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.

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.

An analytical solution of equivalent elastic modulus considering confining stress and its variables sensitivity analysis for fractured rock masses

The equivalent elastic modulus is a parameter for controlling the deformation behavior of fractured rock masses in the equivalent continuum approach.The confining stress,whose effect on the equivalent elastic modulus is of great importance,is the fundamental stress environment of natural rock masses.This paper employs an analytical approach to obtain the equivalent elastic modulus of fractured rock masses containing random discrete fractures(RDFs)or regular fracture sets(RFSs)while considering the confining stress.The proposed analytical solution considers not only the elastic properties of the intact rocks and fractures,but also the geometrical structure of the fractures and the confining stress.The performance of the analytical solution is verified by comparing it with the results of numerical tests obtained using the three-dimensional distinct element code(3DEC),leading to a reasonably good agreement.The analytical solution quantitatively demonstrates that the equivalent elastic modulus increases substantially with an increase in confining stress,i.e.it is characterized by stress-dependency.Further,a sensitivity analysis of the variables in the analytical solution is conducted using a global sensitivity analysis approach,i.e.the extended Fourier amplitude sensitivity test(EFAST).The variations in the sensitivity indices for different ranges and distribution types of the variables are investigated.The results provide an in-depth understanding of the influence of the variables on the equivalent elastic modulus from different perspectives.

Whisker Orientation Function and Elastic Modulus of the as-cast 20% SiC_W/Mg Composite

The relationship between the plane-orientation function and the space-orientation function of whiskers in whisker-reinforced metal matrix composites was analyzed theoretically. The actual orientation of whiskers in the as- cast 20%SiC_W/Mg composite (SiC_W content in volume fraction) were investigated, and the elastic modulus of the composite was measured with an ultrasonic velocity analyzer. Results show that there is an evident difference be- tween the plane-orientation function and the space-orientation function of whiskers and the space-orientation function can represent the actual condition of the composite. Only by using the space-orientation function of whiskers, the difference of elastic modulus of the as-cast composite in different directions can be explained reasonably.

How believable are published laboratory data?A deeper look into system-compliance and elastic modulus

Elastic modulus(E)interpretation is debatable with limited literature detailing the impact of systemcompliance.To address this impact,a comprehensive testing schedule using an aluminium 6061(Al)sample is carried out on several systems under various test setups.Al is chosen as it is extruded and adheres to well defined shape tolerances and elastic properties.A robust method,using the Savitzky-Golay filter,is introduced to identify significant slope changes in the stressestrain curve.Since the load in the test system is well defined,the recorded deformation is corrected to the expected value of Al resulting in a system-compliance factor.The results across the testing systems and test setups showed significant variance,with the recorded E always lower than the anticipated EAl.The number of components within the system over which the deformation is measured had the most significant impact,lowering the expected E by up to 50%.Additionally,the system-compliance factor is inconsistent across different systems and setups.Thus,it is evidently proved that each setup must be separately evaluated for its system-compliance and that no single value exists across systems and setups.The findings are then projected onto a series of uniaxial compressive strength(UCS)tests carried out on Stanstead granite(SS GR)samples.The corrected Et50 and Eavg values for system-compliance of the samples are within1%for each system as opposed to being50%pre-correction.The findings conclude that it is deemed necessary and of utmost importance that the deformation be corrected to accommodate the systemcompliance to obtain reliable results.

Elastic modulus of SiC_w/6061Al alloy composites as-squeeze-cast

By using the system of image analyzer connected with scanning electron microscope, the whisker orientation in the SiC w/6061Al alloy composite as squeeze cast was measured. According to the shear lag model and the actual distribution function of whisker in composite, the inhomogeneity of elastic modulus in composite was analyzed. With the method of ultrasonic velocity, the elastic modulus of composite was measured. The results showed that, the whiskers of composite are preferred in an orientation normal to the direction of squeeze cast. The higher the volume fraction of whisker, the more extent of preferred orientation of it, and the inhomogeneity of elastic modulus is mainly due to the differences of whisker distribution in composite.

