Stress-strain Constitutive Equation Research Articles

Experimental investigation of mechanical properties of GGBS-FA-SF blended geopolymer concrete at elevated temperatures

Geopolymer has excellent mechanical properties at elevated temperatures, but geopolymer concrete may not be so because of the large difference in thermal properties between geopolymer and aggregate which could lead to substantial thermal stresses when they are in a high temperature environment. In this paper we present an experimental investigation on the mechanical properties of GGBS-FA-SF blended geopolymer concrete with and without steel fibres at elevated temperatures. The influences of exposure temperature, coarse aggregate and steel fibre on the failure mode, compressive strength, elastic modulus, peak strain, and ductility of the geopolymer mortar and geopolymer concrete are examined. Based on the experimentally obtained data, empirical temperature-dependent stress-strain constitutive equations are also proposed, which can be used for the fire safety analysis and design of geopolymer concrete with and without steel fibres.

Mechanical behavior and constitutive relationship of bond interface in steel plate-reinforced shield tunnels

In order to explore the mechanical properties and failure mechanism of the bond interface of steel plate reinforced shield tunnels, a series of uniaxial tensile and uniaxial shear experiments were conducted in this study. The impact of bond interface parameters on the mechanical properties of the reinforced interface was mainly analyzed, including the failure mode, ultimate bearing capacity, average bond strength, and stress-strain relationship of the bond interface. To enable numerical simulation of the mechanical behavior at the bond interface, a stress-strain constitutive relationship equation for the bond interface is established using the least squares method. The main conclusions are as follows: For steel plate-concrete interface bonded with epoxy resin, the shear resistance of the bond interface generally surpasses the tensile resistance under the same interface parameters. Tensile load predominate leads to the cohesive failure of the concrete while the interface layer remains undamaged. In contrast, shear load mainly results in the detachment between the steel plate and the interface layer. The ultimate bearing capacity and bond strength of the interface can be enhanced by decreasing the interface thickness or increasing the interface roughness. Moreover, an expansion bolt can further increase the mechanical property of the bond interface, and the improvement effect intensifies with higher expansion bolt grades. The stress–strain curve of the bond interface can be divided into three stages with elastic stage, softening stage and debond stage. The main difference of stress–strain curve under different bond interface parameters lies in the stage before the softening of the bond interface. The interface stress-strain curve is primarily influenced by the thickness of the bond interface and the grade of expansion bolts, whereas the roughness of the concrete surface has minimal effect.

Effect of steel fiber on the permeability of freeze-thaw damaged concrete under splitting tensile and compressive loads

This study investigated the effect of steel fibers on the permeability and mechanical properties of freeze-thaw damaged concrete under splitting tensile and compressive loads. A specially designed permeability apparatus is used to investigate the continuous permeability performance of steel fiber reinforced concrete (SFRC) subjected to loads. Results demonstrated that for the concrete without load, the addition of steel fibers exhibits a negative effect on the impermeability performance of the concrete matrix without freeze-thaw damage. The initial permeability of SFRC specimens is between 81.7 % and 180 % higher than that of NC specimens. The addition of steel fibers shows a positive effect on the impermeability of concrete subjected to freeze-thaw cycles. The permeability of SFRC under loads can be categorized into two stages. In the first stage, the concrete matrix is the main water channel. The addition of steel fiber can effectively increase the maximum radial deformation of the first stage and maintain low permeability of concrete in a large radial deformation range. In the second stage, concrete cracks are the main water channels. Both the addition of steel fibers and freeze-thaw cycles can reduce the permeability of the concrete in the second stage. Furthermore, under compressive load, with the increasing of stress level, the permeability of SFRC exhibits a slowly decreasing trend, this is followed by a significant increasing trend. The addition of steel fibers can maintain low permeability performance in a large stress level range, and as the steel fiber content increases, the permeability at peak load gradually decreases. The strain–permeability curves of SFRC under splitting tensile and compressive loads subjected to freeze-thaw cycles are investigated. The permeability of SFRC gradually increases with the increasing of the number of freeze-thaw cycles when the compressive strain exceeds 0.002. However, the opposite trend is observed under splitting tensile load. Notably, the reduction in concrete permeability due to the steel fibers is more significant under splitting tensile load than that under compressive load. Future work might integrate this research with stress-strain constitutive equations and finite element analysis. This will offer a foundational framework for engineering applications aimed at enhancing the permeability of steel fiber concrete under freeze-thaw conditions.

