Plastic-damage Constitutive Model Research Articles

Numerical simulation and experimental verification studies on a unified strength theory-based elastoplastic damage constitutive model of shale

The purpose of this study is to establish an elastic–plastic damage constitutive model of shale and simulate the elastic–plastic damage characteristics of shale under stress. Based on the unified strength theory and the mechanics of shale rock samples characterized in laboratory tests, a new elastic–plastic damage constitutive model for shale is established by introducing compression factors and damage variables. The main considerations include the compressibility of primary fractures and pores in the shale core, and the formation of secondary cracks in the rock matrix under stress. A fully implicit backward Euler regression mapping algorithm has been used to solve the model, and the numerical simulation results are in good agreement with the experimental results. The results show that the model established in this paper can accurately simulate the elastic–plastic damage characteristics of shale under stress, and that it provides a new numerical simulation method for describing the elastic–plastic damage in shale.

Rock plastic-damage constitutive model based on energy dissipation

Rock plastic-damage constitutive model based on energy dissipation

Seismic damage assessment of a historic masonry building under simulated scenario earthquakes: A case study for Arge-Tabriz

Damage prediction of existing buildings against natural events is a challenge for engineers. Although several approaches have been proposed in the bibliography for damage assessment of steel and concrete structures, more studies are required to survey the damage state of masonry buildings.In this research, seismic damage of a historical masonry building, named Arge-Tabriz, has been assessed using region-specified simulated ground motion records. The main goal of the research is to predict the damage levels of Arge-Tabriz monument under probable earthquakes. Potential scenario earthquakes with different magnitudes are simulated to evaluate the seismic damage of the Arge-Tabriz building. For ground motion simulation of the scenario earthquakes, the stochastic finite-fault methodology, which employs a finite-fault approach comprised of point-source models, is used. The building is modeled using macro-modeling approach; and for the masonry material, concrete damaged plasticity constitutive model is utilized. After performing nonlinear dynamic analyses of the model in ABAQUS commercial software, the damage state of the building is assesses through failure area and failure volume methods, Park-Ang damage index, performance limits proposed by FEMA 356, and finally tensile damage variable DAMAGET as ABAQUS output variable. The accuracy of the employed numerical method is verified through comparison of the developed damage patterns with the existing damage patterns of the building. The results disclose that failure area and failure volume indices have the highest accuracy, while the drift limits of FEMA 356 have the lowest precision to predict the damage level of the building. The application of region-specific simulated scenario earthquakes reveals that the building has adequate strength to resist against weak seismic events and it experiences moderate damage, keeping up its whole stability under moderate potential events; while it is susceptible to collapse against severe earthquakes, and therefore, a rehabilitation scheme seems to be essential for preserving this valuable heritage.

Numerical Investigation of the Composite Action of Axially Compressed Concrete-Filled Circular Aluminum Alloy Tubular Stub Columns.

This paper studied the composite action of concrete-filled circular aluminum alloy tubular (CFCAT) stub columns under axial compression. A fine-meshed finite three-dimensional (3D) solid element model making use of a tri-axial plastic-damage constitutive model of concrete and elastoplastic constitutive model of aluminum alloy was established. A parametric study utilizing the verified finite element (FE) model was carried out and the analytical results were exploited to investigate the composite actions of concrete-filled circular aluminum alloy tubular stub columns subjected axial compression. Compared with the concrete-filled steel tube (CFCST) stub columns, the aluminum alloy tube exerted a weaker constraint effect on the infilled concrete due to its lower elastic modulus. Based on the FE analytical results and regression method, the composite action model of concrete-filled circular aluminum alloy tubular stub columns was proposed. By generalizing the stress nephogram of the concrete-filled circular aluminum alloy tubular stub column at the limit state, a design formula was proposed to estimate the ultimate bearing capacity the columns using the superposition method. The predicted results of the proposed formula show a good agreement with both the experimental and FE analytical results. The comparison between the proposed formula and current design methods indicates that the proposed formula is more accurate and convenient to use.

