Uniaxial Stress-strain Relation Research Articles

A Novel Method to Describe Large-Range Stress-Strain Relations of Elastic-Plastic Materials Based on Energy Equivalence Principle.

Due to the unique structure of tensile sheet specimens with a circular hole (CHS specimen), a novel method is proposed to predict the large-range uniaxial stress-strain relations of elastic-plastic materials analytically. Based on the energy equivalence principle, a load-displacement semi-analytical model of the CHS specimen is proposed. Subsequently, a semi-analytical model of constitutive parameters of elastic-plastic materials is developed by virtue of the load-displacement relation of the CHS specimen, and the prediction of the material's stress-strain relations is obtained. To examine the validity of the models, numerical simulations with a series of materials were performed. The results demonstrated that the dimensionless load-displacement curves and stress-strain relations obtained using the proposed models correspond well with those obtained using finite element analysis. In addition, tensile tests were performed on the CHS specimen for four elastic-plastic materials (T225 titanium alloy, 6061 aluminum alloy, Q345 steel, and 3Cr13 steel), and the validity of the models is also verified by the experimental results. Compared with the conventional uniaxial tensile tests, the stress-strain relation of elastic-plastic material captured by the novel method corresponds to a larger strain, which is of great importance for engineering design and safety assessment.

Models for uniaxial stress-strain relationship and thermal properties of fine recycled aggregate concrete exposed to elevated temperatures

The models for the stress-strain relationship under elevated temperatures and thermal properties of recycled aggregate concrete (RAC) are essential in the fire resistance design of RAC structures, while no such models are available for RAC made with fine recycled aggregate (FRA). To establish the above models, 33 RAC prisms with three FRA replacement levels (0%, 50%, and 100%) under five temperatures (20 °C, 200 °C, 400 °C, 600 °C, and 800 °C) were tested for the uniaxial compressive stress-strain relationship; Meanwhile, thermal properties (including the specific heat, thermal conductivity, and thermal expansion) of these concrete mixes under a temperature range of 20–800 °C were also tested. A prediction model for the RAC stress-strain relationship under elevated temperatures was proposed by extending the model for RAC under normal temperature. Based on the test data, models for the thermal properties of RAC with FRA were also established. Results showed that the FRA does not change the shear failure mode of concrete, while decreased the peak stress by up to 33% and elastic modulus by up to 31%; The influence of FRA keeps similar when temperature varies from 20 °C to 800 °C; the specific heat increases by 16% on average while the thermal conductivity decreases by 8%–15% with the FRA replacement ratio increased to 100%; the thermal expansion of concrete under temperature higher than 500 °C decreased by up to 22% when using 100% FRA; the proposed models have good accuracy for the stress-strain relationship and thermal properties of RAC.

On Flexure-Shear Interaction in Fibre Model for the Analysis of RC Section

This paper investigates the effects of flexure-shear interaction on the force-deformation response of RC section. The analysis is performed using an improved version of fibre section model to consider the interaction of shear force. The model uses a supplementary shear strain field, in addition to the ‘plane-section’ hypothesis, for section kinematics. The concrete is modelled using a bi-axial stress-strain model based on a rotating, smeared-crack model with equivalent uniaxial stress-strain relation in principal directions. The confining effect of stirrups is considered by using Mander model. The reinforcing bars are modelled using a uniaxial stress-strain relation. The use of bi-axial model allow the flexure-shear interaction to reflect at the material point. The fibre section model is used to analyse an RC section to study the moment-curvature and shear force-shear strain response for increasing levels of shear forces and bending moments. The results shows that the moment-curvature and shear force-shear strain diagrams are significantly influenced by the presence of large shear force and bending moment respectively.

Uniaxial compressive stress–strain relationship of mixed recycled aggregate concrete

• This study aims to investigate the uniaxial stress–strain relation of mixed recycled aggregate concrete (MRC). • The stress–strain relation of MRC cannot be well predicted by existing models. • The proposed model can effectively predict the stress–strain relation of MRC. The purpose of this paper is to study the uniaxial stress–strain relationship of mixed recycled concrete (MRC), which composed of brick recycled aggregate (BRA), concrete recycled aggregate (CRA) and natural aggregate (NA). MRC with various replacement ratio of MRA and various contents of BRA was studied under uniaxial compression. The stress–strain characteristic and toughness of MRC were studied firstly, and the results exhibited that the peak stress and elastic modulus decreased with the increase of MRA replacement ratio and BRA content, while the opposite trend was observed for the ultimate and peak strain. Then, the test stress–strain data were compared with existing stress–strain models of natural or recycled concrete. The comparison results indicate that the existing models cannot be well predicted the stress–strain relationship of MRC. According to the test results in this study, the stress–strain constitutive model of MRC was established by modifying of the shape parameters for the CRA concrete (RAC) constitutive model, which can well predict the stress–strain relationship of MRC.

