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.

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.

NANOINDENTATION OF THIN-FILM-SUBSTRATE SYSTEM DETERMINATION OF FILM HARDNESS AND YOUNG'S MODULUS

In the present paper,the hardness and Young's modulus of film-substrate systems are determined by means of nanoindentation experiments and modified models.Aluminum film and two kinds of substrates,i.e.glass and silicon,are studied.Nanoindentation XP Ⅱ and continuous stiffness mode are used during the experiments.In order to avoid the influence of the Oliver and Pharr method used in the experiments,the experiment data are analyzed with the constant Young's modulus assumption and the equal hardness assumption.The volume fraction model(CZ model)proposed by Fabes et al.(1992)is used and modified to analyze the measured hardness.The method proposed by Doerner and Nix(DN formula)(1986)is modified to analyze the measured Young's modulus.Two kinds of modified empirical formula are used to predict the present experiment results and those in the literature,which include the results of two kinds of systems,i.e.,a soft film on a hard substrate and a hard film on a soft substrate.In the modified CZ model,the indentation influence angle,(?), is considered as a relevant physical parameter,which embodies the effects of the indenter tip radius, pile-up or sink-in phenomena and deformation of film and substrate.

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.

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.

A Finite Element Study of Elastic-Plastic Hemispherical Contact Behavior against a Rigid Flat under Varying Modulus of Elasticity and Sphere Radius

The present study considers a finite element analysis of elastic-plastic axi-symmetric hemispherical contact for a frictionless deformable sphere pressed by a rigid flat. The material of the sphere is modeled as elastic perfectly plastic. Analysis is carried out to study the effect of varying modulus of elasticity and sphere radius in wide range of dimensionless interference until the inception of plasticity as well as in plastic range. Results are compared with previous elastic-plastic models. It is found that materials with Young’s modulus to yield strength (E/Y) ratio less than and greater than 300 show strikingly different contact phenomena. The dependency of E on dimensionless interference at which the plastic region fully covers the surface is observed. However with different radius, finite element study exhibits similar elastic-plastic phenomena.

Analytic elasticity solution of bi-modulus beams under combined loads

A unified stress function for bi-modulus beams is proposed based on its mechanic sense on the boundary of beams. Elasticity solutions of stress and displacement for bi-modulus beams under combined loads are derived. The example analysis shows that the maximum tensile stress using the same elastic modulus theory is underestimated if the tensile elastic modulus is larger than the compressive elastic modulus. Otherwise, the maximum compressive stress is underestimated. The maximum tensile stress using the material mechanics solution is underestimated when the tensile elastic modulus is larger than the compressive elastic modulus to a certain extent. The error of stress using the material mechanics theory decreases as the span-to-height ratio of beams increases, which is apparent when L/h ≤ 5. The error also varies with the distributed load patterns.

Measurement of elastic modulus and evaluation of viscoelasticity of foundry green sand

Elastic modulus is an important physical parameter of molding sand; it is closely connected with molding sand’s properties. Based on theories of rheology and molding sand microdeformation, elastic modulus of molding sand was measured and investigated using the intelligent molding sand multi-property tester developed by ourselves. The measuring principle was introduced. Effects of bentonite percentage and compactibility of the molding sand were experimentally studied. Furthermore, the essential viscoelastic nature of green sand was analyzed. It is considered that viscoelastic deformation of molding sand consists mainly of that of Kelvin Body of clay membrane, and elastic modulus of molding sand depends mainly on that of Kelvin Body which is the elastic component of clay membrane between sands. Elastic modulus can be adopted as one of the property parameters, and can be employed to evaluate the viscoelastic properties of molding sand.

EFFECT OF DISPERSION OF MICA IN MATRIX ON YOUNG'S MODULUS OF MICA FILLED POLYETHYLENE

The correlation between Young's modulus of mica-filled high density polyethylene (HDPE), low density polyethylene(LDPE) and the state of dispersion of plasma-treated mica in the polymer matrices was studied. The modulus and the number average diameter of mica aggregates in matrix were determined with tensile testing and image analysis respectively. The interface structure of the filler/matrix and the bulk structure of matrix were examined through the dielectric spectrometry, differential scanning calorimetry (DSC) and dynamic viscoelastic spectrometry. The results show that the Young's modulus of the filial polyethylene depends to a great extent upon the state of dispersion of filler in matrix, but it is independent of the interface structure and bulk structure. The better the dispersion, the higher the Young's modulus.