High-temperature compression deformation behavior of the high Nb-containing TiAl alloys doped with Sn

In this work, the high-temperature compression behavior of high Nb-containing TiAl–Sn alloys was investigated at deformed temperatures of 700 °C–1000 °C and strain rates of 0.002 s−1–0.2 s−1. The true stress-strain curves, microstructures, and constitutive equations of TiAl-xSn (x = 0, 0.5, 1, 1.5) alloys under different deformation conditions were systematically compared. Sn addition can increase the flow stress of TiAl alloys at the same deformation temperature, which is caused by the solid solution strengthening effect. At 800 °C/0.002 s−1, the peak flow stress of TiAl–1Sn alloy increases by 180 MPa compared with TiAl–0Sn alloy of 600 MPa. Below the peak stress, the flow stress increases with the increase of strain. Above the peak stress, the flow stress first decreases and then gradually trends to a steady state as the increase of deformation. Furthermore, the Sn addition decreases the brittle-ductile transition temperature of TiAl alloys. The TiAl-xSn (x = 0.5, 1, 1.5) alloys displays obvious flow softening behavior at 700 °C while TiAl–0Sn alloy fractures before reaching the target deformation. The relationship between of the flow stress, strain rate, and deformation temperature for TiAl–0Sn and TiAl–1Sn alloys is suitable for the hyperbolic sinusoidal equation. The dominant softening mechanism of hot deformation for TiAl-xSn (x = 0, 1) alloys is dynamic recrystallization (DRX). The activation energies Q of hot deformation for TiAl–0Sn and TiAl–1Sn alloys are 311 kJ mol−1 and 429 kJ mol−1 at condition of 700–1000 °C/0.002–0.2 s−1, indicating that the TiAl–1Sn alloy exhibits a better stability under the same application condition.

Nonlinear shear characteristics of frozen loess-concrete interface.

Under the different temperature environment, the precast pile-soil interface characteristics has an important impact on the safety and long-term stability for pile foundation. A large precast pile-soil shear experimental device is used to carry out the direct shear test of concrete-loess interface with different moisture contents under different freezing temperatures. The variation laws of shear strength parameters are revealed with influencing factors, and the shear mechanism of interface is discussed. The stress-strain constitutive equation of interface is proposed, and the shear strength criterion is established with considering the effects of temperature and moisture content on cohesion and internal friction angle. The results show the curve of shear stress and shear displacement can be divided into three stages: elastic deformation stage, plastic deformation stage and sliding failure stage, which macroscopically reflects the shear failure mechanism of the frozen soil-concrete interface. The shear strength of the interface is affected by the test temperature, sample moisture content and normal stress. The lower the test temperature, the greater the shear strength of the interface; With the increase of normal stress, the shear strength of interface increases; With the increase of moisture content, the shear strength of the interface increases and then decreases. The relationship of shear stress and shear displacement of frozen soil-concrete interface can be well described by the piecewise combination of hyperbolic function and linear function.

Failure analysis from microcracks to a dominant crack in MEMS thin films using combined damage and fracture mechanics

Reliability issues in MEMS devices are generally rooted in the evolution of microdefects in materials. Although the failure occurs at the top level of the device (macroscopic function), the root cause of the functional failure can be traced back to the bottom level (material micro defects). Therefore, it is crucial to consider the influence of material damage in the stress–strain constitutive equations to calculate the magnitude of crack propagation force. In this paper, a combined method of damage and fracture is considered for calculating the stress of crack tip of MEMS thin films. To calculate the initiations and growths of microcracks, continuum damage mechanics (CDM) is used. Based on the CDM method, a relationship between material degradation and the increase of electrical resistance is established. Through the established computational methods, we can perform a calculation analysis on the failure of MEMS caused by cracks. A multiscale quantification result establishes pairwise connections between material degradation characterization (damage D), crack propagation (tip stress K), and macroscopic performance (resistance R). This article provides a valuable theoretical basis for investigating the failure mechanisms of MEMS.