Different influence of replacement ratio of recycled aggregate on uniaxial stress-strain relationship for recycled concrete with different concrete strengths

This paper experimentally investigated whether the replacement ratio of recycled coarse aggregate (r) has different influence on stress–strain relation of concrete with different strength grades. The studied concrete specimens had two strength grades of C30 and C50, each with r ratios of 0, 25%, 50%, 75% and 100%. Test results showed that r ratio had significantly different influence on compressive strength, peak strain (the strain at peak stress, ε0) and deformability (the ratio between ultimate strain and peak strain) of concrete with different concrete strengths. To account for such different influences, a stress–strain model of recycled aggregate concrete (RAC) was proposed by modifying key parameters in existing model of natural aggregate concrete (NAC), where r ratio and concrete strength were the main parameters. The proposed model was benchmarked against available test results of 58 RAC specimens.

Experimental study and theoretical modeling for the compressive stress-strain relationship of multi-scale hybrid fiber-reinforced SHCC

In order to better match the multi-level structural characteristics and multi-scale fracture process of cementitious composite, multi-scale hybrid fiber-reinforced strain hardening cementitious composite (MsHySHCC) was designed by adding hooked steel fiber and calcium carbonate (CaCO3) whisker into conventional polyvinyl alcohol (PVA) fiber-reinforced SHCC. Compressive properties of PVA-SHCC and MsHySHCC were evaluated experimentally. The results indicate that the designed MsHySHCC had a better compressive performance than that of PVA-SHCC. Moderately partially substituted PVA fibers by steela fiber and CaCO3 whisker enhanced the compressive parameters, however, further substitution of PVA fibers by increasing the content of CaCO3 whisker didn’t bring a higher promotion. Two kinds of semi-theoretical compression constitutive models were developed from the perspective of damage mechanics theory and geometrical mathematical description, respectively. It was found that both of the proposed models can be applied to predict the uniaxial compressive stress-strain relationships of PVA-SHCC and MsHySHCCs.

Anisotropic mechanical response, high negative thermal expansion, and outstanding dynamical stability of biphenylene monolayer revealed by machine-learning interatomic potentials

Recently, the two-dimensional (2D) biphenylene network with a specific arrangement of four-, six-, and eight-membered carbon rings has been fabricated over the gold surface via a two-step polymerization technique (Science 372(2021), 852). Inspired by the aforementioned experimental advance and exciting physics of full-carbon 2D lattices, for the first time, we herein employ machine-learning interatomic potentials (MLIPs) to explore the mechanical properties, failure behavior, dynamical stability, and thermal expansion of the biphenylene monolayer. The remarkable accuracy of the developed MLIP-based models is concluded by comparing the predicted direction-dependent uniaxial stress-strain relations and failure mechanism of the biphenylene monolayer with those obtained by density functional theory simulations. Analysis of phonon dispersion relations reveals an outstanding dynamical stability of the biphenylene monolayer. Similarly to graphene, the biphenylene network also exhibits a negative thermal expansion, but with around twice the value of graphene at room temperature. We also studied the temperature effect on the tensile strength and failure strain of the biphenylene monolayer. The presented results provide a useful vision concerning the thermo-mechanical properties of the 2D biphenylene network.

Earthquake damage estimation of the Koyna concrete gravity dam using explicit GFVM model considering fluid–structure interaction

In this paper, an Explicit Galerkin Finite Volume Method (E-GFVM) is employed to estimate damage paths in concrete structures through the definition of nonlinear behavior of concrete. Furthermore, to verify the accuracy and efficiency of the present method, the E-GFVM outcomes are compared with the Explicit Finite Element Method (E-FEM) which is a well-known numerical method for investigating numerous solid mechanics problems. Due to the essence of explicit methods, the method in question uses a few matrix operations in nonlinear analysis, so it diminishes computation workloads for time-dependent cases with small time-step. The reason for using E-GFVM was its simplicity and high accuracy in estimating stresses and displacements for the analysis of Computational Solid Mechanics (CSM) problems. Furthermore, one important feature of FVM is its local conservation properties which guarantee the global conservation of variables that provides more stability, particularly in dealing with complex problems. To model the nonlinear behavior of concrete, the two equivalent uniaxial stress–strain relations, taking into consideration the softening and hardening behavior in both compression and tension, are implemented in the proposed numerical method. In other words, the bi-axial concrete behavior is defined by applying the idea of current strength in principal stress space. Therefore, this study aims to introduce a new numerical method that in addition to reducing time consumption, can maintain the accuracy of the results. For reaching this purpose, first, the nonlinear behavior of concrete is modeled and two different specimens are placed under pure pressure and tension loads. The results calculated by the E-GFVM are compared with other literature. After verification of the nonlinear behavior of concrete using E-GFVM, the ability of the proposed method for analysis of a real-world case under time-dependent conditions, namely Koyna concrete gravity dam which experienced a destructive earthquake in 1967, is tested, considering the impacts of dam–reservoir interaction. Then, this problem with the same conditions is modeled and analyzed using the E-FEM. The results show that, in spite of good harmony between two utilized methods for estimating the damage on the body of Koyna dam, the CPU time of the E-GFVM became about 3 times less than the E-FEM.

