A novel relationship between elastic modulus and void ratio associated with principal stress for coral calcareous sand

Elastic moduli,e.g.shear modulus G and bulk modulus K,are important parameters of geotechnical materials,which are not only the indices for the evaluation of the deformation ability of soils but also the important basic parameters for the development of the constitutive models of geotechnical materials.In this study,a series of triaxial loading-unloading-reloading shear tests and isotropic loading-unloadingreloading tests are conducted to study several typical mechanical properties of coral calcareous sand(CCS),and the void ratio evolution during loading,unloading and reloading.The test results show that the stress-strain curves during multiple unloading processes are almost parallel,and their slopes are much greater than the deformation modulus at the initial stage of loading.The relationship between the confining pressure and the volumetric strain can be defined approximately by a hyperbolic equation under the condition of monotonic loading of confining pressure.Under the condition of confining pressure unloading,the evolution of void ratio is linear in the e-lnp0 plane,and these lines are a series of almost parallel lines if there are multiple processes of unloading.Based on the experimental results,it is found that the modified Hardin formulae for the elastic modulus estimation have a significant deviation from the tested values for CCS.Based on the experimental results,it is proposed that the elastic modulus of soils should be determined by the intersection line of two spatial surfaces in the G/K-e-p’/pa space(pa:atmosphere pressure).“Ye formulation”is further proposed for the estimation of the elastic modulus of CCS.This new estimation formulation for soil elastic modulus would provide a new method to accurately describe the mechanical behavior of granular soils.

Effects of Initial Defects on Effective Elastic Modulus of Concrete with Mesostructure

An exquisite mesostructure model was presented to predict the effective elastic modulus of concrete,in which concrete is realized as a four-phase composite material consisting of coarse aggregates,mortar matrix,interfacial transition zone(ITZ),and initial defects.With the three-dimensional(3D)finite element(FE)simulation,the highly heterogeneous composite elastic behavior of concrete was modeled,and the predicted results were compared with theoretical estimations for validation.Monte Carlo(MC)simulations were performed with the proposed mesostructure model to investigate the various factors of initial defects influencing the elastic modulus of concrete,such as the shape and concentration(pore volume fraction or crack density)of microspores and microcracks.It is found that the effective elastic modulus of concrete decreases with the increase of initial defects concentration,while the distribution and shape characteristics also exert certain influences due to the stress concentration caused by irregular inclusion shape.

Impacts of artificial dams on terrestrial water storage changes and the Earth's elastic load response during 1950-2016: A case study of medium and large reservoirs in Chinese mainland

The construction of dams for intercepting and storing water has altered surface water distributions, landsea water exchanges, and the load response of the solid Earth. The lack of accurate estimation of reservoir properties through the land surface and hydrological models can lead to water storage simulation and extraction errors. This impact is particularly evident in many artificial reservoirs in China. The study aims to comprehensively assess the spatiotemporal distribution and trends of water storage in medium and large reservoirs(MLRs) in Chinese mainland during 1950-2016, and to investigate the gravity,displacement, and strain effects induced by the reservoir mass concentration using the load elasticity theory. In addition, the impoundment contributions of MLRs to the relative sea level changes were assessed using a sea-level equation. The results show impoundment increases in the MLRs during1950-2016, particularly in the Yangtze River(Changjiang) and southern basins, causing significant elastic load effects in the surrounding areas of the reservoirs and increasing the relative sea level in China's offshore. However, long-term groundwater estimation trends are overestimated and underestimated in the Yangtze River and southwestern basins, respectively, due to the neglect of the MLRs impacts or the uncertainty of the hydrological model's output(e.g., soil moisture, etc.). The construction of MLRs may reduce the water mass input from land to the ocean, thus slowing global sea level rise. The results of the impact of human activities on the regional water cycle provide important references and data support for improving the integration of hydrological models, evaluating Earth's viscoelastic responses under longterm reservoir storage, enhancing in-situ and satellite geodetic measurements, and identifying the main factors driving sea level changes.

