Plasticity Constitutive Model Research Articles

Nonlinear Finite-Element Analysis for Structural Investigation and Preservation of Reinforced Hybrid Thin Tile–Concrete Domes of the Historic School of Ballet Classrooms in Havana, Cuba

The striking tiled domes of the Ballet School of the Instituto Superior de Arte (ISA) in Havana are internationally acclaimed Cuban architectural icons. However, due to their deceptive tiled appearance and their only recently rediscovered hybrid tile–concrete constructive system, the domes have eluded the structural study and characterization which increasingly is demanded not only because of their unique morphology and monumental status, but also because of their visible damage. This work defined a suitable numerical analysis method for diagnosing these hybrid structures by applying both linear elastic and nonlinear, using the concrete damaged plasticity constitutive model, numerical analyses. A site investigation campaign provided materials and geometric data that informed the model creation and damage documentation that validated the analyses results. A new synthesis of architectural and technical sources covering the development and spread of the hybrid structural system allowed the ISA domes to be placed, for the first time, in their proper structural context and, consequently, for their conception and design to be understood more fully. The analyses, construction records, and site tests indicated a rebar placement error as the primary structural damage cause, and the contextual analysis informed a discussion of its possible sources, both technical and managerial. Because the investigation indicated significant risk of irreversible damage or failure without timely intervention, preliminary intervention explorations were conducted and, based on the holistic understanding of the structures, the technically, architecturally, and culturally optimal solution was identified. The study concluded that the homogeneous solids model, coupled with the concrete damaged plasticity mechanical model, yields realistic and insightful results illuminating the structural behavior, efficiency, condition or status, and collapse mode of the domes, providing necessary insight for the preservation planning for the Ballet School domes, which also will inform the study and understanding of other structures of similar composition and significance.

Research on the 2A11 Aluminum Alloy Sheet Cyclic Tension–Compression Test and Its Application in a Mixed Hardening Model

The increasing application of aluminum alloy, in combination with the growth in the complexity of components, provides new challenges for the numerical modeling of sheet materials. The material elastic–plasticity constitutive model is the most important factor affecting the accuracy of finite element simulation. The mixed hardening constitutive model can more accurately represent the real hardening characteristics of the material plastic deformation process, and the accuracy of the material property-related parameters in the constitutive model directly affects the accuracy of finite element simulation. Based on the Hill48 anisotropic yield criterion, combined with the Voce isotropic hardening model and the Armstrong–Frederic nonlinear kinematic hardening model, a mixed hardening constitutive model that considers material anisotropy and the Bauschinger effect was established. Analysis of the tension–compression experiment on the sheet using finite element method. Using the finite element model, the optimum geometry of the tension–compression experiment sample was determined. The cyclic deformation stress–strain curve of the 2A11 aluminum alloy sheet was obtained by a cyclic tensile–compression test, and the material characteristic parameters in the mixed hardening model were accurately determined. The reliability and accuracy of the established constitutive model of anisotropic mixed hardening materials were verified by the finite element simulation and by testing the cyclic tensile–compression problem, the springback problem, and the sheet in bending, unloading, and reverse bending problems. The tensile–compression experiment is an effective method to directly and accurately obtain the characteristic parameters of constitutive model materials.

Study of mechanical properties of grouting defective sleeve

When sleeves are grouted at the construction site, grouting defects occur inside the sleeves owing to the structure of the grout sleeve, plugging time of the grout outlet hole, and connection form of the sleeve. Grouting defects reduce the connection strength of grout sleeves and further affect the safety performance of assembled building structures. In this study, the failure modes of grout defects and their influencing factors were fully investigated, which provides guidelines for the standardization of sleeve grouting construction. First, a uniaxial tensile test was performed on 33 grouting defect specimens to study the mechanical properties of the grouting defect. Second, the Concrete damaged plasticity (CDP) and Brittle Cracking (BC) constitutive models of grout were considered and optimized, and the corresponding numerical models were established to further analyze the failure modes of sleeve grouting. The numerical analysis results were compared with the test results. The comparison results show that adopting the optimized CDP constitutive model in the numerical simulation is more consistent with the test results. Finally, the stress mechanism of the grout sleeve was theoretically analyzed, and the calculation equation for the anchorage length was improved. The experimental study revealed that the ultimate bearing capacity and displacement of the specimen were affected by the specimen size, and the large-size specimen was more prone to pull-out failure. In addition, theoretical analysis showed that the specimen was in a safe state when the anchorage length of the rebar was greater than 6d. Based on the investigation results, the improved anchorage length equation can be used to calculate the anchorage length of the grout sleeve in sleeve grouting construction. Moreover, the middle and lateral grout defects of the grout sleeve should be focused on in sleeve grouting construction to ensure the quality of sleeve grouting.