Mechanical properties of calcium silicate hydrate under uniaxial and biaxial strain conditions: a molecular dynamics study.

Calcium silicate hydrate (C-S-H) is the main hydration product of cementitious materials, often experiencing complex stress conditions in practical applications. Therefore, reactive molecular dynamics methods were used to investigate the mechanical response of the atomistic structure of C-S-H under various uniaxial and biaxial strain conditions. The results of uniaxial simulations show that C-S-H exhibits mechanical anisotropy and tension-compression asymmetry due to its layered atomistic structure. By fitting the stress-strain data, a stress-strain relationship that accurately represents the elastoplasticity of C-S-H was developed. The biaxial yield surface obtained from biaxial simulations was ellipsoidal, again reflecting the anisotropy and asymmetry of C-S-H. Four yield criteria (von Mises, Drucker-Prager, Hill, and Liu-Huang-Stout) were further investigated, and it was found that the Liu-Huang-Stout criterion can effectively capture all the major features of the yield surface. During a uniaxial tensile process in the z direction, multi-crack propagation was observed, which was aggravated and weakened by y direction tensile and compressive strains respectively. The results of chemical bond analyses revealed that, for different strain conditions, the CaW-OS and CaS-OS bonds play different roles in resisting deformation.

Uniaxial Stress-Strain Relationship and Thermal Properties of Concrete with Fine Recycled Aggregate Under Elevated Temperatures

Uniaxial Stress-Strain Relationship and Thermal Properties of Concrete with Fine Recycled Aggregate Under Elevated Temperatures

The Uniaxial Stress-Strain Relationship of Hyperelastic Material Models of Rubber Cracks in the Platens of Papermaking Machines Based on Nonlinear Strain and Stress Measurements with the Finite Element Method.

Finite element analysis is extensively used in the design of rubber products. Rubber products can suffer from large amounts of distortion under working conditions as they are nonlinearly elastic, isotropic, and incompressible materials. Working conditions can vary over a large distortion range, and relate directly to different distortion modes. Hyperelastic material models can describe the observed material behaviour. The goal of this investigation was to understand the stress and relegation fields around the tips of cracks in nearly incompressible, isotropic, hyperelastic accouterments, to directly reveal the uniaxial stress–strain relationship of hyperelastic soft accouterments. Numerical and factual trials showed that measurements of the stress–strain relationship could duly estimate values of nonlinear strain and stress for the neo-Hookean, Yeoh, and Arruda–Boyce hyperelastic material models. Numerical models were constructed using the finite element method. It was found that results concerning strains of 0–20% yielded curvatures that were nearly identical for both the neo-Hookean, and Arruda–Boyce models. We could also see that from the beginning of the test (0–5% strain), the curves produced from our experimental results, alongside those of the neo-Hookean and Arruda–Boyce models were identical. However, the experiment’s curves, alongside those of the Yeoh model, converged at a certain point (30% strain for Pieces No. 1 and 2, and 32% for Piece No. 3). The results showed that these finite element simulations were qualitatively in agreement with the actual experiments. We could also see that the Yeoh models performed better than the neo-Hookean model, and that the neo-Hookean model performed better than the Arruda–Boyce model.

