of three specimens involving different configurations of top and seat angle connections with long bolts is examined. The experimental set-up, connection details and material properties are introduced first, followed by a detailed account of the testing procedure and results. The experimental outcomes enable a direct comparative assessment of the connection strength, hysteretic response, joint ductility, failure mode and energy dissipation capacity. In addition, finite element analyses employing a newly proposed damage-plasticity constitutive model of wood are presented together with a detailed description of the adopted modelling approach. The numerical output of these simulations at the local level, expressed in terms of strains and damage indices, is discussed and compared against the experimental measurements of local damage in the wood obtained through Digital Image Correlation (DIC) techniques. It is demonstrated that the connections under consideration are able to sustain their bending capacity without a significant deterioration in their stiffness or strength even up to large levels of deformation and several repetitions of loading cycles. Besides, the results and discussion presented in this paper support the conventional definition of global failure as a post-peak strength reduction higher than 20% of the capacity but so long as the strength measurements are obtained from the stabilized envelope curves of the specimens. The applicability of damage mechanics concepts to provide a reliable prediction of crack zones and damage accumulation in timber structures under the action of cyclic loads is also highlighted.Finally, general recommendations for avoiding brittle failure modes in this type of connection are given.

Stress–Energy Mechanism for Rock Failure Evolution Based on Damage Mechanics in Hard Rock

To investigate the quantification of the extent of damage by considering the energy during rock failure, the pattern of energy dissipation and energy conversion, and the stress–energy mechanism for induced rock failure were analysed under cyclic loading/unloading. Based on damage mechanics, rock mechanics, and energy conservation theory, the test data were analysed. The results showed that the characteristics of hard rock compression are small deformation, high energy, and sudden failure; an elastic–plastic damage constitutive model and a stress–energy–rigidity–damage multi-criteria model for rock failure were established for hard rock. We compared the numerical curves and the experimental curves and found that they coincide. Rock failure is a combination of the results of elastic strain accumulation and dissipation by stress propagation. The key to inducing the energy storage capacity of rock before failure is closely related to the rock damage evolution. The pattern of energy release and dissipation through stress during rock failure was revealed from the perspective of energy using the constitutive model and multi-criteria model established for rock failure; these theoretical studies are very helpful in elucidating the mechanism of rock failure.

Quantitative assessment of the concrete gravity dam damage under earthquake excitation using electro-mechanical impedance measurements

A rare but remarkable accident is the dam failure due to earthquake that can trigger catastrophes on economic and life losses. It is essential to monitor the presence and development of seismic damage of dam structures in the early stage of emergence of damage and take steps to prevent the full structural failure. In this research, only seismic damage and dynamic performances of a roller compacted concrete (RCC) dam were investigated using an electromechanical impedance (EMI)–based structural health monitoring (SHM) technique enabled by lead-zirconate-titanate (PZT) ceramic sensors network. The finite element model of the PZT sensor and damage monitoring method were verified by comparing the scanning conductance signals obtained from the experimental tests. A quasi 3D finite element model of the RCC dam using concrete damaged plasticity (CDP) constitutive model was built and assumed to be subjected to different degrees of earthquake excitations to initiate the dam damage due to tension. The conductance signals were measured by the PZT sensors network which are excited by inputting unit harmonic voltage. In addition, the normalized root-mean-square deviation (RMSD) was used as a damage index to quantify and evaluate the variations in conductance signals measured at the PZT sensors. Furthermore, two damage indices, namely the RMSD based damage volume ratio (DVR) and RMSD based displacement, were proposed to predict the damage levels and maximum horizontal displacement at the crest of dam under seismic loading. It is clearly demonstrated that the EMI technique based PZT sensors network can keenly detect the seismic damage of dam and the proposed damage indices can effectively quantify the damage levels and predict the dynamic response performances.