Anomalies in Young's modulus behavior after annealing in polycrystalline SmS

In this paper,the dependencies of Young's modulus and attenuation decrement on samarium sulfide polycrystals(SmS)under various annealing temperatures are studied by the piezoelectric ultrasonic composite oscillator technique at a frequency of 100 kHz in the temperature range of 80-300 K.A decrease in Young's modulus with an increase of the annealing temperature due to the texturing of the material was revealed.At the same time,attenuation peaks were observed at temperatures about 90 and 125 K,presumably due to Niblett-Wilks and Bordoni relaxations.

ELASTICITY MODULUS OF RANDOM COMPOSITE AND ELASTIC PERCOLATION FAILURE OF SOLIDS

The elasticity modulus of random composite is obtained in 2 and 3 dimensional spaces,based on the solutions of over-matching problems in elastic mechanics.A system with 2 components is also considered,and the calculated results are in good agreement with available references.Further,taking the voids and defects in materials as the second phase with zero modulus,one can easily obtain the expressions for predicting modulus and threshold of the elastic percolation failure of materials containing voids,and the results agree excellently with those in available literatures.

Dynamic Modulus of Elasticity of Some Mortars Prepared from Selected Jordanian Masonry Cements

In light of the highly demanding cement market in Jordan, comprehensive studies should be undertaken to investigate the properties of the different cement types. This paper studies the Dynamic modulus of elasticity (DME) at 2, 7 and 28 days in mortars using six cement Jordanian types with CaO contents less than that of the ordinary Portland cements. It was found that the DME has strong relation with compressive strength. At the age of 28 days the mortars had some different values of DME. One important result of our work is that DME at the age of 28 days can be derived from those of the two days mixes. To account for the differences in dynamic modulus of elasticity with time, it is highly recommended to study in detail the mortars petrography under the light microscope. Using the scanning electron microscope (SEM), usually with attachment for chemical analysis at the crystal scale, in addition to X-ray diffraction technique may help characterization of the cement phases qualitatively and quantitatively.

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.

高温后冷却方式对玄武岩纤维混凝土力学性能的影响

高温处理后混凝土力学性能是工程建设中评价混凝土结构安全性能的重要指标之一。对不同玄武岩纤维(BF)掺量混凝土的力学性能进行了测试,将最优掺量的玄武岩纤维混凝土(BFRC)与普通混凝土(OC)进行高温处理(200、400、600、800℃),研究不同冷却方式(自然冷却和喷水冷却)对高温后BFRC性能劣化的影响,分析BFRC在不同温度和冷却方式下的力学性能变化规律。结果表明,当BF掺量为0.05%(体积分数)时,BFRC抗压强度、劈裂抗拉强度达到最大值,分别为50.2、3.5 MPa,较OC分别提高了14.87%、34.62%。BF的掺入能够有效增加混凝土的韧性以及抵抗开裂变形的能力。随着温度增加,BFRC试件的弹性模量减小但始终大于OC试件。同一冷却方式下OC的峰值应变均大于BFRC,不同冷却方式下的延性指数较常温均有所提高。

机车用钛合金弹簧的设计与制备

钛合金弹簧替代钢制弹簧应用于机车悬架弹簧可以减重40%~60%,而且钛合金弹簧具有良好的耐蚀性和阻尼特性,不仅能够抵御恶劣环境的腐蚀,增加机车的行驶里程,还能增强机车的操控性和乘架的舒适性。通过赛车用悬架弹簧实例,详细介绍TB9钛合金弹簧的设计方法和制备过程。计算得到钛合金悬架弹簧的螺旋角为9.45°,已经超出弹簧设计国家标准范围,因此对公式进行了修正。此外,还研究了温度对TB9钛合金弹簧刚度的影响。研究发现,随着温度的上升,TB9钛合金弹簧的刚度逐渐下降。