Study on Micro-Structure and Tensile Mechanical Properties of Dissimilar Metal Weld Joint Connecting Steam Generator Nozzle and Safe-End

The safe-end of a steam generator (SG) nozzle dissimilar metal weld (DMW) for pressurized water reactors (PWRs) is the weakest point of failure which is crucial for the safe operation of a nuclear power station. Related to materials micro-structures, a uniaxial stress–strain relationship is the basic input parameter for nuclear power plant design, safety evaluation, and life management. In this paper, the micro-structure and tensile mechanical properties of a DMW of a European pressurized water reactor (EPR) were studied. Vickers hardness tester, optical microscope, and electron back scatter diffraction were used to analyze the micro-structure of the DMW joint. In addition, the residual strain of the DMW joint base material, heat-affected zone, weld metal, and fusion boundary region were studied. Based on digital image correlation (DIC) technology, tensile mechanical properties of the DMW joint were obtained. The results show that an accurate tensile stress–strain relationship of dissimilar metal welded joints can be obtained by using the DIC technique, the weld is the relatively weak link, and the residual strain is concentrated in the heat-affected zone. This study provides valuable engineering information regarding nuclear power plant design, in-service performance testing, and structural analysis and evaluation of welds containing defects.

Modelling catastrophic degradation of flexural-dominated RC columns at ultimate displacements based on fibre beam-column model

Catastrophic degradation of the mechanical strength of reinforced concrete (RC) columns at ultimate displacements is one of the critical factors for the seismic collapse of structures. Accurately predicting this degradation is critical to assess the seismic collapse capacity of structures. However, the mechanism and theory about the degradation of RC columns are insufficient at present. This study is devoted to revealing the cause of catastrophic degradation and establishing an updated fibre beam-column model for predicting the catastrophic degradation of RC columns at ultimate displacements. First, the de-confinement effect of kernel concrete at ultimate loading displacements is described based on experimental observation and the stress state analysis of the confined concrete. The kernel concrete in the confined zone is shifted from confinement state to de-confinement state during the loading cycles. Next, an updated fibre beam-column model is proposed where a uniaxial stress-strain relation considering the de-confinement effect is introduced to represent the behaviour of kernel concrete during the loading cycles. The validity of the proposed model is confirmed by comparing experimental results and model results. Compared with the classical fibre beam-column model, the detailed discussions about the load-displacement response, moment-curvature, and strain distribution during loading cycles showed that the updated model achieves reasonable prediction of catastrophic degradation of RC columns by capturing the state shift of kernel concrete. At last, the applicability of the proposed model is discussed. Existing models including Panagiotakos and Fardis model, Eurocode 8 model, and ASCE 41 model are used as comparative models to evaluate the model accuracy of predicting the ultimate drift ratio of RC columns.

Modeling of stress-strain relation of cement-treated sand under compression

Abstract This research work has been conducted to model the uniaxial stress-strain compressive behavior of cement-treated sand and its post-peak softening area. The cylindrical specimens were produced by using limestone powder, sand and high early strength cement. The mixtures were made by using different ratios of water to cement with fixed ratio of limestone powder to cement and cement to sand. The stress-strain behavior in post-peak zone of cement-treated is adjusted with introduction of compression softening factor. Uniaxial compressive stress-strain relationships after amending the Japanese Society of Civil Engineers model are proposed. Finite element analysis shows that the suggested model estimates well the compressive behavior of cement-treated sand.

Calculation model for uniaxial stress–strain relationship of wood plastic composites

AbstractThis paper presents an investigation on the mechanical properties of wood plastic composites under uniaxial stress. Experimental studies of test pieces with tensile and compressive load were performed. Failure modes, stress–strain relationship, and other crucial parameters were recorded and analyzed. The results indicated that brittle failure was the typical failure mode of the tensile test specimens, however, shear‐compression failure and wedge double shear failure were commonly observed for samples under compressive load. Mechanical properties of WPC are better than those of timber according to different national standards. Different analytical models were proposed for evaluating the stress–strain response of the specimens. The fitting between the experimental results and calculations was good.

Spatial asymmetric/symmetric buckling of Mises truss with out-of-plane lateral linear spring

This paper deals with the equilibrium problem of the Mises truss, with out-of-plane lateral linear spring, analyzed as a three DOF system. It is shown that, as a consequence of the geometry of the structure, the system can undergo three buckling modes which are asymmetric in-plane buckling, symmetric out-of-plane buckling and asymmetric out-of-plane buckling. The analysis takes into account the influence of local buckling and yielding of bars on global instabilities.The Green–Lagrange strain is adopted as the strain measure and the theorem of the stationarity of the total potential energy is employed to derive the nonlinear equilibrium equations. The tangent stiffness matrix is derived and, through the solution of the eigenvalue problem, the stability of the equilibrium solutions is investigated. Analytical formulations for the instabilities of the truss are presented.For the numerical approach, a linear elastic constitutive model is assumed for the uniaxial stress–strain relationship of the truss bars. To take into account the yielding of bar elements, a perfect elastoplastic model is assumed. A computer program was developed in Fortran to perform comparisons with the results of the theoretical formulation. Finally, the numerical results obtained demonstrate the accuracy and effectiveness of the presented truss element.The main novelty of this paper is the introduction of an additional DOF in the Mises truss which allows to study a more complex scenario of equilibrium paths and instabilities.