Ultrasonic constitutive model and its application in ultrasonic vibration-assisted milling Ti3Al intermetallics

Ultrasonic vibration-assisted technology is widely utilized in the performance research and manufacturing process of metallic materials owing to its advantages of introducing high-frequency acoustic systems. However, the acoustic plasticity constitutive model and potential mechanism, involving Ti3Al intermetallic compounds, have not yet been clarified. Therefore, the Ultrasonic-K-M hybrid acoustic constitutive model of Ti3Al was established by considering the stress superposition, acoustic thermal softening, acoustic softening and acoustic residual hardening effects according to the dislocation density evolution theory and crystal plasticity theory. Meanwhile, the mechanical behavior of ultrasonic vibration-assisted tension (UVAT) and microstructure of ultrasonic vibration-assisted milling (UVAM) for Ti3Al was investigated. Dislocation density to be overcome from initial deformation to failure of Ti3Al was calculated in UVAT and was verified in UVAM. The results indicated that the Ultrasonic-K-M model showed a good agreement with the experimental data. There was an obviously softening phenomenon after introducing the ultrasonic energy field in the Ti3Al whole deformation region, and the degree of softening was positively correlated with amplitude. Furthermore, the maximum reduction ratio in yield strength of Ti3Al was 16 % and the maximum reduction value in ultimate tensile strength was 206.91 MPa. The elongation rose first and then fell as amplitude enlarged, but only as the vibration was applied in the whole deformation region, the elongation was always greater than 14.58 %. In addition, The UVAM process significantly reduced the dislocation density increment to be overcome for Ti3Al material removal by 1.37 times, and promoted dislocation motion and cancellation to make twisted dislocations evolve into parallel dislocations. As the amplitude increased to 4 μm, the depth of the disturbed area of the plastic deformation layer increased by a maximum of 2.5 times.

Nonproportionally multiaxial cyclic plastic deformation of U75 rail steel: Experiment and modeling

U75V rail steel exhibits cyclic softening and hardening under uniaxial and multiaxial strain-controlled cyclic loadings, respectively. The ratcheting behavior of U75V rail steel depends on the loading paths due to nonproportionally additional hardening. New evolution equations incorporating Tanaka’s nonproportional parameter are introduced into the isotropic and kinematic hardening rules of the cyclic plastic constitutive model to describe the cyclic softening/hardening features and multiaxial ratcheting behavior. The simulated results agree with the corresponding experimental results. A finite element model of wheel-rail cyclic rolling contact is established to investigate the nonproportionally multiaxial effect on the rolling contact fatigue life.

Dynamic numerical prediction of plasticity and damage in a turbofan blade containment test

For the light designs of new aircraft engines, constitutive plasticity and fracture models sensitive to strain rate and temperature are essential for the accurate prediction of deformations and internal stresses of the components during simulations of impact and explosion events. The work described in this article consists of the development and numerical analysis by finite elements of the blade containment test of a commercial aircraft turbofan engine, conducted to evaluate the structural integrity of the casing after being impacted by a detached fan blade. Two simulation models of the test are proposed, in which the resistance behavior of the strain rate-dependent material is described by isotropic laws of strain hardening and Johnson–Cook damage. The strength analysis is based on the numerical field results of equivalent stresses and deformations, along with the internal damage rates of the casing. The first simplified model considers half of the casing impacted by a blade at different speeds and angles of impact. The second model consists of a complete discretization of casing and rotating turbofan, with the initial detached condition of a blade simulated at different rotating speeds of the fan. The material used in this study is the Ti-6Al-4V alloy. The results analysis and advances obtained make it possible to approach an efficient computational tool with more accurate calculations to study a casing redesign with a safe reduction in mass and that fulfills the certification requirements using the blade containment test.