Numerical analysis of bending property of bi-modulus materials and a new method for measurement of tensile elastic modulus

In nature,there are widely distributed bi-modulus materials with different deformation characteristics under compressive and tensile stress states,such as concrete,rock and ceramics.Due to the lack of constitutive model that could reasonably consider the bi-modulus property of materials,and the lack of simple and reliable measurement methods for the tensile elastic parameters of materials,scientists and engineers always neglect the effect of the bi-modulus property of materials in engineering design and numerical simulation.To solve this problem,this study utilizes the uncoupled strain-driven constitutive model proposed by Latorre and Montáns(2020)to systematically study the distributions and magnitudes of stresses and strains of bi-modulus materials in the three-point bending test through the numerical method.Furthermore,a new method to synchronously measure the tensile and compressive elastic moduli of materials through the four-point bending test is proposed.The numerical results show that the bi-modulus property of materials has a significant effect on the stress,strain and displacement in the specimen utilized in the three-point and four-point bending tests.Meanwhile,the results from the numerical tests,in which the elastic constitutive model proposed by Latorre and Montáns(2020)is utilized,also indicate that the newly proposed measurement method has a good reliability.Although the new measurement method proposed in this study can synchronously and effectively measure the tensile and compressive elastic moduli,it cannot measure the tensile and compressive Poisson’s ratios.

3D bioprinting of complex biological structures with tunable elastic modulus and porosity using freeform reversible embedding of suspended hydrogels

Three-dimensional(3D)bioprinting has been used widely for the construction of hard tissues such as bone and cartilage.However,constructing soft tissues with complex structures remains a challenge.In this study,complex structures characterized by both tunable elastic modulus and porosity were printed using freeform reversible embedding of suspended hydrogels(FRESHs)printing methods.A mixture of alginate and gelatin was used as the main functional component of the bioink.Rheological analysis showed that this bioink possesses shear thinning and shear recovery properties,supporting both cryogenic and FRESH printing methods.Potential printing capabilities and limitations of cryogenic and FRESH printing were then analyzed by printability tests.A series of complex structures were printed by FRESH printing methods which could not be realized using conventional approaches.Mechanical tests and scanning electron microscopy analysis showed that the printed structure is of excellent flexibility and could be applied in various conditions by adjusting its mechanical modulus and porosity.L929 fibroblast cells maintained cell viability in cell-laden-printed structures,and the addition of collagen further improved the hydrogels’biocompatibility.Overall,all results provided useful insight into the building of human soft tissue organ blocks.

Comparative study on three dynamic modulus of elasticity and static modulus of elasticity for Lodgepole pine lumber

The dynamic and static modulus of elasticity （MOE） between bluestained and non-bluestained lumber of Lodgepole pine were tested and analyzed by using three methods of Non-destructive testing （NDT）, Portable Ultrasonic Non-destructive Digital Indicating Testing （Pundit）, Metriguard and Fast Fourier Transform （FFT） and the normal bending method. Results showed that the dynamic and static MOE of bluestained wood were higher than those of non-bluestained wood. The significant differences in dynamic MOE and static MOE were found between bulestained and non-bluestained wood, of which, the difference in each of three dynamic MOE （Ep. the ultrasonic wave modulus of elasticity, Ems, the stress wave modulus of elasticity and El, the longitudinal wave modulus of elasticity） between bulestained and non-bluestained wood arrived at the 0.01 significance level, whereas that in the static MOE at the 0.05 significance level. The differences in MOE between bulestained and non-bluestained wood were induced by the variation between sapwood and heartwood and the different densities of bulestained and non-bluestained wood. The correlation between dynamic MOE and static MOE was statistically significant at the 0.01 significance level. Although the dynamic MOE values of Ep, Em, Er were significantly different, there exists a close relationship between them （arriving at the 0.01 correlation level）. Comparative analysis among the three techniques indicated that the accurateness of FFT was higher than that of Pundit and Metriguard. Effect of tree knots on MOE was also investigated. Result showed that the dynamic and static MOE gradually decreased with the increase of knot number, indicating that knot number had significant effect on MOE value.

ElasticDAG:弹性图式区块链

图式区块链采用有向无环图(directed acyclic graph,DAG)的并行拓扑结构,相较于基于串行拓扑结构的传统链式区块链,能够显著提升系统性能,已受到业界广泛关注.然而,现有图式区块链的共识协议与存储模型高度耦合,缺乏灵活性,难以适应多元化应用需求.同时,大部分图式区块链在共识协议层面上缺乏灵活性,局限于概率性共识协议,难以兼顾确认延迟和安全性,尤其对于延迟敏感型应用很不友好.为此,提出弹性图式区块链系统ElasticDAG,其核心思想是将存储模型和共识协议进行解耦,让两者并行、独立地运行,从而灵活适配多元化应用.针对提升系统吞吐量和活性的需求,为存储模型设计自适应区块确认策略和基于划分的确认区块排序算法;针对降低交易确认延迟的需求,设计低延迟DAG区块链混合共识协议.实验结果表明,ElasticDAG原型系统在广域网下的吞吐量高达11 Mb/s,并具有10秒级确认性能.与OHIE相比,Elastic DAG在实现同等吞吐量的情况下,可将确认延迟降低17倍;与Haootia相比,Elastic DAG在实现同等共识延迟的情况下,可将安全性从91.04%提升到99.999914%.

