Effective Stress-strain Relations Research Articles

Rate sensitive plasticity-based damage model for concrete under dynamic loading

In this manuscript, a rate-sensitive plasticity-based damage model for concrete subjected to dynamic loads is presented. The developed rate-sensitive damage model incorporates the key experimental evidence related to strain rate and damage rate. With increasing strain rates, the model is able to predict a decrease in the rate of damage evolution due to artificial stiffening effects together with a final higher level of damage. The major contribution of the work is to include the effect of damage rate, strain rate and also to consider all the physical mechanisms of damage. This is achieved by using a power law model to relate the rate of damage to the equivalent plastic strain rate. The damage parameter considers hydrostatic, tension and compression damage. Such a damage definition helps in the prediction of pulverized damage due to a loss in cohesive strength at increased hydrostatic stress, shear-induced compressive damage and tensile microcracking. Strong volumetric deformation of the material that includes hydrostatic and compaction damage is also considered in the model. Because hydrostatic damage accounts for the reduction in stiffness and compaction damage accounts for the increase in stiffness under pure compressive loading. A strain rate-dependent failure surface is considered and with increasing strain rate there is an increase in the size of the failure surface which is capped at an upper limiting value. The incremental effective stress-strain relationship is defined in terms of rate of damage, accumulated damage and viscosity parameters reflecting the inherent inertial, thermal and viscous mechanisms respectively. The stress-strain relationship in the model also accounts for stress reversals that occur due to interference of an incident and reflected wave, by including a Heaviside function. The developed model is implemented in LS-DYNA using vectorized UMAT. Verification, validation and parameterization of the developed model have been made through several numerical analyses.

Modeling of cyclically loaded square thin-walled CSFT columns stiffened by diagonal ribs using OpenSees

Among various proposed stiffening forms, the diagonal binding ribs, made of thin-walled steel plates with circular holes and welded to the steel tube, were found to particularly effective in improve the cyclic-bending and cyclic-shear behavior of square thin-walled concrete-filled steel tubular (CFST) columns. Although the mechanical behavior can be obtained from the experiments, numerical models are still needed to expand the range of investigation beyond what was tested physically and to facilitate the practical design. A 3D model using shell and solid elements is able to explicitly show the influence of different parameters, and simulate the details including the holes in diagonal ribs and the contact interaction between different parts. However, such analyses are relatively complicated, time-consuming, and are susceptible to numerical issues that cause lack of convergence. By contrast, a 2D model using fiber-based beam–column elements is far more efficient thus allowing for a wider range of investigation. In this work, the fiber models of flexure-dominated diagonal ribs stiffened square thin-walled concrete-filled steel tubular (DSCFST) columns were firstly developed in OpenSees and validated based on the effective stress–strain relationships of steel tubes and moment–rotation curves of RC bases. The fiber models of shear-dominated DSCFST columns were further developed by defining the nonlinear shear force–deformation relationships at the section level. These models were verified by the test results, and then the effect of the deformable RC base, tube local buckling, shear effect, and types of beam–column elements was analyzed in detail. Based on extensive parametric analyses, the effective stress–strain relationships applicable to various square thin-walled steel tubes stiffened by diagonal ribs and infilled concrete were derived, and the simplified shear force–deformation relationships were proposed. These results facilitate understanding of the behavior of DSCFST columns and lay a foundation for further system-level analysis.

Fiber-based model for simulating strength and stiffness deterioration of high-strength steel beams

This paper focuses on the behavior, modeling, and evaluation of high-strength steel beams used as girders in moment resisting frame systems (MRFs). The results of the evaluation have led to the development and calibration of effective (phenomenological) stress–strain curves and fiber-based finite element approaches for modeling the behavior of high-strength steel beams. The key parameters influencing the cyclic behavior of high-strength steel beams are: (i) shape/geometric details, (ii) flange and web slenderness ratios, (iii) material stress–strain behavior, and (iv) fracture/damage failure criteria. This paper summarizes prior experimental results on the cyclic behavior of high-strength steel beams and develops 3D finite element models to simulate their behavior. The models are developed cognizant of the parameters (i)–(iv) listed above. The models are validated against experimental data and then used to conduct parametric studies to evaluate the effects of material and geometric parameters on the cyclic behavior and ductility of high-strength steel beams. The developed effective stress–strain relationships hold the key to developing potential design methods based on allowable strain criteria and/or continuous strength methods recently developed by other researchers.

