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.

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.

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.

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.

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.

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.

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.

A Statistical Analysis of the Modulus of Elasticity and Compressive Strength of Concrete C45/55 for Pre-stressed Precast Beams

Random behavior of concrete C45/55 XF2 used for prefabricated pre-stressed bridge beams is described on the basis of evaluating a vast set of measurements. A detailed statistical analysis is carried out on 133 test results of cylinders 150 ~ 300 mm in size. The tests have been running in laboratories of the Klokner Institute. A single worker took all specimens throughout the period, and the subsequent measurements of the static modulus of elasticity and the compressive strength of the concrete were performed. The measurements were made at the age of 28 days after specimens casting, and only one testing machine with the same capping method was used. Suitable theoretical models of division are determined on the basis of tests in good congruence, with the use of Z2 and the Bernstein criterion. A set of concrete compressive strength （carried out on 133 test results of cylinders 150 ~ 300 mm after test of static modulus of elasticity） shows relatively high skewness in this specific case. This cause that limited beta distribution is better than generally recommended theoretical distribution for strength the normal or lognormal. The modulus of elasticity is not significantly affected due to skewness because the design value is based on mean value.

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.

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.

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.

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.