Equivalent Elastic Modulus Research Articles

Elastic response of anisotropic Gyroid cellular structures under compression: Parametric analysis

Triply periodic minimal surface (TPMS) isidentifiedas a suitable model for designing porous structures. Gyroid cellular structure (GCS) is the most widely studied type of TPMS structure. The majority of previous studies on GCS have focused on its isotropic structure. However, as a potential candidate for bone repair, anisotropic structures need to be considered. This study presented a strategy to control the anisotropy of GCS by changing its geometrical parameters. The finite element method was subsequently applied to determine the elastic response of anisotropic GCS under compression. The degree of anisotropic (DA) of GCS was evaluated in terms of the ratio of equivalent elastic modulus in vertical and horizontal directions. Within the parameters considered, the DA of GCS varied from 0.17 to 3.6, as compared with 0.2 to 4 for human bones. The main factors affecting the anisotropic elastic response of GCS were structure anisotropy, porosity, and loading direction. The elastic modulus of the anisotropic GCS was in the range 0.03 to 5.6GPa for titanium alloy, as compared with 0.1 to 4.5GPa for human trabecular bone. Combining the porosity and anisotropic models of GCS can offer a scaffold that matches closely the human bone mechanical environment.

Energy harvesting of sandwich beam with laminated composite core and piezoelectric face sheets under external fluid flow

In the present study, the generation of electrical energy from induced vibrations in a composite beam with piezoelectric layer are studied. Accordingly, using Euler-Bernoulli beam theory and considering two types of air damping (external damping) and structural damping (internal damping), the equations of motion for sandwich beam are obtained and then using the Kantorovich method, the output voltage relations for a composite beam with a piezoelectric layer are extracted. After validating the analytical results with the results in the literature, the effect of various parameters such as external fluid flow rate, fiber angle, and how the piezoelectric layer composite beams are arranged on energy harvesting. Also, the maximum oscillation amplitude are investigated. The results show that by using composite materials and with proper layer design and fiber angle in each layer, a different equivalent modulus of elasticity can be created in the composite beam, which will change the normal frequency of the system and the output voltage range of the circuit. The results show that the angle of the fibers has a significant effect on the damping coefficient of the structure, flexural stiffness, natural frequency and finally energy harvesting. According to the results, it can be seen that the minimum value of voltage per use of fibers with an angle of 50 degrees and the maximum amount of voltage per use of fibers with an angle of zero degrees are occurred.

Mechanical behaviour of 2D hybrid structure fabricated by doping graphene with triangular h-BN cells

A two dimensional (2D) hybrid structure has been fabricated by doping graphene with hexagonal boron nitride (h-BN) cells. Substantial changes are expected as carbon-carbon (C) bonds are substituted by B–N bonds and C–B and C–N bonds are formed between the BN cells and graphene. In this paper, molecular dynamics simulations are performed to explore the tensile behaviour and fracture mechanisms of the 2D HS, and reveal how and to what extent the BN cells impact its overall tensile properties. A comprehensive study of free boundary effects is also conducted for the first time for 2D materials. Herein, the 2D nonlinear elastic constitutive relation has been formulated in terms of the equivalent elastic modulus Ye that decreases almost linearly with BN content α due to the distinct elastic properties between B–N bonds and C–C bonds. The downward trend of the fracture stress with growing α is also achieved due to the α− dependence of Ye and the limit on the fracture strain imposed by the newly formed C–B bonds. In addition, evidence has been accumulated showing that the free boundaries can significantly decrease the elastic moduli and fracture stress but largely enhance the fracture toughness of the 2D nanosheets.

Modeling, simulation, and experimental verification on material removal and rounding process of centerless cylindrical finishing with free abrasives and soft pad

In this paper, the centerless finishing process using free abrasives and soft pad was developed and applied in fine machining the bearing cylindrical roller of AISI 52100 steel on self-made machine, improving roundness and its deviation on roller’s circular profile. A novel modeling and simulation method of material removal and rounding process for cylindrical workpiece was proposed in three-body abrasive wear pattern, combining geometry, kinematics, elastic contact, and single grain’s micro-cutting. The equivalent elastic modulus of roller and pad in contact is a key parameter for simulation, and its value was obtained through loading experiment and data processing. The finishing simulation and experiments were carried out under different loading forces. Their diameter’s results are in good agreement, and roundness’s results are in considerable agreement with error of less than 7%, demonstrating the validity of modeling and simulation method. Through data processing and analysis, it is indicated that the roundness is improved obviously; but with a slight material removal rate, the effect of loading force on roundness is greater than that of material removal. The reasons for above results are analyzed and discussed, taking into account three-body elastic contact, contact area and depth, and number of abrasive grains in finishing region.