Effect of Wrapping Force on the Effective Elastic Behavior of Packed Cylinders

Abstract When cylinders are packed and wrapped by the bands around the surface, the effective elastic behavior in the cross section of the assembly, which is of significance to its stability and integrity, can be controlled by the wrapping force in the band. The wrapping force is transferred to the cylinders through the Hertz contact between each pair of neighboring cylinders, which is validated by the experiments. The Singum model is introduced to study the mechanical behaviors of the packed cylinders with two-dimensional (2D) packing lattices, in which an inner cylinder is simulated by a continuum particle of Singum and the inter-cylinder force is governed by the Hertz contact model so as to derive the effective stress-strain relationship. The wrapping force will produce configurational forces given a displacement variation, which significantly changes the effective stiffness of the packed cylinders. The hexagonal packing exhibits isotropic elasticity whereas the square packing is anisotropic. The efficacy of our model is demonstrated by comparing the closed form elasticity against the numerical simulation and the previous models. The explicit form of elasticity can be used for packing design and quality control of cable construction and installation.

Multiscale 3D finite element analysis of aluminum matrix composites with nanoµ hybrid inclusions

The present work proposed a multiscale finite element (FE) analytical approach to investigate the mechanical behavior of elasto-plastic aluminum matrix composites reinforced with nano-micro hybrid inclusions. To study the effect of microstructural effects, 3D representative volume elements (RVEs) of nano- and micro-scales are established, where the nano-RVE considers the aluminum matrix with carbon nanotubes (CNTs)-reinforcement whose homogenization is treated as the equivalent matrix (EM) phase for micro-RVE with SiC particles. The FE-based ABAQUS simulation is employed to recover the local stress distributions within RVE of either scales, and the corresponding effective stress–strain relationship, damage and failure behavior are calculated and predicted. Results generated from the present simulations are validated against the experimental measurement of CNTs/SiC/Al composites and good agreement is generally obtained. What’s more, several microstructural parameters are tested on the composites’ effective behavior, including the elaso-plastic constitutive relation and damage response of aluminum matrix, the elastic-brittle failure mechanical behavior of the micro-scale SiC particles. We also consider the traction-separation mechanical behavior at the SiC-Al interface. It is demonstrated that the present numerical method is suitable to study the comprehensive behavior of composites with hybrid inclusions.

Comprehensive Analysis of Stress-strain Relationships for Recycled Aggregate Concrete

There is a growing demand of suitable substitute materials of concrete ingredients especially fine and coarse aggregates in order to achieve sustainable development in the era of rapid urbanisation. Therefore, the concrete making process by utilisation of aggregates that recycled from construction and demolition (C&D) debris has emerged as a primary objective for many government agencies. Consequently, the utilisation of recycled aggregate concrete (RAC) in structural applications become essential aspect. However, RAC can be employed in structural applications only if effective stress-strain relationship is available. The stress-strain models developed for natural aggregate concrete (NAC) are not fully suitable for RAC. Hence, the selection of good model which has precise prediction capacity plays a crucial role. Moreover, the stress-strain models provide the basis for the analysis and modern design procedures especially in FEA packages. In the present study, the stress-strain models for RAC have been selected from the literature and critically reviewed in order to evaluate their predictive efficacy. The test samples in the form of measured stress-strain relations–hips derived from literature have been compared with the predictions of each selected model. Besides the comparison of measured and predicted stress-strain profiles, the output of selected models in terms of normalized toughness and ductility index was assessed. The consistency of output of models are further evaluated by employing statistical tools such as coefficient of variance and root mean square error. The outcomes of the model in the form of polynomial expression was relatively more accurate to that of other counterparts.