Study on Explicit–Implicit Simulation and In-Situ Measurement of Floor Failure Law in Extra-Thick Coal Seams

A reliable numerical simulation method and large-scale in-situ test method for super-thick coal seams are very important to determine the failure range of mining floors, which is often the basis to protect Ordovician limestone water, an important drinking water source for people in North China. This paper takes Yushupo Coal Mine as an example; the explicit–implicit coupling simulation method and the corresponding double scalar elastic–plastic constitutive model were established to predict the failure depth of the floor numerically, and verified by the full section borehole stress–strain in-situ testing method. The results show that the explicit–implicit coupling numerical program and the double scalar elastoplastic constitutive model are suitable for predicting the floor failure depth under the condition of extra-thick coal seams. In this condition, the overburden moves violently, resulting in a loading–unloading–reloading process with large stress variation amplitude in the mining floor, which leads to serious rock failure compared with that of medium-thick coal seam conditions. In Yushupo 5105 working face, the floor failure starts to develop from 9.3–24.2 m ahead of the coal wall of working face, and the failure depth no longer increases after 35 m behind the coal wall, with the maximum failure depth of 28 m; the envelope line of the floor failure depth presents an inverted saddle distribution. The above research results lay a foundation for further protecting the Ordovician limestone water, and realizing green coal mining.

Experimental Analysis and Constitutive Modeling of Cyclic Behavior of 304 L Stainless Steel: Introduction of Isotropic Hardening Fading Effect

Abstract In this study, the mechanical behavior of austenitic stainless steel 304 L under low cycle fatigue was investigated under different uni-axial strain-controlled loadings of 0.5%, 0.8%, 1.0%, 1.2%, and 1.5%. The analysis of the experimentally determined strain versus stress hysteresis curves was carried out to achieve stress quantities such as amplitude stress, peak effective stress, and peak back stress. It was observed that in the early stage of cyclic loading, material underwent initial hardening, followed by softening phenomena which were more considerable in the lower strain range. Before the failure, the secondary hardening was observed at the final stage. In addition to accumulated plastic strain, it was shown that the peak back stress and peak effective stress which is associated with isotropic hardening and kinematic hardening behavior, respectively, are influenced by the strain range effect. Therefore, the coefficient of recall term that appeared in the Armstrong–Frederick nonlinear kinematic hardening model was considered to be dependent on the radius of the memory surface. Furthermore, to increase the ability of the plasticity constitutive model to show a smooth transition between various hardening stages, the radius of the yield surface which is associated with the isotropic hardening rule was equipped with the fading effect. Finally, by the comparison of numerical and experimental results, the capability of the rate-dependent constitutive model over classical rate-independent plasticity in the prediction of mechanical behavior of steel 304 L under strain-controlled cyclic loading was revealed.

Incremental strain gradient plasticity model and torsion simulation of copper micro-wires

Experimental observations show that the torsional deformation of copper micro-wires exhibits obvious sample and grain size effects. In this work, based on the framework of the cyclic plastic J2 flow rule, an incremental higher-order strain gradient constitutive model is established to describe the size effect observed in the torsional deformation of copper micro-wires. A novel kinematic hardening evolution rule is constructed in which the coupling effect of sample and grain sizes on the plastic hardening has been considered. In terms of numerical implementation, a finite element iterative algorithm which can independently solve the gradient field and plastic strain increment is proposed. Finally, the proposed model is implemented into the finite element software ABAQUS using a three-dimensional user-defined element and user-defined material subroutine. Simulated results show that the proposed model can capture the size-dependent torsional deformation of copper micro-wires since both the effects of sample and grain sizes are considered reasonably. This provides a good basis for the combination of strain gradient plasticity theory and cyclic plasticity constitutive model.