Experimental and numerical study of influence of crude oil products on the behavior of reactive powder and normal strength concrete slabs

This paper examines the usefulness of using reactive powder concrete (RPC) as a better option for constructing crude oil tanks. The effect of 2 types of crude oil products (kerosene and gas oil) on the structural behavior of RPC and normal strength concrete (NSC) slab specimens is experimentally and numerically investigated after being immersed for 180 days. The experimental program consisted of three groups of slab specimens; reference group (cured normally and tested at the age of 180 days), immersed in kerosene product group, and immersed in gas oil product group. Each of the groups consisted of testing (3) RPC slabs with a thickness of (20, 40 and 60 mm), and (1) NSC slab with (60 mm) slab thickness. A numerical finite element (FE) analysis has been done for the reference and immersed RPC slabs using the damage-plasticity constitutive model that readily available in the software package ABAQUS. The test results showed that the effect of each type of crude oil products on the load-bearing capacity of RPC slabs was nearly negligible with the highest reduction of 2.58% from its ultimate load after immersion in gas oil product. On the other hand, NSC slabs lost about (10.15 and 12.57%) of the ultimate load after being soaked in kerosene and gas oil respectively.

Confinement coefficient of concrete-filled square stainless steel tubular stub columns

The objective of this paper is to investigate the confinement coefficient of concrete-filled square stainless steel tubular (CFSSST) stub columns under axial loading. A fine finite 3D solid element model was established, which utilized a constitutive model of stainless steel considering the strain-hardening characteristics and a triaxial plastic-damage constitutive model of concrete with features of the parameter certainty under axial compression. The finite element analysis results revealed that the increased ultimate bearing capacity of CFSSST stub columns compared with their carbon steel counterparts was mainly due to that the composite action of CFSSST stub columns is stronger than that of carbon steel counterparts. A further parametric study was carried out based on the verified model, and it was found that the stress contribution of the stainless steel tube is higher than the carbon steel tube. The stress nephogram was simplified reasonably in accordance with the limit state of core concrete and a theoretical formula was proposed to estimate the ultimate bearing capacity of square CFSSST stub columns using superposition method. The predicted results showed satisfactory agreement with both the experimental and FE results. Finally, the comparisons of the experimental and predicted results using the proposed formula and the existing codes were illustrated.

Seismic response and damage analysis of underground structures considering the effect of concrete diaphragm wall

This paper investigates the effect of concrete diaphragm wall on the seismic response of underground structures using numerical simulation. The seismic response of a two-story subway station supported by concrete diaphragm walls located in Nanjing, southeast China was analyzed. A finite element model was developed to simulate the soil-diaphragm wall-underground structure interaction during earthquakes. This model simulated the nonlinear dynamic behavior of soils using a visco-plastic model and concrete damage using a plastic-damage constitutive model. The effect of the diaphragm wall was explored related to the burial depth of the subway station. The simulation results showed that during a strong earthquake, the diaphragm wall reduced the lateral deformation of the lower story of the structure. However, the effect was very limited to the upper story of the structure. In contrast, during a small earthquake, the diaphragm wall increased the lateral deformation of the upper story of a deeply buried structure. The concrete diaphragm wall also increased the settlement of a deeply buried structure. The earthquake damage to the underground structure increased with the increase of the burial depth. The seismic tensile damage to the diaphragm wall was found adjacent to the invert of the structure. The damage to the diaphragm wall increased the uplift potential of a shallowly buried structure during earthquakes. Findings from this paper provide guidance to the seismic design of large underground structures buried in similar grounds.

Performance Assessment of Shield Tunnel Damaged by Shield Shell Extrusion During Construction

A shield tunnel can be damaged by shield shell extrusions, such as shield tunnel floating, which may cause contact (even a squeezing action) between the shield tunnel and shield shell. To fully analyze this problem, a detailed 3D-finite element model (FEM) of a shield tunnel under the effect of a squeezing action in the shield tail, soil pressure, jacking force, and grouting pressure, was established by applying a plastic-damage constitutive model of concrete. A full-scale test of three segment rings was conducted, and the test results verified the feasibility of the constructed FEM. In this study, different squeezing positions and deflection angles of the shield shell were analyzed. The results indicated that the area squeezed by the shield shell experienced the most damage, and the tensile damage to a segment reduced gradually as the squeezing position approached the circumferential seam. The damage range gradually increased with the increase in deflection angle. The effect of the squeezing position of the shield shell on the bending moment was larger than the effect of the deflection angle on the bending moment. However, the effect of the squeezing position and that of the deflection angle on the shear force were the same.