Study on the Compressive Stress–Strain Curve and Performance of Low-Slump Polypropylene Fiber Concrete after High Temperature

This study aims to investigate the effect of high temperature on the mechanical properties of low-slump polypropylene fiber (PPF) concrete, and tests the tensile and compressive properties of 204 groups of low-slump PPF concrete with eight different dosages and four different lengths at normal temperature and after high temperature. The results of the compressive test showed that PPF can significantly improve the mechanical properties of concrete after high temperature when the fiber content is small, and the compressive strength of low collapse polypropylene fiber concrete after high temperature showed a tendency to rise and then fall at the same temperature with an increase of the fiber admixture. When the fiber content was 0.5 kg/m3, the compressive strengths of 3 mm, 9 mm, 15 mm and 19 mm reached their maxima, which were 9.65%, 11.33%, 7.90% and 2.87% higher than that of ordinary concrete, respectively. With an increase in fiber length, the effect of PPF on the compressive strength of concrete is not obvious. PPF at high admixture further increases the pore and air content in concrete, which decreases the compactness of the concrete, thus leading to a decrease in the compressive strength of the concrete. When the temperature was 800 °C and the fiber admixture was 5.0 kg/m3, the compressive strength of PPF concrete with different lengths reduced by 17.83%, 17.27%, 22.59% and 23.92%, respectively, compared to normal concrete. In addition, according to the results, the optimal combinations of strength at room temperature and after high temperature were 3 mm fiber length and 1.0 kg/m3 dosing and 9 mm fiber length and 0.5 kg/m3 dosing, respectively, which increased the compressive and tensile strengths by 17.15% and 25.72% at room temperature and by at least 6% and 20% after high temperature, compared to the concrete without fiber dosing. Moreover, the stress–strain constitutive equations of PPF concrete at normal temperature and after high temperature were established, which can be used for finite element simulation and related mechanical analysis of PPF after high temperature.

Dynamic recrystallization and precipitation behavior of a novel Sc, Zr alloyed Al-Zn-Mg-Cu alloy during hot deformation

The hot deformation behavior of a novel Sc, Zr alloyed Al-Zn-Mg-Cu alloy was explored in the isothermal hot compression test with a temperature range of 300–500 °C and a strain rate of 0.001–10 s −1 . The stress-strain curve, constitutive equation, and processing map were integrated to evaluate the flow behavior and hot workability of the studied alloy. Besides, the relationship between dynamic recrystallization and precipitation behavior and the Zener-Hollomon (Z) parameter during hot deformation was deeply explored. As lnZ decreased, the dislocation density decreased, while the misorientation angle increased. Meanwhile, with the decrease of lnZ, the amount of low-angle grain boundaries and medium-low-angle grain boundaries decreased. Moreover, dynamic recovery is the dominant dynamic softening mechanism, while three different dynamic recrystallization (DRX) mechanisms were the main DRX mechanisms at different lnZ values. Discontinuous DRX dominated at high lnZ value (lnZ ≥33.33); Continuous DRX (CDRX) dominated at middle lnZ value (23.4 < lnZ < 33.33); Geometric DRX dominated at low lnZ value (lnZ ≤23.44). Meanwhile, increasing lnZ value is conducive to precipitation behavior. The intragranular precipitates and grain boundary precipitates are identified as the phase containing Al, Fe, Mn, and Si, the equilibrium η phase containing Cu and Al 3 (Sc, Zr) particles. • The following constitutive equation of the experimental alloy is constructed: ɛ ̇ =1.110 × 10 13 [sinh (0.0160σ)] 5.170 exp(16981/RT). • The microstructure relied on the lnZ value during hot compression. • DDRX, CDRX, and GDRX were the dominant DRX processes at high, medium and low lnZ values respectively. • Increasing lnZ value is conducive to precipitation behavior.