The Equivalent Modulus of Elasticity of Soil Mediums for Designing Shallow Foundations

As known, in a Winkler type of analysis the soil medium underneath the foundation is violently replaced by a row of parallel springs having constant ks. For the effective calculation of the latter, which is called the modulus of subgrade reaction, the two elastic constants of the soil (the elastic modulus, E and the Poisson’s ratio, ν) must be known. Although for homogenous soils this generally seems not to be a problem, the same does not stand for stratified mediums or mediums with linearly increasing modulus with depth. In addition, in a Winkler type of analysis, the proper pair of elastic constant values of soil should be selected. This refers to a Poisson’s ratio value equal to zero corresponding to the deformation pattern of springs (compression with no lateral expansion) and the respective modulus. In the present paper a method for calculating the equivalent elastic constants for the above mentioned mediums is proposed based on the theory of elasticity combining the principle of superposition. Various cases are considered, since the equivalent modulus, Eeq, depends on the rigidity and the shape of the footing. As shown, the derived Eeq values not only return reliable settlement results, but also settlement profiles that are similar to those corresponding to the original soil mediums.

Accounting of Damage of Asphalt Concrete in the Criteria for Calculating the Pavement

The aim of the article is to develop a general method for accounting for the accumulation of damage in asphalt concrete when calculating pavement according to strength criteria. The article analyzes the methods of calculating pavement according to the criteria: elastic deflection, resistance of the asphalt concrete to tensile bending, and shear resistance in the soil of subgrade. It is established that at present the fatigue of materials is taken into account by mathematical functions that connect the strength parameters of asphalt concrete with the number of applied loads. However, there is no single solution that take into account the effect of damage of asphalt concrete in the pavement on stresses and deformations that occur in the pavement and other layers of pavement. It is proposed to use the principle of equivalent deformation of a damaged and undamaged body to calculate the damage of asphalt concrete. In accordance with the formula of this principle, the elastic modulus decreases with increasing damage. The resulting formula allows to calculate the modulus of elasticity of the upper layer of a two-layer system when calculating pavement according to the criteria of coating resistance to tensile from bending and shear in the soil of subgrade. The same formula allows us to calculate the equivalent elastic modulus of a two-layer system. Thus, the proposed calculation method contains one general approach to accounting for damage accumulation in all three criteria for calculating pavement on strength.

An experimental and theoretical study of the cyclic contact behaviour for rock sphere

Improved knowledge of cyclic contact behaviour of brittle particle can deepen the understanding of cyclic behaviour of brittle particle assembly and help to obtain more realistic numerical simulations. The cyclic compression tests of rock spheres were performed and the results were analyzed through elastoplastic contact theory. Three modified contact models and a semi-theoretical cyclic contact model were proposed. Local plastic deformation and macroscopic tensile cracks were observed. The cyclic compression tests reveal the significant difference of cyclic contact behaviour between the first cycle and the subsequent cycles. The modified Kogut and Etsion loading model and modified Etsion unloading model perfectly agree with the experimental force-displacement curve of the first cycle. The equivalent modulus of elasticity increases with the increasing number of cycle and decreases with the increasing maximum contact force. All the main characteristic of cyclic contact behaviour can be well reproduced by the proposed semi-theoretical cyclic contact model

General Statistics-Based Methodology for the Determination of the Geometrical and Mechanical Representative Elementary Volumes of Fractured Media

The upscaling of mechanical properties of fractured media requires the definition of an appropriate size for the Representative Elementary Volume (REV). Because of the stochastic nature of the fracture networks, the REV size is not deterministic and should be defined based on the variability of the equivalent properties. This work presents a new general methodology to define the size of the REV for the geometrical and elastic moduli of fractured media. Following previous works on heterogeneous materials, the decision criterion is based on the precision error that arises from the statistical theory of samples. The proposed methodology also relies on the use of the Central Limit Theorem (CLT) to assess the REV of fractured rocks. The CLT is shown to theoretically apply to both the geometrical and the elastic equivalent properties. From that observation, a general equation is drawn to predict the variance of an equivalent property for any REV candidate size, provided that the variance for one size only is known. These concepts are tested using numerous finite element simulations to obtain the distribution of the equivalent elastic moduli of two-dimensional samples containing two fracture networks previously studied for their elastic properties. These properties are confirmed to tend to a normal distribution, as stated by the CLT. Also, the standard deviations associated with the tested REV sizes were predicted with accuracy from the standard deviation obtained in the numerical simulations of only one proper reference volume. The mechanical REV was compared with the geometrical REV, which is based on the first invariant of the fracture tensor. In addition, to reduce computational costs, a procedure to reduce the number of simulations of the reference volume was proposed. A preliminary verification of the applicability of the methodology to non-elastic problems was made. Proper predictions were obtained for the standard deviation of the compression strength calculated in two studies that considered, altogether, both two-dimensional and three-dimensional samples, as well as plastic and damage models.