Nonlinear Material Model for Quasi-Unidirectional Woven Composite Accounting for Viscoelastic, Viscous Deformation, and Stiffness Reduction.

To clarify the individual contribution of viscoelastic and viscous deformation to the global nonlinear response of composites, multilevel cyclic loading-unloading recovery tensile tests were carried out. The experimental results show that there is a linear relationship between the viscous strain and viscoelastic strain of composites, regardless of the off-axis angle or loading stress level. On the basis of experimental results, a coupled damage-plasticity constitutive model was proposed. In this model, the plasticity theory was adopted to assess the evolution of viscous strains. The viscoelastic strain was represented as a linear function of viscous strains. Moreover, the Weibull function of the effective stress was introduced to evaluate the damage variables in terms of stiffness reduction. The tensile stress-strain curves, predicted by the proposed model, showed a good agreement with experimental results.

Applicability of damage plasticity constitutive model for ultra-high performance fibre-reinforced concrete under impact loads

This paper presents a numerical investigation on assessing whether the concrete damage plasticity (CDP) constitutive model can be used to simulate new ultra-high performance fibre reinforced concrete (UHP-FRC) material under impact loading rates at different damage stages. The performance of the numerical models is verified by comparing numerical results to the experimental data that were previously tested by the authors. This paper also presents experimental tests that aimed to characterize the strain rate effect on UHP-FRC. The numerical simulations have been performed using ABAQUS/Explicit. CDP parameters are identified based on impact test results of a control specimen. Subsequently, the predictive capability of calibrated model has been investigated by simulating two UHP-FRC plates with varied steel reinforcement ratios tested under repeated drop-weight impact loads.It has been found that compressive and tensile strength enhancement predicted using CEB-FIP Model Code (1990) fits well with test results of the strain rate effect on UHP-FRC material. The numerical results demonstrate the feasibility of the CDP constitutive model for analyzing UHP-FRC under dynamic loading rates. Computed responses are sensitive to CDP parameters related to the tension, fracture energy, and plastic volumetric change. The effect of tensile strain hardening response could be ignored in the nonlinear finite element (FE) analysis of UHP-FRC materials with low strain-hardening behaviour.

Inelastic anisotropic constitutive models based on evolutionary linear transformations on stress tensors with application to masonry

The formulation of constitutive models for anisotropic materials such as masonry is a problem of large complexity. One possible way is to define linear transformations on the stress tensors using fourth-order transformation tensors that carry all the anisotropic information of the material. In the present paper, a new type of evolutionary linear transformation tensor is defined, which can change the values of its components along with the evolution of internal variables. This means the transformation laws are defined according to the current plastic and damage levels, and allows the constitutive model to describe totally different hardening and softening behaviours of the material along different directions. First, a general procedure of formulation of anisotropic constitutive models is given. Second, as a specific example, an orthotropic plastic–damage constitutive model for masonry is presented. Finally, the proposed constitutive model is validated by comparing finite element results with experimental ones pertaining to simple masonry structures under static and cyclic loading.

Hydro-mechanical network modelling of particulate composites

Differential shrinkage in particulate quasi-brittle materials causes microcracking which reduces durability in these materials by increasing their mass transport properties. A hydro-mechanical three-dimensional periodic network approach was used to investigate the influence of particle and specimen size on the specimen permeability. The particulate quasi-brittle materials studied here consist of stiff elastic particles, and a softer matrix and interfacial transition zones between matrix and particles exhibiting nonlinear material responses. An incrementally applied uniform eigenstrain, along with a damage-plasticity constitutive model, are used to describe the shrinkage and cracking processes of the matrix and interfacial transition zones. The results showed that increasing particle diameter at constant volume fraction increases the crack widths and, therefore, permeability, which confirms previously obtained 2D modelling results. Furthermore, it was demonstrated that specimen thickness has, in comparison to the influence of particle size, a small influence on permeability increase due to microcracking.