Tensile Elastic Modulus, Strength and Fracture of δ-Al_2O_(3f)/Al Alloy Composites

Based on the experimental and theoretical analysis, the tensile elastic modulus, strength and fracture characteristics of squeeze casting δ-Al2O3/Al alloy composites were studied. The fracture characteristics of composites were observed by SEM. The elastic modulus was predicted by the finite element method based on the energy equivalence principle, and the strength was predicted by the statistical integration average method using the maximum energy criterion of composite strength. In the prediction, the distribution density functions of the fiber’s. orientation and length were considered. These functions were gained by experimental measurement. It is shown that the predicted results are in agreement with the experimental values well and the microstructure feature of composites controls the fracture characteristics.

Evaluating high temperature elastic modulus of ceramic coatings by relative method

The accurate evaluation of the elastic modulus of ceramic coatings at high temperature(HT)is of high significance for industrial application,yet it is not easy to get the practical modulus at HT due to the difficulty of the deformation measurement and coating separation from the composite samples.This work presented a simple approach in which relative method was used twice to solve this problem indirectly.Given a single-face or double-face coated beam sample,the relative method was firstly used to determine the real mid-span deflection of the three-point bending piece at HT,and secondly to derive the analytical relation among the HT moduli of the coating,the coated and uncoated samples.Thus the HT modulus of the coatings on beam samples is determined uniquely via the measured HT moduli of the samples with and without coatings.For a ring sample(from tube with outer-side,inner-side,and double-side coating),the relative method was used firstly to determine the real compression deformation of a split ring sample at HT,secondly to derive the relationship among the slope of load-deformation curve of the coated ring,the HT modulus of the coating and substrate.Thus,the HT modulus of ceramic coatings can be evaluated by the substrate modulus and the load-deformation data of coated rings.Mathematic expressions of those calculations were derived for the beam and ring samples.CVD-SiC coatings on graphite substrate were selected as the testing samples,of which the measured modulus ranging from room temperature to 2100℃demonstrated the validity and convenience of the relative method.

The influence of spark plasma sintering temperatures on the microstructure,hardness,and elastic modulus of the nanocrystalline Al-xV alloys produced by high-energy ball milling

Al-xV alloys(x=2 at.%,5 at.%,10 at.%)with nanocrystalline structure and high solid solubility of V were produced in powder form by high-energy ball milling(HEBM).The alloy powders were consolidated by spark plasma sintering(SPS)employing a wide range of temperatures ranging from 200 to 400°C.The microstructure and solid solubility of V in Al were investigated using X-ray diffraction analysis,scanning electron microscope and transmission electron microscope.The microstructure was influenced by the SPS temperature and V content of the alloy.The alloys exhibited high solid solubility of V–six orders of magnitude higher than that in equilibrium state and grain size<50 nm at all the SPS temperatures.The formation of Al3V intermetallic was detected at 400℃.Formation of a V-lean phase and bimodal grain size was observed during SPS,which increased with the increase in SPS temperature.The hardness and elastic modulus,measured using nanoindentation,were significantly higher than commercial alloys.For example,Al-V alloy produced by SPS at 200℃ exhibited a hardness of 5.21 GPa along with elastic modulus of 96.21 GPa.The evolution of the microstructure and hardness with SPS temperatures has been discussed.

Relation between Modulus of Elasticity and Compressive Strength of Ultrahigh-Strength Mortar with Mixed Silicon Carbide as Fine Aggregate

Ultrahigh-strength mortar mixed surface-oxidized silicon carbide as a fine aggregate was prepared by means of press-casting followed by curing in an autoclave. The relation between modulus of elssticity up to 111 GPa and compressive strength up to 360 MPa of mortar mixed silicon carbide was discussed and it was revealed that the contributions of the aggregate hardness and of the interfacial strength between the aggregate and the cement paste on the elasticity of mortar were imporant.

考虑轴向大拉伸下弹性模量对聚酯系泊动态响应的影响

Owing to the particularity of a polyester fiber material,the polyester mooring undergoes large axial tensile deformation over long-term use.Large axial tensile deformation significantly impacts the dynamic response of the mooring system.In addition,the degrees of large axial tension caused by different elastic moduli are also different,and the force on the mooring line is also different.Therefore,it is of great significance to study the influence of elastic modulus on the dynamic results of the mooring systems under large axial tension.Conventional numerical software fails to consider the axial tension deformation of the mooring.Based on the theory of slender rods,this paper derives the formula for large axial tension using the method of overall coordinates and overall slope coordinates and provides the calculation programs.Considering a polyester mooring system as an example,the calculation program and numerical software are used to calculate and compare the static and dynamic analyses to verify the reliability of the calculation program.To make the force change of the mooring obvious,the elastic moduli of three different orders of magnitude are compared and analyzed,and the dynamic response results after large axial tension are compared.This study concludes that the change in the elastic modulus of the polyester mooring changes the result of the vertex tension by generating an axial tension.The smaller the elastic modulus,the larger the forced oscillation motion amplitude of the top point of the mooring line,the more obvious the axial tension phenomenon,and the smaller the force on the top of the polyester mooring.