Coupled hydro-mechanical analysis of compacted bentonite behaviour during hydration

This study analyses the response of compacted bentonites upon hydration based on a coupled hydro-mechanical elasto-plastic framework. As an alternative to multi-porosity interpretation, the framework was selected based on the experimental evidence of adsorbed water behaviour in bentonites and the volumetric response at saturated states, apparently independent of its initial state. Based on these premises, a water retention model was formulated using an explicit distinction between adsorbed water and free water, enabling the postulation of the water properties and behaviour depending on its state. In order to effectively account for the transition between unsaturated to saturated state, that can occur in a wide range of suctions, the stress–strain constitutive equations are written in terms of an effective stress and degree of saturation framework. The mathematical formulation was implemented in a finite element code and used to simulate and interpret the behaviour of MX-80 bentonite compacted in different forms during hydration for several stress paths, including loading and unloading cycles after saturation. A good agreement of the model with experimental results was obtained using a consistent set of parameters describing the saturated state behaviour. The typical non-linear swelling pressure development was interpreted through the two-way coupling between the water retention behaviour and elasto-plastic compressibility. The possible high suctions at saturated states explain the swelling potential after full hydration. Overall, this study offers new perspectives on the role of hydro-mechanical interactions in bentonite behaviour upon hydration.

Spatiotemporal linear stability of viscoelastic free shear flows: Nonaffine response regime

We provide a detailed comparison of the two-dimensional, temporal, and spatiotemporal linearized analyses of the viscoelastic free shear flows (inhomogeneous flows with mean velocity gradients that develop in the absence of boundaries) in the limit of low to moderate Reynolds number and elasticity number obeying four different types of stress–strain constitutive equations: Oldroyd-B, upper convected Maxwell, Johnson–Segalman (JS), and linear Phan-Thien–Tanner (PTT). The resulting fourth-order Orr–Sommerfeld equation is transformed into a set of six auxiliary equations that are numerically integrated via the compound matrix method. The temporal stability analysis suggests (a) elastic stabilization at higher values of elasticity number {shown previously in the dilute regime [Sircar and Bansal, “Spatiotemporal linear stability of viscoelastic free shear flows: Dilute regime,” Phys. Fluids 31, 084104 (2019)]} and (b) a nonmonotonic instability pattern at low to intermediate values of elasticity number for the JS as well as the PTT model. To comprehend the effect of elasticity, Reynolds number, and viscosity on the temporal stability curves of the PTT model, we consider a fourth parameter, the centerline shear rate, ζc. The “JS behavior” is recovered below a critical value of ζc, and above this critical value, the PTT base stresses (relative to the JS model) are attenuated thereby explaining the stabilizing influence of elasticity. The Briggs idea of analytic continuation is deployed to classify regions of temporal stability and absolute and convective instabilities, as well as evanescent modes, and the results are compared with previously conducted experiments for Newtonian as well as viscoelastic flows past a cylinder. The phase diagrams reveal the two familiar regions of inertial turbulence modified by elasticity and elastic turbulence as well as (a recently substantiated) region of elastoinertial turbulence and the unfamiliar temporally stable region for intermediate values of Reynolds and elasticity number.