Elastic modulus determination at different levels of periodontal ligament in nanoindentation

In order to investigate the material properties ofperiodontal ligament （ PDL） in different locations, the nanoindentation method is used to survey the elastic modulus of the PDL at different levels. Cadaveric specimens of human mandibular canine were obtained from 4 adult donors, 16 transverse specimens were made from the sections of cervical margin, midroot and apex using the slow cutting machine. The prepared specimens were tested in different sections （along the longitudinal direction） and different areas （in the circumferential direction）. According to the Oliver-Phair theory, the mean values of elastic modulus were calculated foreach area and the differences among them were compared. In the midroot section, the average elastic modulus is ranging from 0. 11 to 0. 23 MPa, the changing range of the cervical margin and apex are from 0. 21 to 0. 53 MPa and 0. 44 to0.62 MPa, respectively. Experimental results indicate that the average elastic modulus in the midroot is lower than that in the cervical margin and apex, and relatively small changes occur among them. However, there is a large change to the elastic modulus value in the cicumferential direction for the PDL.

ELASTIC MODULUS REDUCTION METHOD FOR LIMIT LOAD EVALUATION OF FRAME STRUCTURES

A new strategy for elastic modulus adjustment is proposed based on the element bearing ratio （EBR）,and the elastic modulus reduction method （EMRM） is proposed for limit load evaluation of frame structures. The EBR is defined employing the generalized yield criterion,and the reference EBR is determined by introducing the extrema and the degree of uniformity of EBR in the structure. The elastic modulus in the element with an EBR greater than the reference one is reduced based on the linear elastic finite element analysis and the equilibrium of strain energy. The lower-bound of limit-loads of frame structures are analyzed and the numerical example demonstrates the flexibility,accuracy and effciency of the proposed method.

A New Elasticity and Finite Element Formulation for Different Young's Modulus When Tension and Compression Loadings

This paper presents a new elasticity and finite element formulation for different Young's modulus when tension and compression loadings in anisotropy media. The case studies, such as anisotropy and isotropy, were investigated. A numerical example was shown to find out the changes of neutral axis at the pure bending beams.

Freeze-thaw damage mechanism of elastic modulus of soil-rock mixtures at different confining pressures

As a frequently-used roadbed filler,soil-rock mixture is often in the environment of freeze-thaw cycles and different confining pressures.In order to study the freeze-thaw damage mechanism of elastic modulus of soil-rock mixtures at different confining pressures,the concept of meso-interfacial freeze-thaw damage coefficient is put forward and the meso-interfacial damage phenomenon of soil-rock mixtures caused by the freeze-thaw cycle environment is concerned;a double-inclusion embedded model for elastic modulus of soil-rock mixtures in freezing-thawing cycle is proposed.A large triaxial test was performed and the influences of confining pressure and experimental factors on elastic modulus of soil-rock mixtures were obtained,and then the accuracy of the double-inclusion embedded model to predict the elastic modulus of soil-rock mixtures in freezing-thawing cycle is verified.Experiment results showed that as to soil-rock mixtures,with the increase of confining pressure,the elastic modulus increases approximately linearly.The most crucial factors to affect the elastic modulus are rock content and compaction degree at the same confining pressure;the elastic modulus increases with the increase of rock content and compactness;as the number of freeze-thaw cycles increases,the freeze-thaw damage coefficient of meso-structural interface and the elastic modulus decrease.

Elastic modulus of claystone evaluated by nano-/micro-indentation tests and meso-compression tests

Toarcian claystone such as that of the Callovo-Oxfordian is a qualified multiphase material. The claystone samples tested in this study are composed of four main mineral phases: silicates(clay minerals, quartz,feldspars, micas)(z86%), sulphides(pyrite)(z3%), carbonates(calcite, dolomite)(z10%) and organic kerogen(z1%). Three sets of measurements of the modulus of deformability were compared as determined in(i) nanoindentation tests with a constant indentation depth of 2 mm,(ii) micro-indentation tests with a constant indentation depth of 20 mm, and(iii) meso-compression tests with a constant displacement of 200 mm. These three experimental methods have already been validated in earlier studies. The main objective of this study is to demonstrate the influence of the scaling effect on the modulus of deformability of the material. Different frequency distributions of the modulus of deformability were obtained at the different sample scales:(i) in nano-indentation tests, the distribution was spread between 15 GPa and 90 GPa and contained one peak at34 GPa and another at 51 GPa;(ii) in the micro-indentation tests, the distribution was spread between 25 GPa and 60 GPa and displayed peaks at 26 GPa and 37 GPa; and(iii) in the meso-compression tests, a narrow frequency distribution was obtained, ranging from 25 GPa to 50 GPa and with a maximum at around 35 GPa.