Modeling the cyclic behavior of composite plate shear walls/concrete filled (C-PSW/ CF)

This paper summarizes experimental results and discusses the development and benchmarking of detailed 3D finite element method (FEM) models for large-scale planar composite plate shear wall/concrete filled (C-PSW/CF) specimens subjected to constant axial force and cyclic lateral loading. The results from the benchmarked 3D FEM models are used to develop phenomenological effective stress-strain relationships for the steel plates and concrete infill of the tested C-PSW/CF specimens. The proposed effective stress-strain relationships implicitly account for various aspects governing behavior such as: (i) steel yielding and hardening in tension, (ii) steel yielding and local buckling in compression; (iii) concrete cracking in tension, (iv) concrete inelasticity in compression, and (v) composite interaction resulting in biaxial stresses in the tension steel and confinement of the concrete in compression. These proposed effective stress-strain relationships are used in simpler 2D FEM models and fiber-based FEM models along with calibrated cyclic hysteresis rules and damage models to simulate the cyclic behavior of C-PSW/CF specimens and compare with experimental results. These simpler 2D FEM models and fiber-based FEM models are recommended for simulating the seismic response of planar C-PSW/CF walls. The detailed 3D FEM models are recommended for conducting additional parametric studies investigating the structural behavior and design of planar C-PSW/CF walls.

Anisotropic Damage Model of Soft and Hard Composite Rock and Experimental Verification

Abstract In order to derive the anisotropic damage model of soft and hard composite rock and to study the influence law of damage on the deterioration degree of material mechanical parameters in different directions, the transversely isotropic elastic constitutive equation was corrected by two sets of damage variables in the local coordinate system of bedding plane. By coordinate transformation, an effective stress–strain relationship in the global coordinate system was formed. The rationality of the damage model was verified by the results of uniaxial compression test. The results show that (1) The damage of soft and hard composite rock has transversely isotropic characteristics. (2) The change trend of damage variables varying with strain is closely related to each stage of the damage process; at the same strain level, the damage variables increase first and then decrease with the increase of the bedding plane’s dip angle (0°~90°) and have a good corresponding relation with the damage model. (3) The strength and deformation parameters calculated by the damage model of soft and hard composite rock can reflect the test results well and have obvious anisotropy. The calculated curves before failure are also consistent with the experimental results. (4) Through the damage model, the stress–strain relationship at each dip angle can be determined by the two sets of deformation parameters for the bedding plane’s dip angles of 0° and 90°. Because the damage deterioration effect during loading process is considered, the mechanical behavior of the specimens after failure can be predicted, which has some guiding significance for the experimental research, theoretical calculation, and engineering construction based on soft and hard composite rock.

Simplified Nonlinear Simulation of Rectangular Concrete-Filled Steel Tubular Columns

In detailed three-dimensional (3D) finite-element modeling, two-dimensional and/or 3D elements are widely used because of their high accuracy and ease of use despite the high computational cost. In contrast, simplified modeling based on fiber beam element (FBE) formulation is preferred for developing macro models to simulate structural frames due to its simplicity and computational efficiency. As for the FBE simulation of concrete-filled steel tubular (CFST) columns, its accuracy largely depends on the input steel and concrete material models, which should implicitly consider the material nonlinearity and interaction between the steel and concrete components. The authors have previously developed a FBE model for circular CFST columns, and this paper is a continuation of the previous work. In this paper, uniaxial effective stress–strain relationships are developed for the steel and concrete materials in rectangular CFST columns based on rigorous analysis of data generated from 3D finite-element modeling of stub columns. Thus, the material models have implicitly considered the effects of yielding and local buckling of the steel tube and passive confinement to the concrete. Meanwhile, the size effect is also considered in the concrete model. The accuracy of the proposed material models is verified against a database of rectangular CFST stub columns covering a wide range of material and geometric parameters. The developed material models are further used to simulate rectangular CFST slender columns and beam-columns, and a reasonably good agreement is achieved between the experimental and predicted load–deformation curves.