Study on Mechanical Properties of PET Fiber-Reinforced Coal Gangue Fine Aggregate Concrete

In recent years, with the rapid development of the construction industry, the demand for natural river sand has become increasingly prominent. Development of alternatives to river sand has become an interesting direction for concrete research. In this paper, coal gangue was proposed to replace part of the river sand to produce coal gangue fine aggregate concrete, while waste polyethene terephthalate (PET) bottles were used as raw materials to make PET fibers to improve the mechanical properties of coal gangue fine aggregate concrete. There were two parts of the test conducted. In the first part, the compressive strength of the gangue fine aggregate concrete cube, splitting tensile strength, axial compressive strength, and static elastic modulus were studied when the substitution rate of coal gangue increased from 0% to 50%. Referring to the equation of the full stress-strain curve of plain concrete, the stress-strain constitutive equation of coal gangue fine aggregate concrete was analyzed and studied. By comparing with plain concrete, it was found that the coal gangue concrete with a replacement rate of 50% had higher compressive strength and tensile strength, but its brittleness was significantly greater than that of plain concrete in the later stage. In the second part, by studying the effect of different PET fiber content on the mechanical properties of coal gangue fine aggregate concrete with a replacement rate of 50%, it was found that when the addition of PET fiber was 0.1% and 0.3%, not only were compressive strength, splitting tensile strength, static elastic modulus, and flexural strength of the gangue fine aggregate concrete effectively improved but also the brittleness of concrete can be significantly reduced. The study found that after adding 0.3% PET fiber, the coal gangue fine aggregate concrete with a replacement rate of 50% has better mechanical properties and less brittleness.

Effect of freeze-thaw cycles on the mechanical properties and constitutive model of saline soil

The freeze-thaw cycle is one of the most common natural physical processes in cold regions and will significantly affect the deformation characteristics of saline soil. To study the mechanical properties and constitutive relationship of saline soil under freeze-thaw cycles, in this paper, a series of freeze-thaw cycle tests and consolidated-drained (CD) triaxial tests were conducted on remodeled saline soil in the Qian'an area of western Jilin, China. Based on the elliptic-parabolic double yield surface constitutive model, a modified model considering the effects of freeze-thaw cycles is established. The results show that the specimen exhibits a strain-hardening stress-strain relationship, and the volumetric strain during shearing exhibits a shear-shrinkage characteristic overall. As the number of freeze-thaw cycles increases, the volumetric strain gradually increases, and the shear strength gradually decreases. As the confining pressure increases, the volumetric strain gradually increases. Then, the elliptic function and parabolic function are selected to describe the volume yield surface and the shear yield surface on the p-q plane respectively. By introducing the correlation flow rule, the functional relationship between the deviating stress increment and the axial strain increment and volumetric strain increment is derived. Based on the results of the triaxial test, the variation in the model parameters with the number of freeze-thaw cycles was determined. The results show that as the number of freeze-thaw cycles increases, c, φ, h, K, n, M1, M2, and a show a decreasing rule, while t shows a gradually increasing rule, and all factors can use logistic function to fit the regression relationship between the model parameters and the number of freeze-thaw cycles. The expression of the model parameters with the number of freeze-thaw cycles as a factor is substituted into the stress-strain increment constitutive equation, and a modified double yield surface model considering the effects of freeze-thaw cycles is established. The calculated values of the model are basically consistent with the measured values. This shows that the double yield surface constitutive model can be applied to saline soil.

Experimental study and constitutive modeling on viscoelastic-plastic mechanical properties of ETFE foils subjected to uniaxial monotonic tension at various strain rates

Apart from the well-known excellent basic properties, the mechanical behaviors of ETFE (ethylene tetrafluoroethylene) foils are more fundamental for the refined design and analysis of ETFE membrane structures. This paper investigates the nonlinear mechanical properties of ETFE foils at varying strain rates (0.01 to 10 min−1) through a combination of experiments and modeling. First, the uniaxial tensile tests at nine loading strain rates were completed on ETFE foil dumbbell specimens. The analysis of experimental results shows that ETFE foils exhibit the rate-sensitive and viscoelastic-plastic behaviors with two distinct yield points. Next, to simulate the nonlinearity of ETFE foils at the former deformation stage, the stress–strain constitutive equations at certain strain rates are established based on the generalized Maxwell model comprising one basic spring element and several basic Maxwell models. After identifying the model parameters, it is observed that the proposed model can accurately describe the viscoelastic-plastic mechanical behaviors of ETFE foils since good agreement is gained from the comparison between experimental results and model predictions. Finally, through establishing the relationship functions between model parameters and strain rates, the continuum constitutive model can be extended to predict the rate-dependent viscoelastic-plastic behaviors of ETFE foils. The experimental observations and constitutive model concerning the rate-dependent mechanical properties of ETFE foils would be helpful for the refined design, optimization and analysis of ETFE membrane structures.