Fatigue life assessment method of in-service mechanical structure

The most usual failure mode of any mechanical structure is fatigue, which is characterized by an important feature of the decrease of elastic modulus of the material. In this paper, a fatigue life evaluation model based on equivalent elastic modulus is proposed for in-service mechanical structure. In the proposed model, parameters that represent the operating conditions of the mechanical structure, such as load, vibration, and shaft torque, etc., are used as the generalized load. To replace the fatigue stress, the statistical method is used here, which is also used in the conventional fatigue analysis method. The structural strain is also measured simultaneously. Using the statistical theory, the equivalent modulus of elasticity is formulated based on the relationship of stress, strain, and modulus of elasticity. To validate the proposed model, an online fatigue damage experiment has been conducted. The experimental results have been compared with that of the fatigue life prediction model with good agreement. It is expected that the methodology proposed in this paper will be widely used.

Approximate calculation of the static analysis of a lifted stay cable in super-long span cable-stayed bridges

The sag effect of long stay cables is one of the key factors restricting further increase in the span of cable-stayed bridges. Based on the formerly proposed concept of long stay cables lifted by an auxiliary suspension cable in cross-strait cable-stayed bridges, corresponding static approximate calculations and analytical theory based on catenary and parabolic cable configurations are established. Taking a main span 1400 m cable-stayed bridge as the research object, three typical lifting conditions and the whole process of auxiliary cable lifting are analyzed and discussed. The results show that the sag effect is effectively reduced. The support efficiency is only improved when the cables are lifted above the original cable chord. Reduction of the horizontal component force of the cable is limited. The equivalent elastic modulus and the vertical support stiffness of the lifted cables are significantly increased with increased horizontal projection length and not sensitive to the change of the lifting point position. The scheme of lifting the cable to the chord midpoint is more economical because of the less steel required for the auxiliary suspension cable, but its effect on improving the vertical support efficiency is limited. The support efficiency is better when the cable is lifted to the cable end tangential to the original cable chord, but the lifting force and the cross-sectional area of the auxiliary suspension cable are doubled. The approximate calculation results of the lifted cables are very close to the numerical analysis results, which verifies the applicability of the approximation method proposed in this study. The results of parabolic approximation calculations are approximately equal to that of catenary cable geometry. As the parabolic approximation analysis theory of lifted cables is more convenient in mathematical processing, it is feasible to use parabolic approximation analysis theory as the analytical method for the conceptual design of lifted cables of super-long span cable-stayed bridges.

Dependences of Degradation of Long-Term Monitored Pavement from the Perspective of the Diagnosed Bearing Capacity

A necessary condition for the functioning of the road management system is the existence of a database of data from repeated measurements of selected roads on their technical parameters on the road network. The general designation - data means in particular invariable and variable technical parameters of roads, which are necessary for the evaluation of operational capability and condition of road structures. In the article, the authors deals with the analysis of two reference parameters of the pavement in relation to their degradation, namely the parameter Equivalent modulus of elasticity, and the curvature index of the road surface.

Analytical calculation method for the axial equivalent elastic modulus of laminated FRP pipes based on three dimensional stress state

In engineering design, the axial equivalent elastic modulus of laminated FRP pipe was mostly calculated by the average elastic modulus method or the classical laminated plate theory method, which are based on relatively simplified assumptions, and may be not accurate enough sometimes. A new analytical calculation method for the axial equivalent elastic modulus of laminated FRP pipe was established based on three-dimensional stress state. By comparing the results calculated by this method with those by the above two traditional analytical methods and the finite element method, it is found that this method for the axial equivalent elastic modulus fits well not only for thin-walled pipes with orthotropic layers, but also for thick-walled pipes with arbitrary layers. Besides, the influence of the layer stacking on the axial equivalent elastic modulus was studied with this method. It is found that a proper content of circumferential layer is beneficial for improving the axial equivalent elastic modulus of the laminated FRP pipe with oblique layers, and then can reduce its material quantity under the premise that its axial stiffness remains unchanged. Finally, the meso-mechanical mechanism of this effect was analyzed. The improving effect of circumferential layer on the axial equivalent elastic modulus of the laminated FRP pipe with oblique layers is mainly because that, the circumferential fibers can restrain the rigid body rotations of the oblique fibers, which tend to cause the significant deformations of the pipe wall units and the relatively low axial equivalent elastic modulus of the pipe.