Development of constitutive equations identifying methodology for steels for plastic moulding by compression testing

The influence of frictional coefficient on the cylindrical plastic steel specimen under compression is analyzed. The considered methodology allows determining effective stress dependence on effective strains by compression testing. It is found that the reason for the barrel-shaped plastic steel compressive test specimen form is only friction between contact surfaces of tested specimens and supports. The standard methodology suggests using various friction reduction technologies to reduce the friction effect on stress-strain diagram determination. These can be special lubricants or changes in the shape of the specimen bearing surfaces. But all approaches to the issue with stress-strain diagram determination are unable to be implemented under temperatures above 300°C due to not being able to use lubricants. The plastic steel compression process experiment behind the model with varying only friction coefficients is suggested in order to determine the effect of friction coefficient on the shape of a compressed specimen. This approach makes it possible to search into the effect of friction coefficient and compare the results with a full-scale experiment. The plastic steel compression diagram, having been obtained from a full-scale experiment, permits to determine effective stress-strain relationship, which, in turn, allows calculating the constitutive equation coefficients of the material model necessary for carrying out simulations of plastic steels deformation under both room indoor temperature and temperatures up to 900°C, including the plastic deformation influence. The proposed methodology also provides the possibility to obtain an effective stress-strain relationship and varying the friction coefficient between the specimen end surface and the supports being exposed to elevated temperatures, which cannot be treated by standard test methods. It is shown that the initial data for obtaining the effective stress-strain relationship are the difference in specimen diameters and the force-displacement diagram.

Compression tests of octagonal concrete-filled thin-walled tube columns

The compression behavior of octagonal concrete-filled thin-walled tube (OCFT) columns was investigated. Eight OCFT columns with different tube sections were tested under monotonic compressive loading. The tests showed that the thin-walled tubes underwent elastic or inelastic local buckling, and the slenderness ratio (or width-to-thickness ratio) and section shape of the tubes significantly affected their buckling modes. Despite such local buckling, the load-deformation behavior of the OCFT columns all was highly ductile, due to confinement to the infilled concrete. The design strengths of AISC 360-16 agreed well with the test strengths. In this study, effective stress–strain relationships of the tube and infilled concrete were proposed to account for the local buckling and confinement. The maximum strength and post-buckling behavior were estimated through the strain-compatibility analysis, and the results were compared with the tests.

An efficient multiscale surrogate modelling framework for composite materials considering progressive damage based on artificial neural networks

Modelling of the progressive damage behaviour of large-scale composite structures presents a significant challenge in terms of computational cost. This is due to the detailed description in finite element (FE) models for the materials, i.e., with each unidirectional layer defined as required by the applicability of laminate failure criteria, and numerous iterations required to capture the highly nonlinear behaviour after damage initiation. In this work, we propose a method to accelerate the nonlinear FE analysis by using a pre-computed surrogate model which acts as a general material database representing the nonlinear effective stress-strain relationship and the possible failure information. Developed using artificial neural network algorithms, the framework is separated into an offline training phase and an online application phase. The surrogate model is first trained with a vast number of sampling data obtained from mesoscale unit cell models offline, and then used for online predictions on a macroscale FE model. The prediction accuracy of the surrogate model was examined by comparing the results with conventional FE modelling and good agreement was observed. The presented method enables progressive damage analysis of composite structures with significant savings of the online computational cost. Lastly, the surrogate model is only based on material designs and is reusable for other structures with the same material.

Fibre beam element models for nonlinear analysis of concentrically loaded circular CFT columns considering the size effect

The fibre beam element (FBE) method has been widely used to investigate the behaviors of concrete-filled steel tube (CFT) columns for its high efficiency and accuracy. The existing models were generally developed or calibrated by using specimens with relatively small size, in which the size effects were ignored or poorly incorporated. Additionally, most existing FBE models focused on CFT stub columns. In this paper, a new FBE model for nonlinear analysis of concentrically loaded stub and slender columns was proposed, in which the size effects on the effective stress-strain relationships of steel tube and core concrete were well incorporated. The proposed FBE models were then used to develop an ultimate strength model for the design of both stub and slender columns. A total of 1029 specimens assembled from 72 previous studies were used to verify the proposed models. The results suggested that the proposed FBE model performs quite well for both small- and large- size CFT stub columns and predicts the behaviors of slender columns with reasonable accuracy. Moreover, the ultimate strength model developed based on the proposed FBE models was found to make satisfying prediction of test results.