On the numerical modelling of bond for the failure analysis of reinforced concrete

The structural performance of reinforced concrete relies heavily on the bond between reinforcement and concrete. In nonlinear finite element analyses, bond is either modelled by merged, also called perfect bond, or coincident with slip, also called bond-slip, approaches. Here, the performance of these two approaches for the modelling of failure of reinforced concrete was investigated using a damage-plasticity constitutive model in LS-DYNA. Firstly, the influence of element size on the response of tension-stiffening analyses with the two modelling approaches was investigated. Then, the results of the two approaches were compared for plain and fibre reinforced tension stiffening and a drop weight impact test. It was shown that only the coincident with slip approach provided mesh insensitive results. However, both approaches were capable of reproducing the overall response of the experiments in the form of load and displacements satisfactorily for the meshes used.

An elastic–plastic damage model considering capillary effect for petrol–water saturated sandstone

The mechanical behavior of surrounding rock mass is key important to the water-sealed petrol storage caverns because of the two phase environment. To investigate the strength and damage mechanism of rock mass under petrol–water immersion circumstance, an elastic–plastic damage constitutive model is proposed. The deformation work of rock mass is derived according to the mixture theory and averaging methods. In order to further study the capillary action influence of petrol–water liquid phase on the strength and stiffness of rock mass, the plastic yield condition considering petrol–water circumstance is proposed. Then, the stress–strain increment expression under the influence of both liquid and solid phase is deduced through the consistency condition. Meanwhile, the damage conditions of the rock mass under tensile and compressive stress differ a lot, so the rock mass damage model under petrol–water circumstance is established combining the tensile and compressive damage criterion and the damage evolution law. The proposed constitutive model is adopted to simulate the mechanical property and damage evolution feature of rock mass under axial compression. The results suggest that the increase in the petrol pressure leads to the improvement of the axial strength for rock mass and meanwhile, the occurrence of damage is also advanced. In addition, the elastic–plastic property of the rock material has been well developed below the stress peak point during this process. Ultimately, the proposed elastic–plastic damage constitutive model was verified by making comparisons between the theoretical calculating results and experimental results.

A study on the simulation method for fatigue damage behavior of reinforced concrete structures

This paper mainly focuses on developing an efficient simulation method for fatigue behavior of reinforced concrete structures (RC structures), through which the damage state and the potential fatigue damage failure pattern of the RC structures could be obtained in finite element analysis (FEA). In order to accomplish such object, fatigue behavior of RC structures is studied using the entire history of damage accumulation for both concrete and steel bars. A bi-scalar damage-plasticity constitutive model for concrete and a single-scalar damage constitutive model for reinforcement are first introduced to characterize the fatigue damage state of the structure. Then, a two-scale temporal expediting computational technique is developed for the material constitutive models, by which the original material models could be split into a micro periodic time scale portion and a macro homogenized time scale portion. Through this calculation technique, the original increment-by-increment FEA procedures could be transferred to the two-time scale calculation, which would greatly enhance the efficiency of the structural fatigue simulation. By combining the material constitutive models and the expediting calculation technique with FEA, a set of numerical examples and comparisons are performed, specifically, a column-drilled shaft connection in bridge structure is simulated, which validates the effectiveness and reliability of the current simulation method for the fatigue behavior of RC structures.

Feasibility Study of a Table Prototype Made of High-Performance Fiber-Reinforced Concrete

The challenging and innovative idea of realizing a table totally made of fiber-reinforced concrete is explored through an interdisciplinary research activity, where contributions coming from different fields (design, material science, experimental testing, numerical modeling) are combined. The paper describes the different phases of the study, starting from the design of the table, moving through the development of a purpose-made high-performance fiber-reinforced concrete and the mechanical characterization via experimental testing, and concluding with numerical modeling. Numerical results are determined by implementing a damage plasticity constitutive model in a finite element code. The mechanical response of the table has been analyzed for different loading and boundary conditions, and an exhaustive and complete picture of the possible failure mechanisms has been drawn. Simulations have clearly described the different stress-softening processes of damage evolution and plastic strains localization, pointing out the vulnerable parts of the table. Finally, strategies for improving the table mechanical performances are discussed.