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.

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.

SIMULATION AND STUDY OF THE MODULUS OF ELASTICITY OF NANOCRYSTALLINE MATERIALS

In this paper, a molecular dynamics simulations are provided for atomic structure of nanocrystals(1～3nm)by which t he lattice parameter of X_ray diffraction, cohesive energy and modulus of elas ticity were computed. The results show that the structure of grain and grain bou ndaries in the same in both nanocrystal and coarse grain materials. The decrease of grain size and the increase volume fraction of grain boundaries lead to a se ries of different features, the modulus of elasticity of nanocrystalline materia ls have been found to be much reduced.

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.

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.

Adhesion strength of tetrahydrofuran hydrates is dictated by substrate stiffness

Understanding the hydrate adhesion is important to tackling hydrate accretion in petro-pipelines.Herein,the relationship between the Tetrahydrofuran(THF)hydrate adhesion strength(AS)and surface stiffness on elastic coatings is systemically examined by experimental shear force measurements and theoretical methods.The mechanical factor-elastic modulus of the coatings greatly dictates the hydrate AS,which is explained by the adhesion mechanics theory,beyond the usual factors such as wettability and structural roughness.Moreover,the hydrate AS increases with reducing the thickness of the elastic coatings,resulted from the decrease of the apparent surface elastic modulus.The effect of critical thickness for the elastic materials with variable elastic modulus on the hydrate AS is also revealed.This study provides deep perspectives on the regulation of the hydrate AS by the elastic modulus of elastic materials,which is of significance to design anti-hydrate surfaces for mitigation of hydrate accretion in petro-pipelines.

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.

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.

A theoretical model for impact protection of flexible polymer material

The relationship between the protective performance of flexible polymer material and material parameters(elasticmodulus,viscosity coefficient)is explored,an impact collision motion equation between two bodies is establishedfrom the viscoelastic material constitutive,and the relationship between the kinematic response and the materialparameters is obtained.Based on the Kelvin constitutive model,a theoretical model for impact between the pro-tective body and the protected body is established,then the dynamic response is obtained.The feasibility of themodel was verified by drop hammer experiment,and the material parameters(elastic modulus,viscosity coeffi-cient)were obtained by formula.The model is discretized and the relationship between local impact response andmaterial parameters is analyzed.The discussion results on the relationship between the impact response and theprotective material performance indicate that adjusting the elastic modulus,viscosity coefficient,and thicknessof the protective material can effectively improve protective effect.

An Rapid Assessment Method for Bearing Capacity of RC Girder Bridges Based on Residual Strain

In order to realize the in-situ evaluation of reinforced concrete bridges subjected to fatigue for a long time or after earthquake, an evaluation method for cumulative damage of concrete structures based on unloading elastic modulus was proposed. First, according to the concrete stress-strain curve and the statistical relationship between residual strain and cumulative strain, the calculation method of static equivalent strain and residual strain concrete based on unloading elastic modulus and the method for estimating the strength of concrete after damage were proposed. The detailed steps of field test and analysis and the practical damage indicators of residual strain were given. Then, the evaluation method of existing stress and strain of Reinforced Concrete Bridge under dead load and the concept of “equivalent dead load bending moment” were put forward. On this basis, the paper analyzed the root cause of the decrease of bearing capacity of Reinforced Concrete Bridge after fatigue damage, and pointed out that the equivalent strain or residual strain of reinforced concrete increases under the fatigue effect, which led to the decreasing of actual live moment and deformation performance while the ultimate load-carrying capacity remained constant or very little decrease. The evaluation method of structure residual capacity was given, and through comparative analysis of eight T reinforced concrete beams that had been in service for 35 years with the static failure tests, the effectiveness of the method was verified.

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.

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.

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.

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.

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.

Microstructure,Elastic Modulus and Tensile Properties of Ti-Nb-O Alloy System

In the present study Ti-Nb binary alloy system was chosen because it has excellent biocompatibility as well as reasonable mechanical properties,aiming at understanding oxygen content on microstructural formation, elastic modulus and tensile properties in Ti-Nb alloy system.Small alloy buttons of 50 mm in diameter were prepared by arc melting on a water-cooled copper hearth under an argon gas atmosphere with a non-consumable tungsten electrode.The button ingots were then heat treated in a vacuum atmosphere at 1273 K for 0.5 h followed by water quenching in a specially designed heat treatment furnace.Microstructure,elastic modulus and tensile properties were investigated in order to understand the effect of oxygen content in quenched Ti- Nb alloy system.The orthorhombic structuredα″martensite was changed to bcc structuredβ-phase with increasing Nb content.Interestingly,it was found that oxygen makesβ-phase stable in quenched Ti-Nb alloy system.Elastic modulus values were sensitive to phase stability of constituent phases.Yield strength increased with increasing oxygen content.Details will be explained by phase formation and stability behavior.

EFFECT OF AGING ON INTERNAL FRICTION,ELASTIC MODULUS AND MECHANICAL PROPERTIES OF TERNARY Mn-Cu-Al ALLOYS

Internal friction and elastic modulus of ternary Mn-Cu-Al alloys containing 56—60 wt-% Mn,0-3.59 wt-% Al were measured with acoustic frequency,1 kHz,in the tempera- ture range of-150 to 150℃.It was found that when the specimen was aged in the temperature range under the spinodal curve within the miscibility gap(400—500℃),the internal fric- tion increases with an increase of the aging time and reaches a maximum value at a certain ag- ing time which is shorter with a higher aging temperature.Two internal friction peaks which did not appear before the aging were observed above room temperature after a definite aging time.These are respectively the martensitic tranformation peak and the relaxation peak orig- inating from the stress-induced movement of the twin boundaries.The former peak shifts to- ward higher temperatures with an increase of the aging time,whereas the relaxation peak ap- pearing at 15℃,is independent of the aging time and temperature.The activation energy as- sociated with the relaxation peak was found to be 0.56 eV which is about the same as that of the relaxation peak in binary alloy containing 90 wt-% Mn.It was also found that the hardness,strength and the brittleness of the specimen increase when aged below the spinodal curve within the miscibility gap.The addition or Al enhances the strength but reduces the in- ternal friction of the specimen.A choice of suitable aging time and temperature can give an optimum compromise of high strength and high internal friction.Analysis of experimental re- sults suggests that spinodal decomposition leads to Mn-rich zones in the specimen and thus causes the phase transformation and the change of mechanical properties of the specimen.

Dynamic Elastic Modulus of Cement Paste at Early Age based on Nondestructive Test and Multiscale Prediction Model

This paper introduced a nondestructive testing method to evaluate the dynamic elastic modulus of cement paste. Moreover, the effect of water-cement ratio and conventional admixtures on the dynamic elastic modulus of cement paste was investigated, in which three kinds of admixtures were taken into account including viscosity modifying admixture （VMA）, silica.fume （SF）, and shrinkage-reducing admixture （SRA）. The experimental results indicate that the dynamic elastic modulus of cement paste increases with decreasing water-cement ratio. The addition of SF increases the dynamic elastic modulus, however, the overdosage of VMA causes its reduction. SRA reduces the dynamic elastic modulus at early age without affecting it in later period. Finally, a multiscale micromechanics approach coupled with a hydration model CEMHYD3D and percolation theory is utilized to predict the elastic modulus of cement paste, and the predictive results by the model are in accordance with the experimental data.