Effective stress-strain relationship for grouted sleeve connection: Modeling and experimental verification

This paper describes the development of an effective stress-strain relationship model for grouted sleeve connections. The transverse pressure influence has been calibrated by using the local bond stress-slip experiment including the effect of the initial construction error of the reinforcing bar. Then, the proposed effective stress-strain model was presented by solving the governing equation of the bond stress-slip behavior for the long-bonded grouted sleeve connection. The grouted sleeve connection can be equivalent to a reinforcing bar with a higher elastic modulus and yielding strength. The equivalent elastic modulus decreases with the increase in the initial construction error, and can be calculated by using the proposed model. The experiments on the long-bonded grouted sleeve connection and prefabricated concrete piers were carried out to verify the proposed model. The tested effective stress-strain relationship of the grouted sleeve connection, the maximum slip of the reinforcing bar embedded in this connection, and the strain distribution of the sleeve coupler were successfully predicted. Moreover, the performance of prefabricated concrete piers under cyclic loading was successfully simulated by using the proposed model.

Stability design of single angle member using effective stress-strain method

Single angle members are widely used in transmission line towers due to light weight and easy installation. However, angle members may experience complex behaviors such as flexural, flexural-torsional or lateral-torsional buckling due to unsymmetrical section and eccentric loading. The current design practice is generally based on the effective length method, in which semi-empirical formulas should be used to account for the actual end conditions and member initial imperfections. In contrast, advanced beam-column elements or finite shell elements should be used when using second-order direct analysis method without the need of effective length assumption. Direct model of the failure modes (i.e. local and global failure modes) of angle members is still a challenging task. This paper firstly investigates the sensitivity of the flexural-torsional buckling of eccentrically loaded members compared to the assumed flexural buckling mode about the principal minor axis which is implemented in most of available beam-column elements. Moreover, an effective stress-strain relationship representing the typical failure modes and initial imperfections, which has been calibrated by extensive finite element analysis and experimental results, is developed for the direct analysis of steel structures made of angle sections without use of the effective length method. The proposed method is so simple that it can be incorporated into any conventional beam-column elements to implement the direct analysis of angle structures. The examples show that the proposed method is sufficiently accurate and therefore it can be employed in the practical design of angle structures.

Direct analysis method for noncompact and slender concrete-filled steel tube members

The concrete-filled steel tube (CFT) members made of noncompact/slender sections, experiencing complex behaviors such as local buckling, concrete confinement and slippage between the components, have been increasingly used in the practical engineering structures. However, few reliable design methods were available until the latest AISC 360-16, in which two types of methods are firstly provided. The first one uses P-M interaction curves with reduced or effective stiffness method while the second adopts effective stress-strain relationships based on the fiber section approach. The beneficial effects due to the restraint of steel tube have been implicitly considered in both of them. The first method approximately accounts for the member stiffness and employs the effective length method for stability design while the second method does not fully fulfill the requirements of direct analysis specified in AISC 360-16 as lack of consideration of slenderness effects and initial geometrical imperfections. This paper proposes a flexibility-based beam-column with member imperfections and incorporates the effective stress-strain models into the fiber section for direct analysis of noncompact/slender CFT members. The gradual change of member stiffness and the actual section capacity can be accurately reflected in the analysis process and as a result, the traditional effective length method is no longer required in the proposed direct analysis. It is also found that the initial imperfection of L/1000 is insufficient for CFT members. Some useful recommendations in line with AISC 360-16 are provided for practical design. Several experimental tests demonstrate the accuracy and robustness of the proposed method.

Morphology and micromechanics of liquid rubber toughened epoxies

Abstract In the present work, a diglycidyl ether of bisphenol A (DGEBA)-based epoxy resin was modified with the help of a liquid rubber (LR) obtained from the pyrolysis of rubber. Tensile tests on samples of rubber modified epoxy resins (REs) containing varying rubber volume fractions (RVF) were conducted to obtain their tensile properties. Fractographic analysis of fractured samples using field emission scanning electron microscopy (FESEM) revealed the presence of phase separated rubber zones characterized by microvoids, distributed uniformly in the epoxy domain. Young’s modulus and yield strength of REs were observed to drop with RVF. A three-dimensional (3D) finite element model was employed to predict the elastic properties and stress distributions in REs. Various stress distributions and their dependence on the properties of rubber were examined in detail through the model. The effect of rubber properties on bulk elastic properties of the REs were also studied. Lastly, the effective stress-strain relationship was predicted with the help of an elastic-plastic analysis. Predicted results showed coherence with experimental results.