The buckling behavior of single-layer MoS2 sheets with kirigami-inspired structures under compression

The buckling behavior of single-layer MoS2 sheets under both uniaxial and biaxial compression is studied in the present paper. The critical strain, critical stress, equivalent elastic modulus as well as post-buckling morphologies are comprehensively studied. It is found that both the critical stress and equivalent elastic modulus of SLMoS2 sheets with kirigami-inspired structures are reduced significantly compared with perfect ones. The geometric parameters of kirigami-inspired structures in armchair and zigzag directions have different effects on the compressive behavior of SLMoS2 sheets. SLMoS2 sheets that sustain more strain could be realized by introducing kirigami-inspired structures. What is more, a desired post-bulking morphology can be obtained by properly tuning kirigami-inspired structures. The results should be helpful for various practical and potential applications of the new 2D material.

The unique carrier mobility of Janus MoSSe/GaN heterostructures

Heterostructure is an effective approach in modulating the physical and chemical behavior of materials. Here, the first-principles calculations were carried out to explore the structural, electronic, and carrier mobility properties of Janus MoSSe/GaN heterostructures. This heterostructure exhibits a superior high carrier mobility of 281.28 cm2·V−1·s−1 for electron carrier and 3951.2 cm2·V−1·s−1 for hole carrier. Particularly, the magnitude of the carrier mobility can be further tuned by Janus structure and stacking modes of the heterostructure. It is revealed that the equivalent mass and elastic moduli strongly affect the carrier mobility of the heterostructure, while the deformation potential contributes to the different carrier mobility for electron and hole of the heterostructure. These results suggest that the Janus MoSSe/GaN heterostructures have many potential applications for the unique carrier mobility.

Vibration Characteristics Analysis and Experimental Study of Carbon-Fiber Reinforced Plastic-Metal Hybrid Drive Shaft

Carbon-Fiber-Reinforced Plastic (CFRP) has several advantages, such as light weight, high strength, small thermal expansion coefficient and high damping ratio. The CFRP-metal hybrid drive shaft is taken as the study object to analyze its vibration characteristics. The laminate mode of the CFRP shaft tube is designed as [±15°3/ ±45° / ± 88° / ±88° / ±45° / ± 15°3 /88°]s, and the equivalent elastic modulus, equivalent shear modulus and modal damping of the CFRP shaft tube can be obtained by theoretical calculation. The change rule of the torsional vibration angle for the CFRP shaft tube is obtained by the finite-element analysis. Furthermore, the same bending vibration and torsional vibration are measured for the CFRP-metal hybrid drive shaft and the metal drive shaft using an acceleration sensor. The measured first-order bending resonance speed of the hybrid drive shaft is 1094.64 r/min, and its resonance amplitude is 0.118 mm. The measured first-order bending resonance speed of the metal drive shaft is 1,298.2 r/min, and its resonance amplitude is 0.21 mm. The maximum torsional vibration stress of the CFRP shaft tube is 330.0733 Mpa, which is far higher than the maximum torsional vibration stress (125.99 Mpa) of the metal drive shaft. It can be seen that the CFRP drive shaft has higher resistance to bending, torsion and vibration than the metal drive shaft.

Natural Frequency Response Evaluation for RC Beams Affected by Steel Corrosion Using Acceleration Sensors.

This paper presented a laboratory investigation for analyzing the natural frequency response of reinforced concrete (RC) beams affected by steel corrosion. The electrochemical acceleration technique induced the corroded RC beams until the predetermined value of the steel corrosion ratio was achieved. Then, the natural frequency responses of the corroded beams were tested utilizing piezoelectric acceleration sensors. The damage states of the corroded beams were assessed through the measurement of crack parameters and the equivalent elastic modulus of the beams, which aims to clarify the fundamental characteristics of the dynamic response for the corroded RC beam with the increased steel corrosion ratio. The results revealed that steel corrosion reduces the bending stiffness of the RC beams and, thus, reduces the modal frequency. The variation of natural frequency can identify the corrosion damage even if no surface cracking of the RC beam, and the second-order frequency should be more indicative of the damage scenario. The degradations of stiffness and the natural frequency were estimated in this study by the free vibration equation of a simply supported beam, and a prediction method for the RC beam’s residual service life was established. This study supports the use of variations in natural frequency as one diagnostic indicator to evaluate the health of RC bridge structures.