Random field characterization of uniaxial compressive strength and elastic modulus for intact rocks

Rock properties exhibit spatial variabilities due to complex geological processes such as sedimentation,metamorphism, weathering, and tectogenesis. Although recognized as an important factor controlling the safety of geotechnical structures in rock engineering, the spatial variability of rock properties is rarely quantified. Hence, this study characterizes the autocorrelation structures and scales of fluctuation of two important parameters of intact rocks, i.e. uniaxial compressive strength(UCS) and elastic modulus(EM).UCS and EM data for sedimentary and igneous rocks are collected. The autocorrelation structures are selected using a Bayesian model class selection approach and the scales of fluctuation for these two parameters are estimated using a Bayesian updating method. The results show that the autocorrelation structures for UCS and EM could be best described by a single exponential autocorrelation function. The scales of fluctuation for UCS and EM respectively range from 0.3 m to 8.0 m and from 0.3 m to 8.4 m.These results serve as guidelines for selecting proper autocorrelation functions and autocorrelation distances for rock properties in reliability analyses and could also be used as prior information for quantifying the spatial variability of rock properties in a Bayesian framework.

Elastic modulus affects the growth and differentiation of neural stem cells

It remains poorly understood if carrier hardness, elastic modulus, and contact area affect neural stem cell growth and differentiation. Tensile tests show that the elastic moduli of Tiansu and SMI silicone membranes are lower than that of an ordinary dish, while the elastic modulus of SMI silicone membrane is lower than that of Tiansu silicone membrane. Neural stem cells from the cerebral cortex of embryonic day 16 Sprague-Dawley rats were seeded onto ordinary dishes as well as Tiansu silicone membrane and SMI silicone membrane. Light microscopy showed that neural stem cells on all three carriers show improved adherence. After 7 days of differentiation, neuron specific enolase, glial fibrillary acidic protein, and myelin basic protein expression was detected by immunofluorescence. Moreover, flow cytometry revealed a higher rate of neural stem cell differentiation into astrocytes on Tiansu and SMI silicone membranes than on the ordinary dish, which was also higher on the SMI than the Tiansu silicone membrane. These findings con- firm that all three cell carrier types have good biocompatibility, while SMI and Tiansu silicone membranes exhibit good mechanical homogenization. Thus, elastic modulus affects neural stem cell differentiation into various nerve cells. Within a certain range, a smaller elastic modulus re- sults in a more obvious trend of cell differentiation into astrocytes.

Prediction of uniaxial compressive strength and modulus of elasticity for Travertine samples using regression and artificial neural networks

Uniaxial Compressive Strength (UCS) and modulus of elasticity (E) are the most important rock parameters required and determined for rock mechanical studies in most civil and mining projects. In this study, two mathematical methods, regression analysis and Artificial Neural Networks (ANNs), were used to predict the uniaxial compressive strength and modulus of elasticity. The P-wave velocity, the point load index, the Schmidt hammer rebound number and porosity were used as inputs for both meth-ods. The regression equations show that the relationship between P-wave velocity, point load index, Schmidt hammer rebound number and the porosity input sets with uniaxial compressive strength and modulus of elasticity under conditions of linear rela-tions obtained coefficients of determination of (R2) of 0.64 and 0.56, respectively. ANNs were used to improve the regression re-sults. The generalized regression and feed forward neural networks with two outputs (UCS and E) improved the coefficients of determination to more acceptable levels of 0.86 and 0.92 for UCS and to 0.77 and 0.82 for E. The results show that the proposed ANN methods could be applied as a new acceptable method for the prediction of uniaxial compressive strength and modulus of elasticity of intact rocks.