Analytical Modelling of LACFCST Stub Columns Subjected to Axial Compression

This paper presents a numerical investigation of lightweight aggregate concrete-filled circular steel tubular (LACFCST) stub columns under axial compression. A finite 3D solid element model of the LACFCST stub column was established by adopting a plastic-damage constitutive model of lightweight aggregate concrete (LAC). The finite element model (FEM) analysis results revealed that the confinement effect of the steel tube on the infilled LAC was weaker than that on the infilled conventional concrete. A parametric study making use of 95 full-scale FEMs was conducted to investigate the influences of various design parameters of LACFCST stub columns on their ultimate axial bearing capacity and the composite actions. Moreover, a numerical model of the axial and transverse stress of steel tubes at the ultimate state of LACFCST columns was proposed using the regression method. Based on the equilibrium conditions and the proposed model, a practical design formula making use of an enhancement factor was derived to estimate the ultimate bearing capacity of LACFCST stub columns by using the superposition method. The validity of the proposed formula was verified against the experimental data of 49 LACFCST stub column specimens under the axial loading available in the literature. Meanwhile, the accuracy and conciseness of the proposed formula were evaluated by comparison with the formulas suggested by the existing design codes.

Numerical Study on Confinement Effect and Efficiency of Concentrically Loaded RACFRST Stub Columns

The mechanical behaviors of recycled aggregate concrete (RAC) are upgraded by outer steel tube confinement, and the performance of recycled aggregate concrete-filled steel tubular (RACFST) columns is similar to that of the traditional concrete-filled steel tube (CFST) columns. The purpose of this study is to investigate the behaviors of recycled aggregate concrete-filled rectangular steel tubular (RACFRST) stub columns under axial loading. Three-dimensional finite element (FE) models were established, which utilized a triaxial plastic-damage constitutive RAC model considering the replacement ratio of recycled aggregates. The finite element analysis results indicated that the lessened ultimate bearing capacity of RACFRST stub columns compared with their traditional concrete infilled counterparts was mainly due to the weakened confinement effect and confinement efficiency. A simplified formula of the bearing capacity of concentrically loaded RACFRST stub columns was proposed. The cross-sectional stress nephogram was reasonably simplified by the limited state of infilled concrete. The basics of proposed formula were the equilibrium condition and the superposition method. Finally, the formula for the bearing capacity of RACFRST stub columns was evaluated by comparing its accuracy and feasibility to some design formulae proposed by specialists and some design codes of different regions.

Finite element analysis of rectangular RC beams strengthened with FRP laminates under pure torsion

AbstractComposite materials have attracted wide attention in strengthening of structural members. In this study, the behavior of rectangular reinforced concrete (RC) strengthened with fiber reinforced polymer (FRP) laminates under pure torsion was investigated numerically and validated by existing data from literature. Various practical strengthening configurations were considered and the efficiency of them was illustrated. Concrete damage plasticity constitutive model was used and required parameters was drawn. Good agreement in terms of torque–twist behaviors of RC beams strengthened with FRP laminates before and after cracking was found. Reasonable steel and FRP reinforcement responses as well as crack patterns were achieved and the failure modes of all the specimens were modeled correctly. A parametric study was carried out and parameter such as number of FRP plies, concrete compressive strength, and FRP strip orientations were considered. The results showed that the torsional capacity could improves by increasing the number of FRP plies and concrete compressive strength. Moreover, no significant change in the torsional capacity of RC beams when it was strengthened with a 45° or with a 90° FRP laminate was observed.

Parameter optimal investigation of modular prefabricated two-side connected buckling-restrained steel plate shear wall

This paper research the optimal scope of width-to-thickness ratio α1 of connection steel plate (CSP), thickness ratio α2 between CSP and inner steel plates (ISP), and width-to-thickness ratio α3 between the width of CSP and the thickness of the ISP of modular fabricated two-side connected buckling-restrained steel plate (MTBSP) shear wall. The finite element model (FEM) of the MTBSP shear wall is established based on the ABAQUS platform, which, considering the plastic-damage constitutive model of both concrete and steel materials. Through the result of a comparison between the test and FEM, it can be concluded that the FEM can effectively reflect the mechanical behavior of the MTBSP shear wall. Based on the verified FEM, the mechanical behavior of 93 computational cases with different ratios of α1, α2, and α3 of MTBSP shear wall is investigated and the corresponding optimal scope of α1, α2, and α3 are explored in detail. The results show that the mechanical performance of the MTBSP shear wall can be ensured effectively when the ratio α1,α2, and α3 is in the scope from 10 to 20, from 3 to 5, and from 60 to 80, respectively. Research of this study can be provided supporting the reliable design of the MTBSP shear wall.