Micro mechanical property investigations of Ni-based high-temperature alloy GH4169 based on nanoindentation and CPFE simulation

In this research, the microscopic deformation behavior of GH4169 superalloy is investigated by a series of nanoindentation experiments and simulations based on crystal plasticity finite element (CPFE) model, including hardness, creep displacement and stress distribution around indentation. In this regard, the crystal plasticity constitutive model based on dislocation slip for face-centered cubic (FCC) crystal of concern is summarized and numerically implemented at first. Moreover, nanoindentation experiments are performed on specimens with various peak loads and load times to investigate the mechanical response and deformation mechanism at the micro-scale. Nanoindentation test results show that load rate, peak load, and nanoindentation size effect (ISE) all affect the microscopic deformation behavior of GH4169. The value of creep stress exponent, m, calculated from the creep experimental data is greater than 3, indicating that dislocation slip is dominant creep mechanism at room temperature.The nanoindentation simulation data based on the crystal elastic–plastic parameters determined by the trial-and-error method are in good agreement with the experimental data, demonstrating that the CPFE simulation results are credible. Therefore, this study can be used as a reference to investigate other alloy materials.

A hyperbolic model for mechanical behaviour of marginal soil-geosynthetic interface

Locally available marginal soils are of great interest to use as backfill material in geosynthetic reinforced soil structures due to their cost-effectiveness. The advanced stress–strain analysis of these structures necessitates the correct evaluation and the accurate description of marginal soil-geosynthetic interface behaviour. Therefore, the primary objectives of this study are numerical and analytical analysis of the soil-geosynthetic interface behaviour with application of a hyperbolic nonlinear elastic perfectly plastic constitutive model. In this investigation a series of large-scale direct shear tests was performed to evaluate the shear stress-displacement interface behaviour considering two types of marginal soils in contact with five types of geosynthetic materials in different soil moisture conditions. Accordingly, the hyperbolic model was used to simulate the soil-geosynthetic interface behaviour. Moreover, a three-dimensional finite element model of the direct shear test was developed using ABAQUS software and a user-defined subroutine was implemented to consider the hyperbolic interface model. The results indicated a very good agreement between the experimental data and the predicted finite element simulations of the direct shear tests and analytical solutions. Finally, a numerical simulation of a pullout test is presented in this paper with application of the hyperbolic interface model.

Crystal plasticity constitutive modeling of tensile, creep and cyclic deformation in single crystal Ni-based superalloys

A microstructure-sensitive crystal plasticity constitutive framework is proposed for simulating the tensile, cyclic, and creep response of single crystal Ni-based superalloys. In this framework, a non-Schmid model is used to account for the orientation- and temperature-dependent yield anisotropy. A model for the evolution of the slip system-level backstress is developed to simulate the cyclic response. The model accounts for the effect of microstructural features like precipitate volume fraction and size, and matrix channel width, on the associated hardening mechanisms. A physical model for creep deformation has also been developed that accounts for dislocation climb normal to the slip plane and the microstructure evolution due to rafting and isotropic coarsening of the precipitates. Application of the model is demonstrated by predicting the orientation- and temperature-dependent thermo-mechanical deformation of two single crystal superalloys, CMSX-4 and PWA-1484. The model is calibrated to the experimental tensile, cyclic and creep response for these alloys. Finally, the model is qualitatively validated by predicting the creep-fatigue interactions for different loading orientations and a range of thermo-mechanical conditions for CMSX-4 and PWA-1484.

Densification of a polymer glass under high-pressure shear flow

The properties of glasses can change significantly as they evolve toward equilibrium. Mechanical deformation appears to influence this physical aging process in conflicting ways, with experiments and simulations showing both effects associated with rejuvenation away from and overaging toward the equilibrium state. Here we report a significant densification effect in a polymer undergoing shear flow under high pressure. We used the high-aspect ratio geometry of the layer compression test to measure the uniform and homogeneous accumulation of plastic strain during isothermal confined compression of a deeply quenched film of polystyrene glass. Combined scanning transmission x-ray microscopy (STXM) and atomic force microscopy confirmed defect-free deformation leaving up to 1.2% residual densification under conditions of confined uniaxial strain. At higher peak strain, plastic shear flow extruded glass from below the compressing punch under conditions of a high background pressure. A further density increase of 2% was observed by STXM for a highly thinned residual thickness of polymer that nevertheless showed no signs of crystallization or internal strain localization. While the confined uniaxial densification can be accounted for by a simple elastic--plastic constitutive model, the high-pressure extrusion densification cannot.