DEPENDENCE OF MODULUS OF ELASTICITY AND THERMAL CONDUCTIVITY ON REFERENCE TEMPERATURE IN GENERALIZED THERMOELASTICITY FOR AN INFINITE MATERIAL WITH A SPHERICAL CAVITY

The equations of generalized thermoelasticity with one relaxation time with variable modulus of elasticity and the thermal conductivity were used to solve a problem of an infinite material with a spherical cavity.The inner surface of the cavity was taken to be traction free and acted upon by a thermal shock to the surface. Laplace transforms techniques were used to obtain the solution by a direct approach.The inverse Laplace transforms was obtained numerically.The temperature,displacement and stress distributions are represented graphically.

Size effect of the elastic modulus of rectangular nanobeams:Surface elasticity effect

The size-dependent elastic property of rectangular nanobeams （nanowires or nanoplates） induced by the surface elas- ticity effect is investigated by using a developed modified core-shell model. The effect of surface elasticity on the elastic modulus of nanobeams can be characterized by two surface related parameters, i.e., inhomogeneous degree constant and surface layer thickness. The analytical results show that the elastic modulus of the rectangular nanobeam exhibits a distinct size effect when its characteristic size reduces below 1 O0 nm. It is also found that the theoretical results calculated by a mod- ified core-shell model have more obvious advantages than those by other models （core-shell model and core-surface model） by comparing them with relevant experimental measurements and computational results, especially when the dimensions of nanostructures reduce to a few tens of nanometers.

Influence of nickel silicides presence on hardness,elastic modulus and fracture toughness of gas-borided layer produced on Nisil-alloy

The two-stage gas boriding in N_(2)−H_(2)−BCl_(3)atmosphere was applied to producing a two-zoned borided layer on Nisil-alloy.The process was carried out at 910℃ for 2 h.The microstructure consisted of two zones differing in their phase composition.The outer layer contained only a mixture of nickel borides(Ni_(2)B,Ni_(3)B)only.The inner zone contained additionally nickel silicides(Ni_(2)Si,Ni_(3)Si)occurring together with nickel borides.The aim of this study was to determine the presence of nickel silicides on the mechanical properties of the borided layer produced on Ni-based alloy.The hardness and elastic modulus were measured using the nanoindenter with a Berkovich diamond tip under a load of 50 mN.The average values of indentation hardness(HI)and indentation elastic modulus(E_(I))obtained in the outer zone were respectively(16.32±1.03)GPa and(232±16.15)GPa.The presence of nickel silicides in the inner zone reduced the indentation hardness(6.8−12.54 GPa)and elastic modulus(111.79−153.99 GPa).The fracture toughness of the boride layers was investigated using a Vickers microindentation under a load of 0.981 N.It was confirmed that the presence of nickel silicides caused an increase in brittleness(by about 40%)of the gas-borided layer.

Effects of thickness and elastic modulus on stress condition of fatigue-resistant coating under rolling contact

The distribution and magnitude of surface substrates were investigated by finite element method and subsurface stresses of the （FEM）. The models of coating single-layer sprayed-coatings on monolithic configurations with different thicknesses and elastic modulus ratios of coating to substrate were introduced, and the effects of thickness and elastic modulus ratio on the stresses were addressed. The calculation results show that the coating/substrate interface shear stress obviously decreases with increasing coating thickness, due to the location of the maximum shear stress moving away from the coating/substrate interface. At the same time, the magnitude of von Mises stress also declines in the case of thicker coatings. However, the high elastic modulus ratio results in extremely high maximum shear stress and the severe discontinuity of the von Mises stress curves, which leads to the intensive stress concentration on the coating/substrate interface. So the coating configurations with the larger coating thickness and lower difference of elastic modulus between coating and substrate exhibit excellent resistant performance of rolling contact fatigue （RCF）.

Elastic Modulus and Stress Analysis of Porous Titanium Parts Fabricated by Selective Laser Melting

The mismatch of elasticity modulus has limited the application of titanium alloys in medical implants,and porous structures have been proved effective to deal with this problem. However,the manufacturing of porous structures has been restricted from conventional technologies. In this study,selective laser melting( SLM) technology was employed to produce a set of Ti-6Al-4V porous samples based on cubic lattices with varying size of strut width from 200 μm to 600 μm. Then the compression tests were conducted to analyze the influence of the strut width on the elasticity modulus and the ultimate strength. The result shows both of them increases linearly with the growth of strut width or with the decrease of porosity,and the elasticity modulus of porous parts is largely reduced and actually meets the requirement of clinical application. Additionally,a finite element model was established to verify the un-uniform stress distribution of porous parts. It reveals that fractures always initially occur at the vertical struts along the force direction which suffer from the main deformation.