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.

Modelling of the variation of granular base materials resilient modulus with material characteristics and humidity conditions

This study aims to quantify the susceptibility of granular materials used in pavements to changes in moisture content and propose a correlation model to incorporate this susceptibility into seasonal analyses.The fines content and the percentage of fractured coarse aggregates were identified as direct indicators of the resilient modulus susceptibility to changes in water content.The results showed that the percentage of fractured coarse aggregates particles(FR)has a more significant impact on the resilient modulus(Er)of crushed granular materials used in pavement construction than the combined indicator of the fines content and sample volumetrics(nf).Crushed granular materials with a higher percentage of fractured coarse aggregates are relatively insensitive to changes in the degree of saturation,but become more sensitive as the fine fraction porosity decreases.An adjusted model was proposed based on the existing formulation,but considers a complex parameter to describe and adjust the sensitivity of base granular materials to variations in moisture content with respect to fabrication charac-teristics,fines content and volumetric properties.The model shows that the variation of Er values is below10%for fully crushed granular materials.However,it reaches approximately±12%for materials with 75%of crushed coarse aggregates andþ40%and-25%for materials with FR=50%.This model could help select good ag-gregates characteristics and adjust grain-size distribution for environments where significant moisture content variations can occur in the pavement system,such as in the Province of Quebec(Canada).As it is based on pa-rameters that can be easily determined or estimated,it also represents a valuable tool for detailed design and analysis that can consider material characteristics.

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.

Integrated Computational Materials Engineering for the Development and Design of High Modulus Al Alloys

Integrated computational materials engineering(ICME)is to integrate multi-scale computational simulations and key experimental methods such as macroscopic,mesoscopic,and microscopic into the whole process of Al alloys design and development,which enables the design and development of Al alloys to upgrade from traditional empirical to the integration of compositionprocess-structure-mechanical property,thus greatly accelerating its development speed and reducing its development cost.This study combines calculation of phase diagram(CALPHAD),Finite element calculations,first principle calculations,and microstructure characterization methods to predict and regulate the formation and structure of composite precipitates from the design of highmodulus Al alloy compositions and optimize the casting process parameters to inhibit the formation of micropore defects in the casting process,and the final tensile strength of Al alloys reaches420 MPa and Young's modulus reaches more than 88 GPa,which achieves the design goal of the high strength and modulus Al alloys,and establishes a new mode of the design and development of the strength/modulus Al alloys.

Zeta Potential of Aggregate and Dynamic Modulus of HMA Estimation Using Aggregate Silica Content

The mineralogical composition of an aggregate influences its adhesion with bitumen and therefore its dynamic modulus. However, few studies have been conducted on this aspect. One of the most used properties to describe the impact of aggregate on the adhesiveness phenomena is the zeta potential. In this study, the first mineralogical and chemical properties were considered through the percentage of silica in the rock source of aggregates and the electric aggregate particles charge zeta. Dynamic modulus values used for regression process are determined from complex modulus test on nine asphalt concretes mix designed with aggregate types (basalt of Diack, quartzite of Bakel and Limestone of Bandia). The results showed that aggregate with high percentage of silica have higher zeta potential than aggregate with low percentage of silica. The development of a zeta potential predictive model showed a strong sensitivity to silica. The results of the complex modulus tests showed that Hot Mixture Asphalt (HMA) mixed with aggregate containing high silica contents gave better results than those mixed with aggregates containing low percentage of silica. The dynamic modulus predictive models of HMA developed shows that it is the properties of bitumen that influence more. However, the effect of silica although low, is very marked at low temperatures and high frequencies.

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.

Prediction of a superhard material of ReN_4 with a high shear modulus

Using first-principles calculations, this paper systematically investigates the structural, elastic, and electronic properties of ReN4. The calculated positive eigenvalues of the elastic constant matrix show that the orthorhombic Pbca structure of ReN4 is elastically stable. The calculated band structure indicates that ReN4 is metallic. Compared with the synthesized superhard material WB4, it finds that ReN4 exhibits larger bulk and shear moduli as well as a smaller Poisson＇s ratio. In addition, the elastic constant c44 of ReN4 is larger than all the known 5d transition metal nitrides and borides. This combination of properties makes it an ideal candidate for a superhard material.

EFFECTS OF TEMPERING TEMPERATURE AND TIME ON SHEAR MODULUS OF Fe-Mn BASED ALLOYS

Effects of the tempering temperature and time on the shear modulus of Fe-Mn based alloys have been studied.The results show that(ΔG/G)-Tcurves of tempered alloys containing Cr and Ti have two extreme values—maximum and minimum,and that the curves of tem- pered alloys containing Cr,Ni,W and C only have a maximum value.This is the reason that Ni,W and C decrease the transformation point T_N of the antiferromagnetism.The ΔG_λ ef- feet increases gradually with the rise of tempering temperature or with the increase of tem- pering time.

SPLITTING MODULUS FINITE ELEMENT METHOD FOR ORTHOGONAL ANISOTROPIC PLATE BENGING

Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill-conditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.