Improving the Young’s modulus of Mg via alloying and compositing–A short review

Lightweight,high-modulus structural materials are highly desired in many applications like aerospace,automobile and biomedical instruments.As the lightest metallic structural material,magnesium(Mg)has great potential but is limited by its low intrinsic Young’s modulus.This paper reviews the investigations on high-modulus Mg-based materials during the last decades.The nature of elastic modulus is introduced,and typical high-modulus Mg alloys and Mg matrix composites are reviewed.Specifically,Mg alloys enhance Young’s modulus of pure Mg mainly by introducing suitable alloying elements to promote the precipitation of high-modulus second phases in the alloy system.Differently,Mg matrix composites improve Young’s modulus by incorporating high-modulus particles,whiskers and fibers into the Mg matrix.The modulus strengthening effectiveness brought by the two approaches is compared,and Mg matrix composites stand out as a more promising solution.In addition,two well-accepted modulus prediction models(Halpin-Tsai and Rule of mixtures(ROM))for different Mg matrix composites are reviewed.The effects of reinforcement type,size,volume fraction and interfacial bonding condition on the modulus of Mg matrix composites are discussed.Finally,the existing challenges and development trends of high-modulus Mg-based materials are proposed and prospected.

Effect of Axial Deformation on Elastic Properties of Irregular Honeycomb Structure

Irregular honeycomb structures occur abundantly in nature and in man-made products,and are an active area of research.In this paper,according to the optimization of regular honeycomb structures,two types of irregular honeycomb structures with both positive and negative Poisson’s ratios are presented.The elastic properties of irregular honeycombs with varying structure angles were investigated through a combination of material mechanics and structural mechanics methods,in which the axial deformation of the rods was considered.The numerical results show that axial deformation has a significant influence on the elastic properties of irregular honeycomb structures.The elastic properties of the structure can be considered by the enclosed area of the unit structure,the shape of the unit structure,and the elastic properties of the original materials.The elastic properties considering the axial deformation of rods studied in this study can provide a reference for other scholars.

First-principles studies of effects of interstitial boron and carbon on the structural, elastic, and electronic properties of Ni solution and Ni_3Al intermetallics

The effects of boron and carbon on the structural, elastic, and electronic properties of both Ni solution and Ni_3Al intermetallics are investigated using first-principles calculations. The results agree well with theoretical and experimental data from previous studies and are analyzed based on the density of states and charge density. It is found that both boron and carbon are inclined to occupy the Ni-rich interstices in Ni_3Al, which gives rise to a cubic interstitial phase. In addition,the interstitial boron and carbon have different effects on the elastic moduli of Ni and Ni_3Al. The calculation results for the G/B and Poisson's ratios further demonstrate that interstitial boron and carbon can both reduce the brittleness of Ni, thereby increasing its ductility. Meanwhile, boron can also enhance the ductility of the Ni_3Al while carbon hardly has an effect on its brittleness or ductility.

Simulation of Elastic and Fatigue Properties of Epoxy/SiO_(2) Particle Composites through Molecular Dynamics

The influence of different nanoparticle sizes on the elastic modulus and the fatigue properties of epoxy/SiO_(2) nanocomposite is studied in this paper.Here,the cross-linked epoxy resins formed by the combination of DGEBA and 1,3-phenylenediamine are used as the matrix phase,and spherical SiO_(2) particles are used as the reinforcement phase.In order to simulate the elastic modulus and long-term performance of the composite material at room temperature,the simulated temperature is set to 298 K and the mass fraction of SiO_(2) particles is set to 28.9%.The applied strain rate is 109/s during the simulation of the elastic modulus.The results show that the elastic modulus of the material increases with the increase in particle size.Furthermore,fatigue simulation under strain control is performed on the model with SiO_(2) nanoparticle radius of 12˚A.The results indicate that the influence trend of variable frequencies on the fatigue mechanical response is similar,and the mean stress decreases with the increase in number of cycles.In addition,the smaller the loading period and the more the number of cycles,the greater the mean stress reduction.Finally,the change in energy and free volume fraction are evaluated under fatigue loading condition.