Coupled Damage-Plasticity Modelling of Saturated Shale under Undrained Condition

Shale is classified as a poroelastic material as the shale matrix has comparable stiffness with its constituent solid grains. Also, shales at large depth are often fully saturated. Due to their low permeability, which can be in the nano-Darcy range, shales remain undrained during typical loading conditions. Additionally, shales are quasi-brittle materials which can exhibit very pronounced peak shear stress followed by pronounced strain softening during shearing. All these unique aspects of shale behavior must be considered in developing a model that predicts the change of the pore pressure, the effective stress response and the undrained shear strength of shales during loading. This study presents a coupled plastic-damage constitutive model which considers poroelastic effect with the objective to predict the mechanical behavior of saturated shales under undrained condition. The proposed model couples the plastic mechanism, which is formulated on the effective stress space, and the damage mechanism which is responsible for the elasticity degradation and the post-peak softening of shale. Validation of the proposed model against triaxial est results demonstrates that the proposed model can predict the stress-strain behavior, the effective stress path and the pore pressure evolution of shale specimen during shearing.

Finite element analysis of UHPC reinforced masonry structure

Based on the existing UHPC material parameters, masonry parameters and the application of reinforcement projects on the market, ABAQUS's unique concrete plastic damage (CDP) constitutive model can be used for concrete and other brittle materials. The constitutive parameters are obtained by curve fitting experiments by other scholars, and this paper has carried out appropriate calibrations. Numerical analysis is the pseudo-static loading form of UHPC reinforced low-strength masonry walls. Through the analysis and simulation of the hysteresis curve, skeleton curve, equivalent plastic strain Moire diagram, peak stress, strain and other parameters, the changes in shear resistance before and after UHPC reinforced masonry walls are evaluated.

Plastic hinge and seismic structural measures of terminal stirrup-confined rectangular CFT columns under low-cyclic load

Based on the plastic-damage constitutive model of concrete and elastic-plastic mixed strengthen constitutive model of steel material, the finite element software ABAQUS was used to build an elaborate 3D finite element (FE) solid model and perform pseudo-static analysis of terminal stirrup-confined concrete-filled rectangular steel tubular columns (SCFT) in this study. The FE model considers the confinement effect of both the steel tube and the stirrups exerting on the core concrete and the cumulative damage effect due to the horizontal cyclic load. Good agreement was achieved between the FE results and the existing quasi-static experimental results regarding to the load-displacement hysteretic curves, load-displacement skeleton curves, load-strain ratio curves, and local buckling-displacement curves. Based on the validated model, a total of 315 full-scale column models were established and extensive parametric analysis was conducted. The results indicate that: (1) When the axial compression ratio n is up to 0.8, the seismic behavior of rectangular CFT columns with bidirectional stirrups is significantly better than those counterparts with ring stirrups having the same volume stirrup ratio. (2) When the longitudinal compressive strain of steel tube reaches 30 times of the yield strain, plastic hinge is formed at the end of SCFT column and the stirrups can effectively reduce the plastic hinge length. A formula of plastic hinge length suitable for different axial compression ratios and equivalent stirrup ratios is proposed. (3) According to the results of parametric analysis, the seismic structural measures including reasonable equivalent stirrup ratio and region height of terminal stirrups are proposed for different axial compression ratios and strength matching patterns between steel tube and core concrete.

A damage plasticity constitutive model for wavy CNT nanocomposites by incremental Mori-Tanaka approach

In this paper, a novel nonlinear micromechanics constitutive model is proposed to simulate elastoplastic and ductile damage behavior for wavy carbon nanotube (CNT) nanocomposites. A modified Eshelby tensor corresponding to wavy CNT is derived by integrating a rotational transformation of the effective composite stiffness tensor along the sinusoidal wavy CNT. The modified Eshelby tensor was utilized to update local and global strain concentration tensors, rebalancing local strains of inclusions and matrix caused by constantly changing algorithmic tangent operator of the matrix. They were integrated with a general framework for nonlinear MT homogenization. A 3D FE micromechanics model is developed to verify the feasibility and accuracy of the proposed model. Following the verification, effects of CNT waviness are closely investigated under various volume fractions, aspect ratios and loading directions.