Crystal plasticity theory coupled with meso-damage to predict the ratchetting behavior of nickel-based single crystal superalloy

Stress-controlled low cycle fatigue tests with different mean stress of a second-generation nickel-based single crystal superalloy DD6 with [001] orientation is investigated in the current study. The observation of fracture surface and microstructure show that although the phase structure does not change for different conditions, the damage failure mode changes for different mean stress. It is found that ratcheting strain exhibits a significant dependency on mean stress and microstructure damage. Ratcheting strain cannot be simulated only considering the evolution of back stress. To simulate the whole process evolution of ratcheting strain, crystal plasticity constitutive model coupled with a new anisotropic damage is developed. The simulated results showed that the anisotropic damage model could accurately predict the ratcheting strain for different mean stress. Different damage evolution modes are well identified by a damage index in the proposed model.

Bearing Capacity of UHPC-Filled High-Strength Elliptical Steel Tube Composite Columns with Encased High-Strength H-Shape Steel Subjected to Eccentrical Load

In order to investigate the bearing capacity of composite columns composed of ultra-high performance concrete, (UHPC)-filled high-strength elliptical steel tube with encased high-strength H-shape steel (HUCFESTCs) were subjected to eccentric load. Forty-four HUCFESTCs were designed with varying parameters: yield strength of the steel tube (fy), yield strength of the H-shape steel (fy1), concrete-cube compressive strength (fcu), steel tube thickness (t), eccentricity (e), slenderness ratio (λ), the section area of the H-shape steel (AHS), and long–short axis ratio (ψ). Based on a bilinear elastic–plastic constitutive model of steel that considered stress hardening and a nonlinear constitutive model of UHPC, 44 HUCFESTCs models were established by ABAQUS software. The influence of different parameters on the ultimate bearing capacity of the HUCFESTCs was analyzed. The whole process of HUCFESTCs under eccentric load was studied, and the typical failure modes of HUCFESTCs are described. The results show that the main failure mode of the HUCFESTCs subjected to eccentrical load is bulging outward of the steel tube, the buckling of the H-shape steel, and crushing of the concrete in the middle part of the column and the inner part of the H-shape steel. The stiffness of HUCFESTCs increases gradually with the increase in fy, t, and e. The ultimate eccentrical compression bearing capacity of HUCFESTCs improves gradually with increases in fy, t, fy1, AHS, ψ, and fcu, but it decreases gradually with increases in λ and e. By using statistical regression and introducing the reduction coefficient of eccentricity, the calculation formula for the eccentric bearing capacity of HUCFEST columns is developed, which can provide a basis for the application of HUCFESTCs in practical engineering.

Uniaxial Compression Failure and Size Effect of Recycled Aggregate Concrete Based on Meso-Simulation Analysis.

Recycled aggregate concrete (RAC) is a kind of five-phase composite material at the meso-level. It has a more complex interfacial transition zone (ITZ) than ordinary aggregate concrete (NAC), which is an important factor affecting the meso-failure of RAC. In addition, the maximum aggregate size plays an important role in the nonlinear mechanical behavior of concrete, which is closely related to the size effect. In this paper, a 2D random aggregate model of RAC is established based on meso-mechanics. The mechanical properties and failure modes of RAC under uniaxial compression are simulated using a plastic damage constitutive model. Through variable parameter analysis, the effects of the properties and thickness of ITZ on the elastic modulus and peak stress of RAC are studied, and the effect of the maximum aggregate size on the size effect of the compressive strength of RAC is discussed. The results show that the ITZ strength has a positive linear correlation with the peak stress and elastic modulus of RAC, while the ITZ thickness has a negative linear correlation with the peak stress and elastic modulus of RAC. Under the same specimen size (D = 100 mm, 150 mm, 200 mm, 300 mm), with an increase in the maximum aggregate size (dmax =20 mm, 25 mm, 30 mm, 35 mm), the nominal compressive strength of RAC increases by 6–10%, and the size effect is gradually weakened. When the maximum aggregate size reaches 30 mm, a decrease in the size effect tends to slow down compared with the maximum aggregate size of 20 mm. The classical Bažant size effect law is applicable to describe the compressive properties of RAC under different maximum aggregate sizes, and has a certain guiding significance for the prediction of the size effect of RAC in practical engineering.