Evolution of mechanical parameters of Shuangjiangkou granite under different loading cycles and stress paths

Surrounding rocks at different locations are generally subjected to different stress paths during the process of deep hard rock excavation.In this study,to reveal the mechanical parameters of deep surrounding rock under different stress paths,a new cyclic loading and unloading test method for controlled true triaxial loading and unloading and principal stress direction interchange was proposed,and the evolution of mechanical parameters of Shuangjiangkou granite under different stress paths was studied,including the deformation modulus,elastic deformation increment ratios,fracture degree,cohesion and internal friction angle.Additionally,stress path coefficient was defined to characterize different stress paths,and the functional relationships among the stress path coefficient,rock fracture degree difference coefficient,cohesion and internal friction angle were obtained.The results show that during the true triaxial cyclic loading and unloading process,the deformation modulus and cohesion gradually decrease,while the internal friction angle gradually increases with increasing equivalent crack strain.The stress path coefficient is exponentially related to the rock fracture degree difference coefficient.As the stress path coefficient increases,the degrees of cohesion weakening and internal friction angle strengthening decrease linearly.During cyclic loading and unloading under true triaxial principal stress direction interchange,the direction of crack development changes,and the deformation modulus increases,while the cohesion and internal friction angle decrease slightly,indicating that the principal stress direction interchange has a strengthening effect on the surrounding rocks.Finally,the influences of the principal stress interchange direction on the stabilities of deep engineering excavation projects are discussed.

Study on Influence of Ballast Spring Modulus on Track Structure Based on Finite Element Method

The finite element method is used to simulate the orbital structure,and the finite element model of"rail-sleepers-ballast"can be established.The model of the elastic modulus of different ballast and sleeper is calculated,and the rail displacement,the sleeper stress and the fastening force are deduced.The results show that the elastic modulus of the ballast can be increased to reduce the displacement of the rail and the supporting force of the fastener,but the stress of the sleeper will be increased.When the modu-lus of elasticity increases,the rail displacement,small.

Nacre-inspired Zirconia/Carbon Nanocomposites with High Strength and Toughness

Inspired by structures of natural shells,zirconia-carbon nanocomposites were obtained by using natural chitin from shrimp shells as templates via the sol-gel route in this study.Chitin was dispersed in the water and chelated with the zirconia precursors by amidogen.After a heat treatment for carbonization,nacre-like structures of carbon-zirconia nanocomposites were successfully synthesized.Due to the toughening mechanism of tetragonal zirconia,the mechanical properties of carbon-zirconia composites are further improved.The as-received zirconia/carbon nanocomposite with best mechanical property has a hardness of 5.88GPa and an elastic modulus of 80.6 GPa,which is even stronger than natural shells.This work might facilitate a versatile platform for developing green nanocomposites with reasonably good mechanical properties.

Detection of Frost-Resistance Property of Large-Size Concrete Based on Impact-Echo Method

The dynamic elasticity modulus(Ed)is the most commonly used indexes for nondestructive testing to represent the internal damage of hydraulic concrete.Samples with a specific size is required when the transverse resonance method was used to detect the Ed,resulting in a limitation for field tests.The impact-echo method can make up defects of traditional detection methods for frost-resistance testing,such as the evaluation via the loss of mass or strength.The feasibility of the impact-echo method to obtain the relative Ed is explored to detect the frost-resistance property of large-volume hydraulic concretes on site.Results show that the impact-echo method can replace the traditional resonance frequency method to evaluate the frost resistance of concrete,and has advantages of high accuracy,easy to operate,and not affecting by the aggregate size and size effect of samples.The dynamic elastic modulus of concrete detected by the impact-echo method has little difference with that obtained by the traditional resonance method.The one-dimensional elastic wave velocity of concrete has a good linear correlation with the transverse resonance frequency.The freeze-thaw damage occurred from the surface to the inner layer,and the surface is expected to be the most vulnerable part for the freeze-thaw damage.It is expected to monitor and track the degradation of the frost resistance of an actual structure by frequently detecting the P-wave velocity on site,which avoids coring again.