Effects of matrix-fracture interaction and creep deformation on permeability evolution of deep coal

A new model considering effects of matrix-fracture interaction and creep deformation on permeability of deep coal is established under the condition of triaxial stress state. An internal swelling coefficient is defined to characterize the degree of matrix-fracture interaction. The internal swelling coefficient, reflecting contribution of matrix swelling deformation by gas adsorption to the change of bulk volume and fracture volume, is introduced to a classical stress-strain constitutive equation. Moreover, the proposed permeability model is validated by experimental data-based permeability estimated by the fractional derivative transient pulse method and the nonlinear least square method is used to determine the model parameters. It is indicated that the permeability decreases gradually in the primary and secondary creep stage, consistent with the physical process in which the initial fracture and pores are gradually compacted during the creep process. In addition, it is found that with the decrease of pore pressure, the proposed permeability model appears to be better than the existed various classical models in term of description of the evolution trend of permeability. The effects of creep deformation and internal swelling coefficient on the permeability model are discussed, indicating that under the condition of constant effective volumetric strain, a small volume of the internal swelling coefficient makes a leading role of the effective volumetric strain in permeability evolution, and a large volume of the internal swelling coefficient leads to a domination role of the adsorption swelling strain increment in permeability evolution of deep coal.

A novel creep-fatigue stiffness degradation model for composite materials

In this paper, a novel creep-fatigue stiffness degradation model for composite materials is introduced. The model proposed a nonlinear stress–strain constitutive equation in the form of a function of time and cycles simultaneously. The presented model consists of a linear elastic component, which is degraded as a function of cycles, and a nonlinear time-dependent component, which combines both time- and cycle-dependent nature of fatigue phenomena in an integrated formulation. The model predictions are validated by the experimental data taken from the literature for short fiber E-glass/polyamide6,6 and [±45]2s HTA(12 K)/6376 epoxy. It is shown that the model has the capability to predict the stress–strain curve after cycles of loading, taking into account the time-dependent response of composites. It is shown that under high stress levels, the development of fatigue mean strain is dominated by fatigue damages; under lower stress levels, however, the mean strain is mostly controlled by time-dependent viscoelastic strains.

Mechanical properties of the concrete containing ferronickel slag and blast furnace slag powder

This study investigated the mechanical properties of concrete of strength grade C30 and C35, containing different content (10%–50%) of a composite admixture of ferronickel slag and blast furnace slag powder (referred to as F-S powder and F-S concrete hereafter, respectively). The mechanical properties include axial compressive strength, elastic modulus, Poisson’s ratio, splitting tensile strength, and the compressive stress-strain relationship. The difference in mechanical properties between F-S concrete and conventional concrete was analyzed. Test results indicated that the positive correlation of conventional concrete between the axial compressive strength, elastic modulus, splitting tensile strength, and cubic compressive strength was applicable to F-S concrete irresponsible of the specific F-S powder content. Both Poisson’s ratio and the failure mode under compression for F-S concrete were identical to those of conventional concrete. The shape characteristics and fitting parameters of the stress-strain curve were mainly related to F-S concrete strength grade but had little connection with the specific F-S powder content. Furthermore, based on tested data, the stress-strain constitutive equations were established for F-S concrete, which provides a reference for the test analysis of large specimens and corresponding engineering application.