Effect of fly ash on mechanical properties and microstructure of cellulose fiber-reinforced concrete under sulfate dry–wet cycle attack

In this work, the deterioration characteristics of the mechanical properties of cellulose fiber-reinforced concrete (CFRC) under sulfate dry–wet cycles were studied. The influence of 10%, 20%, and 30% cement replacement with fly ash (FA) on the durability of CFRC was also considered. After 180 dry–wet cycles, the CFRC soaked in sodium sulfate solution with 5% concentration was tested. The mechanical properties were evaluated, including mass loss, the uniaxial stress–strain relationship, and the splitting tensile strength. Results show that FA has a negative effect on the initial mechanical properties of CFRC. The sulfate resistance durability of CFRC is greatly affected by the FA content. Compared with CFRC without FA, low-volume FA can significantly improve the mechanical properties. However, 30% FA has a negative impact on the durability of CFRC. In addition, the pore information parameters obtained by nuclear magnetic resonance indicate that macropores have a negative effect on the sulfate resistance durability of CFRC, whereas micropores and mesopores are favorable. In contrast, 20% FA can refine the pores and improve the strength of the matrix, thus improving the durability of CFRC.

Numerical simulations of blast responses for SFRC slabs using an orthotropic model

This paper proposes a material model of steel fiber reinforced concrete (SFRC) subjected to dynamic loadings on the basis of an orthotropic concrete model. The effects of strain rate and fiber reinforcement are taken into account in the material model of SFRC from the uniaxial stress-strain relation to the triaxial strength envelope. The compressive and tensile strains as failure criteria are developed by reflecting the dynamic material properties, respectively. In particular, the post-cracking response according to steel fiber addition is investigated to improve the accuracy of the blast analysis for SFRC structures, and the proposed model is implemented as a user defined material model in LS-DYNA. The numerical results are compared with the experimental data in terms of damage pattern and average diameter of the damaged area for RC and SFRC slabs under explosions. The plastic based concrete models of K&C and CSCM are additionally compared to predict the behavior of SFRC structures. Furthermore, parametric studies are conducted with the proposed model to investigate the effects of reinforcement spacing and steel fiber on improving the structural resistance of SFRC slabs.

Finite Element Analysis on Steel-Concrete Composite Beams Considering the Bond-Slip Effect on the Interface

In order to accurately simulate the bond-slip performance of steel-concrete composite beams, a trilinear stress-strain relation model was adopted to simulate the mechanical properties of steel. A uniaxial stress-strain relation curve was used to study the nonlinear mechanical behaviors of concrete. The resisting shear effects of studs and concrete in the bonding area were equivalent to nonlinear springs. Based on the energy principle, a calculation method of the interfacial bond stiffness of steel-concrete composite beams was proposed and the interfacial bond-slip constitutive relation of steel-concrete composite beams was given. Based on it, the three-dimensional finite element analysis model of steel-concrete composite beams was established by the finite element analysis software ANSYS, and the numerical simulations of existing push-out tests of composite beams were performed. By comparison, it can be seen that the results from finite element analysis in this paper are close to the experimental ones. It indicated that the finite element analysis model can accurately simulate the bond-slip action of the interface, and this model can be applied to the numerical calculation and analysis of steel-concrete composite beams.

A strain rate dependent nonlinear elastic orthotropic model for SFRC structures

A strain rate dependent orthotropic model for steel fiber reinforced concrete (SFRC) structures subjected to impact or blast loads is proposed in this paper. Based on the previously introduced orthotropic model for plain concrete, an improved strain rate dependent material model for SFRC is developed to account for the effect derived from the addition of steel fibers in the concrete matrix and to cope with the multiaxial strain rate dependent behavior of SFRC. In addition to verification of the constructed multiaxial strength envelope of SFRC through correlations with experimental data, improved failure strains in the uniaxial stress-strain relation are also introduced to minimize the mesh size dependency in the numerical results. Finally, the proposed orthotropic model is incorporated into LS-DYNA as a user defined material model. Numerical analyses were performed for experiments of RC and SFRC slabs under projectile impact and blast loading, and the obtained results show that the addition of the steel fibers provides a considerable improvement in the structural resistance and the proposed model effectively simulates the structural responses of SFRC structures while minimizing the mesh size dependency in the numerical results.