Microstructure characterization and damage coupled constitutive modeling of nickel-based single-crystal alloy with different orientations

The mechanical properties of nickel-based single-crystal superalloys are sensitive to temperature and orientation. The present work focuses on the stress and strain responses of a second-generation nickel-based superalloy at different temperatures and with different orientations. Microstructure and dislocation arrangements are observed by scanning and transmission electron microscopy of samples after tensile testing. The results reveal the tensile fracture failure modes and dislocation morphologies (braids, cells, stacking faults, etc.) for different temperatures and orientations. Although the [001] sample shows higher yield strength than the other two orientations, the strain hardening was more significant at [111] orientation and stress softening at [011] orientation due to their different dislocation mechanisms. In addition, a new hardening model and damage evolution law are proposed and coupled with a crystal plastic constitutive model. Numerical analysis results show that the proposed constitutive model can accurately fit the full stress-strain response from tensile experiments for different temperatures and orientations.

A state-dependent hyperelastic-plastic constitutive model considering shear-induced particle breakage in granular soils

An elastic–plastic constitutive model considering particle breakage for simulation of crushable granular soils behavior is proposed. In the model, elastic strain rates are derived from a modified Helmholtz free energy function, and the influence of plastic shear work-induced particle breakage on the elastic properties of sand is taken into account as an elastic–plastic coupling mechanism. A stress ratio-driven mechanism is employed for calculation of the plastic strain rates. The proposed model is capable of tracking the evolution of the grain size distribution (GSD) due to shear-induced particle breakage. The evolving breakage index of Einav (2007) (J Mech Phys Solids 55(6):1274–1297, 2007) is interrelated to the plastic shear work to avoid overestimation of shear-induced particle breakage in loose sands. A direct comparison between the model simulations and laboratory data has been carried out for five series of drained/undrained monotonic and cyclic triaxial tests covering a wide range of initial states. For the sake of comparison, predicted behaviors from a hypoplastic constitutive model specially developed for crushable granular soils are also included. It is shown that the proposed constitutive model can provide reasonable predictions using a single set of parameters for each series of the laboratory data.

A plastic damage constitutive model for rock-like material focusing on the hydrostatic pressure induced damage and the interaction of tensile and shear damages under impact and blast loads

Although many mechanical responses of rock-like material subjected to dynamic loads can be simulated by commonly-used material models, it's still hard to accurately describe the interactive mechanism of tensile and shear damages caused by different kinds of loads. This paper presents a novel constitutive model with three smooth failure strength surfaces and three invariants. The new model can precisely and quantitatively capture the damage mechanisms of hydrostatic pressure based on test data and the interaction of the tensile and shear damages based on the Mohr-Coulomb criterion. Then, the new model is implemented into LS-DYNA, and a series of numerical validations, e.g. TXC, UUC, and UUT tests at single element, SHPB tests, rock blast test, and projectile penetration, are conducted. A satisfactory agreement between the numerical predictions and experimental data shows the suitability and accuracy of the present model for rock-like material under dynamic impact and blast loads.

A VFM-based identification method for the dynamic anisotropic plasticity of sheet metals

The anisotropic plasticity of sheet metals at high strain rates is a critical factor that can influence the fabrication and service safety of engineering parts under dynamic loading conditions. The characterization of dynamic anisotropic plasticity using conventional testing methods usually suffers from the limitations resulted from the homogeneous deformation state and one-dimensional wave propagation preconditions. In this work, a highly efficient approach is proposed for the simultaneous identification of the anisotropic yielding and hardening constitutive parameters at high strain rates based on the heterogeneous impact test and the virtual fields method. First, the identification framework that combines the selected anisotropic plasticity constitutive models and the principle of virtual work concerning the dynamic kinematics term is introduced. In order to validate the proposed identification algorithm, simulated virtual impact tests were performed to provide reference parameters and unpolluted inertial acceleration/strain/strain rate field data. These data were then processed to extract the target dynamic anisotropic parameters. The results show that using the double-notched impact configuration and the proposed identification algorithm the selected anisotropic yielding and hardening parameters can be reasonably identified from a single impact test, significantly simplifying the testing procedures compared to conventional dynamic testing methods. Also, the effects of different processing parameters and influential factors on the identification accuracy have been investigated. From the sensitivity studies, the preferred ranges of the processing parameters have been determined and the robustness of the proposed method within these verified.