A novel observation method for determining the crack stress thresholds of rock based on Hooke's law

AbstractThe crack stress thresholds of rocks have remained a focus in rock mechanics and engineering. Herein, a novel observation method uses Hooke's law to evaluate crack stress thresholds based on transition points in the equivalent elastic modulus. Unlike previous studies, this method considers confining pressure as a variable and involves a differential method to handle the variation of discrete data. To test the method, we compare it with the volumetric strain method and another observation method with respect to the crack stress thresholds of sandstone and granite. The results are within the boundary values presented in the literatures. For the sandstone and granite samples, the proposed method performs better than the other two methods. In summary, the results indicate that the proposed method can be practically applied with that a promising performance. In the future, we will further improve the method by considering more types of rocks with various confining pressures.

Mechanical and failure characteristics of fissured marble specimens under true triaxial compression: Insights from 3-D numerical simulations

In this study, 3-D particle-based discrete element methodology (DEM) is applied to investigate the mechanical and failure characteristics of fissured marble specimens in true triaxial compression with a new loading stress path. The new loading stress path is controlled by two loading parameters: the initial confining pressure σ0 and the loading stress ratio b. In the numerical investigation, eighty-eight numerical fissured marble specimens are designed based on fissure arrangements, such as the fissure length 2a, fissure inclination angle α, fissure ligament length 2L, loading stress ratio b and initial confining pressure σ0. The mechanical properties, including the peak strength and effective elastic modulus, and the associated failure characteristics are quantitatively analyzed. Three different ultimate failure modes of the fissured marble specimens in true triaxial compression are summarized by numerical simulations. Numerical results indicate that the peak strength and equivalent elastic modulus are enhanced with increases in the loading stress ratio and initial confining pressure. It can be found from the numerical results that the influence of the initial confining pressures is more significant. The present numerical investigations on fissured marble specimens under true triaxial compression can provide a deep understanding of mechanical and failure behaviors of rock masses in underground construction.

Vibration Analysis of Piezoelectric Cantilever Beams with Bimodular Functionally-Graded Properties

Piezoelectric materials have been found to have many electromechanical applications in intelligent devices, generally in the form of the flexible cantilever element; thus, the analysis to the corresponding cantilever is of importance, especially when advanced mechanical properties of piezoelectric materials should be taken into account. In this study, the vibration problem of a piezoelectric cantilever beam with bimodular functionally-graded properties is solved via analytical and numerical methods. First, based on the equivalent modulus of elasticity, the analytical solution for vibration of the cantilever beam is easily derived. By the simplified mechanical model based on subarea in tension and compression, as well as on the layer-wise theory, the bimodular functionally-graded materials are numerically simulated; thus, the numerical solution of the problem studied is obtained. The comparison between the theoretical solution and numerical study is carried out, showing that the result is reliable. This study shows that the bimodular functionally-graded properties may change, to some extent, the dynamic response of the piezoelectric cantilever beam; however, the influence could be relatively small and unobvious.

Stress-orientation effects on the effective elastic anisotropy of complex fractured media using the lattice spring models coupled with discrete fracture networks model

Stresses oriented differently often cause azimuthal anisotropy in the effective elastic properties of sedimentary rocks. A quantitative analysis of stress-orientation effects is important to interpret the anisotropic characteristics of mechanical and sonic responses. Brazilian tests are conducted to numerically investigate the stress orientation dependence in complex fractured media. We have developed a consistent workflow of lattice spring models (LSMs) coupled with discrete fracture networks (DFNs). This LSM-DFN model could enable a highly accurate modeling by properly choosing reasonable meshing resolutions, damping values, and strain loading rates. Numerical experiments demonstrate that the angle between the preferred azimuth of cracks and the orientation of the loading stress significantly affect the equivalent elastic moduli. The stress-induced anisotropy of cracked media could be reflected by the tendency of stress-strain responses. LSM-DFN modeling of prestressed cracks has the potential for reconstructing realistic structural attributes and analyzing stress-orientation effects.