Effects of coarse Al2CuLi phase on the hot deformation behavior of Al–Li alloy

The effects of coarse T1 phase (Al2CuLi), produced by homogenization, on the hot deformation behavior of Al–Li alloy was studied using uniaxial compression. Stress-strain curves, constitutive equations and processing maps were established, and the microstructure was observed by EBSD, SEM and TEM. The homogenized alloy with coarse T1 phase presents lower flow stresses and significantly lower deformation activation energy than the solution treated alloy. Besides, the homogenized alloy exhibits the same hot-working region with the solution treated alloy, and possesses lower power dissipation efficiencies. The EBSD investigation confirms the formation of massive recrystallized grains in the homogenized alloy at 340–460 °C, revealing the coarse T1 phase can promote dynamic recrystallization through particles stimulated nucleation. In contrast, the solution treated alloy is softened dominantly via dynamic recovery at 340–490 °C. This work not only merits the beneficial effects of the coarse T1 phase but also suggests the feasibility of obtaining accelerated recrystallization kinetic and good workability during hot working of Al–Li alloys.

Mechanical Analysis of TRB Transition Region

In this paper, the mechanical properties of Tailor Rolled Blank (TRB) transition region was investigated By establishing a true stress-strain constitutive model of the TRB transition region. Firstly, the stress-strain curve obtained by uniaxial tensile test of 1mm, 2mm thick plates is subjected to regression analysis. Based on Ludwig equation, the true stress-strain constitutive equations of 1mm and 2mm thick plates were obtained. Then, The true stress-strain constitutive equation of TRB transition region was established by interpolation method combined with 1mm, 2mm thick plate constitutive equation, volume invariance theory and Von-Mises equivalent strain.Finally, the accuracy of the model is verified by simulation and experimental comparison. The results show: A new constitutive model of TRB was established, which is well responsed to the mechanical properties of the transition region.

Indentation hardness, plasticity and initial creep properties of nanosilver sintered joint

The nanoindentation test was conducted in this paper to investigate the indentation hardness, plasticity and initial creep properties of pressure sintered nanosilver joint at various test temperatures. The effects of strain rate on the indentation hardness were first investigated. Then yield stress of nanosilver sintered joint was studied in various pressures sintered joints and the corresponding plastic stress-strain constitutive equations were gained. The maximum indentation depth of nanosilver sintered joint was obviously affected by the test temperature and sintering pressure. The indentation hardness of nanosilver sintered joint decreased with increasing test temperature from 140 to 200°C, which can be attributed to the increased amount of thermal vacancies at high temperatures. However, the indentation modulus exhibited decrease trend as the temperature increased. It is suggested that the distance between adjacent atoms was enlarged at elevated temperatures and furtherly resulted in the decrease of indentation modulus. In addition, the increased sintering pressure from 5 to 30 MPa improved the indentation hardness and modulus of sintered joint. The initial creep was observed in nanosilver sintered joint at temperatures ranged from 140 to 200°C. The increase of sintering pressure improved the resistance to creep of nanosilver sintered joint.

Analytical and numerical investigations of the collapse of blood vessels with nonlinear wall material embedded in nonlinear soft tissues

In this paper, shapes of nonlinear blood vessels, surrounded by nonlinear soft tissues, and buckled due to radial pressure are solved for analytically and numerically. The blood flow rates through the bucked shapes are then computed numerically. A Fung-type isotropic hyperelastic stress-strain constitutive equation is used to establish a nonlinear mathematical model for radial buckling of blood vessels. The surrounding tissues are modeled as non-linear springs. Novel formulas for critical buckling pressures are derived analytically from the bifurcation analysis. This analysis shows that the nonlinearity of vessel’s wall increases the critical buckling pressure. A numerical differential correction scheme is introduced to solve for post-buckling shapes. And the corresponding blood flow rates are provided before touching of the collapsed walls. The blood flow rate through a one-point wall-touching case is also provided. Numerical results show that both vessel’s wall and soft tissues nonlinearities increase, locally, the flow rate through the buckled blood vessels. More importantly, a nonlinear relation between blood flow rate and the soft tissue spring constants is found.