Nonlinear effects of micro-cracks on long-wavelength symmetric Lamb waves

For an elastic medium containing a homogeneous distribution of micro-cracks, an effective one-dimensional stress-strain relation has been determined with finite element simulations. In addition to flat micro-cracks, voids were considered that contain a Hertzian contact, which represents an example for micro-cracks with internal structure. The orientation of both types of micro-cracks was fully aligned or, for flat micro-cracks, totally random. For micro-cracks with Hertzian contacts, the case of random orientation was treated in an approximate way. The two types of defects were found to give rise to different degrees of non-analytic behavior of the effective stress-strain relation, which governs the nonlinear propagation of symmetric (S0) Lamb waves in the long-wavelength limit. The presence of flat micro-cracks causes even harmonics to grow linearly with propagation distance with amplitudes proportional to the amplitude of the fundamental wave, and gives rise to a static strain. The presence of the second type of defects leads to a linear growth of all harmonics with amplitudes proportional to the power 3/2 of the fundamental amplitude, and to a strain-dependent velocity shift. Simple expressions are given for the growth rates of higher harmonics of S0 Lamb waves in terms of the parameters occurring in the effective stress-strain relation. They have partly been determined quantitatively with the help of the FEM results for different micro-crack concentrations.

High-Strength Rectangular CFT Members: Database, Modeling, and Design of Short Columns

AISC 360-16 (the current AISC Specification) does not endorse the use of high-strength materials (Fy≥525 MPa and fc′≥70 MPa) for concrete-filled steel tube (CFT) columns because of a lack of adequate research and comprehensive design equations. This paper makes a contribution toward addressing this gap and proposes effective stress-strain relationships and design equations for high-strength rectangular CFT members using a three-step method. The first step consists of compiling the experimental database of high-strength rectangular CFT column tests in the literature and evaluating the possibility of extending the current AISC 360-16 design equations to high-strength rectangular CFT short columns. The second step consists of developing and benchmarking detailed three-dimensional (3D) nonlinear finite-element models for predicting the behavior of high-strength CFT columns from the database. The benchmarked models are then used to perform comprehensive parametric studies to (1) address gaps in the database and (2) develop effective stress-strain relationships for modeling the steel tube and concrete infill of high-strength rectangular CFT members, while indirectly accounting for the effects of confinement, yielding, and local buckling. The third step consists of using these effective stress-strain relationships and the enhanced database to propose a new design approach (including equations) for high-strength rectangular CFT short columns. Finally, a reliability analysis is performed to establish a resistance (strength reduction) factor (ϕ) to be used with the proposed design equations.

Modeling of high-strength composite special moment frames (C-SMFs) for seismic analysis

This paper presents the development and validation of a fiber-based numerical modeling approach that can be used to evaluate the seismic response of high-strength composite special moment frames (C-SMFs). The high-strength C-SFMs consist of: (i) CFT columns made from high-strength materials (Fy≥525MPa and f'c≥70MPa), (ii) wide flange (WF) steel beams, and (iii) double split-tee (DST) beam-to-column connections. The fiber-based numerical modeling approach uses fiber-based finite elements to model CFT columns and WF steel beams, and uses spring elements to model DST connections. Consequently, the accuracy of the fiber-based numerical modeling approach depends fundamentally on: (i) uniaxial effective stress-strain (σ-ε) relationships assumed for the fiber-based finite elements modeling high-strength CFT columns and WF beams, and (ii) effective force-displacement (P-∆) relationships assumed for the spring elements modeling DST connections. This paper develops these critical input relationships using a three-step approach. The first step consists of developing and benchmarking detailed 3D nonlinear FEM models of high-strength CFT columns, WF steel beams, and DST connections. The second step consists of conducting parametric studies using the benchmarked FEM models. The third step consists of developing effective σ-ε and P-∆ relationships using results from the parametric studies, and validating these relationships using results from experimental studies. The fiber-based numerical modeling approach for C-SMFs is validated by using them to predict the lateral force-deformation response of C-SMFs subassemblies. The benchmarked numerical modeling approach is recommended for conducting nonlinear time-history analysis of C-SMFs and evaluating their seismic response.