Experimental characterization and constitutive modeling of an aluminum 7085-T711 alloy under large deformations at varying strain rates, stress states, and temperatures

The strain rate, stress state, and temperature dependent mechanical behavior of a hot rolled aluminum 7085-T711 alloy is experimentally observed and subsequently modeled using a continuum Internal State Variable (ISV) plasticity-damage constitutive model. Structure-property relationships for the alloy are quantified using a series of microstructural analyses and mechanical property experiments. The calibrated ISV model for the Al 7085-T711 alloy is implemented in an implicit finite element code (Abaqus) to simulate the deformation of notch Bridgman tension specimens at a variety of stress states and temperatures. The ISV model accurately captures the material's elastoplastic behavior by predicting the stress state difference between tension, compression, and torsion and temperature dependent microstructure evolution under large deformations.

Numerical analysis of bonding between masonry and steel reinforced grout using a plastic–damage model for lime–based mortar

This paper shows a numerical investigation with single-lap shear bond tests between Peruvian brick masonry and SRG system. For this purpose, the finite element method, elements and constitutive models implemented in ABAQUS library were used. Eight-node continuum elements were employed for modelling mortar, masonry and steel fibers assuming a linear-elastic behaviour for the last two materials. Eight-node cohesive elements with zero-thickness were used to model substrate-mortar and steel-mortar interfaces. Due to experimental results showed the detachment of the steel fiber from the mortar accompanied by cracking of the outer mortar layer, the non-linearity of the mortar was also considered by using a Concrete Damage Plasticity constitutive model. The effect of the mortar non-linearity was compared with other models assuming a linear and rigid material for mortar, as recommended by literature. This shows that modelling a non-linear mortar leads to more accurate results for future design and strengthening purposes, thus, its implementation is encouraged. A comparison in time between Bond–Slip Law (BSL) at steel–mortar interface and mortar constitutive law is analysed in order to investigate the stress-transfer mechanism during single–lap shear tests.

On the dynamic response of reinforced concrete beams subjected to drop weight impact

To improve the impact resistance of reinforced concrete structures, a detailed understanding of the dynamic response is required. This study investigates this impact resistance using experiments in combination with 3D non-linear finite element (FE) simulations. The experiments made use of high-speed photography and digital image correlation (DIC), while a damage-plasticity constitutive model for concrete was used in the FE simulations. Drop weight impact tests of simply supported reinforced beams made of plain concrete and fibre reinforced concrete were made, and it was shown that the addition of fibres reduced crack spacing, crack widths and mid-point deflections. For the FE approach, tetrahedral elements were shown to be well suited for capturing inclined shear cracks and the structural response obtained in experiments and analyses agreed very well. The FE analyses showed that the reinforcement strains were more localised for concrete with fibres, and hence predicted an increased risk of reinforcement rupture.

A rate- and pressure-dependent damage-plasticity constitutive model for rock

A new damage-plasticity constitutive model which takes account of the effect of confining pressure and strain rate on the strength and post-peak behaviour is proposed for rock subjected to dynamic loading. The model treats the compressive and tensile damages, both related to plastic and volumetric deformations, separately. The strain rate effect is considered by incorporating a newly developed dynamic increase factor formula, which reflects the pure rate sensitivity of rock, into the yield surface via radial enhancement approach. Fractionally-associated flow rule and lode-angle dependency are employed to capture the shear dilation behaviour of rock. The new model is then implemented into LS-DYNA via a user defined material subroutine to simulate the mechanical response of rock under various loading scenarios including triaxial compression, direct tension, Split Hopkinson Pressure Bar compression, oval-nose projectile penetration and explosive blast action, reported in literature. The robustness and accuracy of the new model are demonstrated by validating against available experimental results and by benchmarking with the reported simulations.