AN ANALYTICAL SOLUTION TO LONGITUDINAL VIBRATION OF A PILE OF ARBITRARY SEGMENTS WITH VARIABLE MODULUS

The vibration problem of a pile of arbitrary segments withvariable modulus modules under ex- citing force is established, inwhich the influence of the soil under pile toe and the surroundingsis tak- en into account. With Laplace transforms, the transmitfunctions for velocity and displacement of pile are derived.Furthermore, in terms of the convolution theorem and inversed Laplacetransform, an analytical solution for the time domain response of apile subjected to semi-sine impulse is developed, which is thetheoretical basis of the sonic method in pile integrity testing. Basedon the solution, the vibration properties of pile with sharp orcontinuous modulus are studied. The validity of this approach isverified through field dynamic tests on some engineering piles. Itshows that the theoretical predic- tion ad the response of the pileare in good agreement.

ELASTIC MODULUS REDUCTION METHOD FOR LIMIT LOAD EVALUATION OF FRAME STRUCTURES

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

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

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

Dynamic shear modulus of undisturbed soil under different consolidation ratios and its effects on surface ground motion

The dynamic shear modulus for three types of undisturbed soil under different consolidation ratios is presented by using the resonant column test method. Its effects on surface ground motion is illustrated by calculation. The test results indicate that the power function is a suitable form for describing the relationship between the ratio of the maximum dynamic shear modulus due to anisotropic and isotropic consolidations and the increment of the consolidation ratio. When compared to sand, the increment of the maximum dynamic shear modulus for undisturbed soil due to anisotropic consolidation is much larger. Using a one-dimensional equivalent linearization method, the earthquake influence factor and the characteristic period of the surface acceleration are calculated for two soil layers subjected to several typical earthquake waves. The calculated results show that the difference in nonlinear properties due to different consolidation ratios is generally not very notable, but the degree of its influence on the surface acceleration spectrum is remarkable for the occurrence of strong earthquakes. When compared to isotropic consolidation, the consideration of actual anisotropic consolidation causes the characteristic period to decrease and the earthquake influence factor to increase.

A method to determine Young's modulus of soft gels for cell adhesion

A convenient technique is reported in this note for measuring elastic modulus of extremely soft material for cellular adhesion. Specimens of bending cylinder under gravity are used to avoid contact problem between testing device and sample, and a beam model is presented for evaluating the curvatures of gel beams with large elastic deformation. A self-adaptive algorithm is also proposed to search for the best estimation of gels＇ elastic moduli by comparing the experimental bending curvatures with those computed from the beam model with preestimated moduli. Application to the measurement of the property of polyacrylamide gels indi- cates that the material compliance varies with the concentrations of bis-acrylamide, and the gels become softer after being immersed in a culture medium for a period of time, no matter to what extent they are polymerized.

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.

Effects of confinement on rock mass modulus:A synthetic rock mass modelling(SRM) study

The main objective of this paper is to examine the influence of the applied confining stress on the rock mass modulus of moderately jointed rocks（well interlocked undisturbed rock mass with blocks formed by three or less intersecting joints）. A synthetic rock mass modelling（SRM） approach is employed to determine the mechanical properties of the rock mass. In this approach, the intact body of rock is represented by the discrete element method（DEM）-Voronoi grains with the ability of simulating the initiation and propagation of microcracks within the intact part of the model. The geometry of the preexisting joints is generated by employing discrete fracture network（DFN） modelling based on field joint data collected from the Brockville Tunnel using LiDAR scanning. The geometrical characteristics of the simulated joints at a representative sample size are first validated against the field data, and then used to measure the rock quality designation（RQD）, joint spacing, areal fracture intensity（P21）, and block volumes. These geometrical quantities are used to quantitatively determine a representative range of the geological strength index（GSI）. The results show that estimating the GSI using the RQD tends to make a closer estimate of the degree of blockiness that leads to GSI values corresponding to those obtained from direct visual observations of the rock mass conditions in the field. The use of joint spacing and block volume in order to quantify the GSI value range for the studied rock mass suggests a lower range compared to that evaluated in situ. Based on numerical modelling results and laboratory data of rock testing reported in the literature, a semi-empirical equation is proposed that relates the rock mass modulus to confinement as a function of the areal fracture intensity and joint stiffness.

Application of numerical modeling and genetic programming to estimate rock mass modulus of deformation

Estimation of the rock mass modulus of deformation(Em)is one of the most important design parameters in designing many structures in and on rock.This parameter can be obtained by in situ tests,empirical relations between deformation modulus and rock mass classifcation,and estimating from laboratory tests results.In this paper,a back analysis calculation is performed to present an equation for estimation of the rock mass modulus of deformation using genetic programming(GP)and numerical modeling.A database of 40,960 datasets,including vertical stress(rz),horizontal to vertical stresses ratio(k),Poisson’s ratio(m),radius of circular tunnel(r)and wall displacement of circular tunnel on the horizontal diameter(d)for input parameters and modulus of deformation for output,was established.The selected parameters are easy to determine and rock mass modulus of deformation can be obtained from instrumentation data of any size circular galleries.The resulting RMSE of 0.86 and correlation coeffcient of97%of the proposed equation demonstrated the capability of the computer program(CP)generated by GP.

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

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

Elastic modulus 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.