A Developed Damage Constitutive Model for Circular Steel Tubes of Reticulated Shells

The aim of this paper is that the precise description of damage behavior is crucial to well catch the mechanical behavior of structures in the dynamic numerical simulation, and address the issue on the coupled plastic-damage constitutive model for circular steel tubes of reticulated shells under severe earthquake. Continuum Damage Mechanics (CDM) constitutive model established by Lemaitre is reviewed at the beginning. Then, an improved damage model for circular steel tubes of reticulated shells is developed based on Lemaitre’s model by replacing the original damage evolution law with a new one suitable for circular steel tubes. In addition, we introduce the stress update process. In this procedure, the well-known operator split strategy, which leads to the standard elastic predictor/return mapping algorithm, is adopted to solve the evolution problem of the improved model. Exploiting user-defined material subroutine, the implementation of the model is achieved within software ANSYS using BEAM189 element. Finally, the dynamic response of reticulated shells under severe earthquake are numerically simulated with the proposed model and with the conventional Prandtl-Reuss model, respectively. The comparison results show that the consideration of material damage accumulation, on the one hand, may change the failure mode of reticulated shells from dynamic instability to strength failure; on the other, may reduce the dynamic ultimate load obviously. This consideration should be taken into account when conducting nonlinear dynamic analysis of reticulated shells.

Experimental investigation of the seismic response of shallow-buried subway station in liquefied soil

In this study, a series of shaking table tests were carried out based on an irregular cross-section subway underground structure. Further, the development laws of pore pressure, structural strain, acceleration intensity, and the propagation law were analyzed. The results show that the peak acceleration of the surface is attenuated, which reflects the isolation effect of the liquefied soil. The spectral characteristics of the liquefied foundation soil reflect the low frequency band concentration and amplification effects. Moreover, there is a significant floating phenomenon in the model structure during the earthquake. With an increase in the degree of liquefaction at the site, the uneven settlement and slope of the variable-section underground structure become more significant. The dynamic strain on each member of the structure shows that the middle column has the largest reaction, the sidewall is the second largest, and the floor has the smallest; the bottom end of the lower middle column is most vulnerable to damage. A modified dynamic constitutive model was used for soil; the rate-independent plastic-damage constitutive model was used for concrete in the numerical simulations using the finite element method. The difference between the results obtained by numerical analysis and shaking table tests is discussed in detail. The results provide insight into how strong ground motion may induce the liquefaction of soil.

Numerical and experimental investigation of electro-mechanical impedance based concrete quantitative damage assessment

This paper presents a numerical and experimental investigation of the concrete quantitative damage assessment using the smart aggregate (SA) sensor based on the electro-mechanical impedance method. In the numerical simulation, a concrete cube finite element model with an embedded SA sensor is established using concrete damaged plasticity constitutive model to simulate the damage process under uniaxial compression. The concrete damage degree is evaluated using the conductance signatures of the embedded SA sensor and damage volume ratio (DVR). In the experimental study, three concrete cubes are casted and subjected to compressive loading. The experimental study verifies the numerical simulation model by comparing the root mean square deviation (RMSD) indices of conductance signals. Furthermore, the DVR is proposed as an effective damage evaluation index. The relationship curve between the DVR and the RMSD is fitted. The results illustrate that the RMSD index of the SA sensor and the DVR of the concrete have a linear relationship. The level of concrete damage can be quantitatively evaluated by RMSD index according the relationship between the RMSD and DVR.

Exploration on Damage Mechanism and Equivalent Damage Model of High Arch Dams under Earthquakes

Damage identification technology of high arch dams has been well developed under strong earthquakes. However, the failure mechanism of high arch dams at different locations remains unclear. For this purpose, a series of deterministic dynamic analyses for a 3D 289-m-high arch dam based on concrete damaged plasticity constitutive model are performed. The failure mechanism at different locations of high arch dams under earthquakes is studied systematically. According to the sensitivity of different indicators to different damaged positions, an effective sensor placement scheme is proposed to assess the seismic reliability in practical engineering. Furthermore, a new effective equivalent damage model based on prior information is proposed, which can improve the efficiency of damage identification, as well as solving the problem that the real damage is concealed by homogenizing the damage in a pre-set region. The results provide suggestions and theoretical basis for sensor placement in actual monitoring of high arch dams; and the equivalent damage model provides a new solution to balance the efficiency and accuracy of damage identification.