Linear Elastic Properties Research Articles

A mathematical formulation to find effective bulk and shear moduli of recycled aggregate concrete

A mathematical formulation incorporating a compatible 6-phase model is proposed and implemented to find the homogenized linear elastic properties of recycled aggregate concrete (RAC) in terms of its effective bulk and shear moduli. The model comprises of five concentric spherical shells to represent new matrix, new Interfacial Transition Zone (ITZ), old matrix, old ITZ and the core raw aggregate embedded in equivalent homogenous medium by following generalized self-consistent scheme. The model is built on the primary assumption that RAC is made of only recycled aggregates, which are described by spherical inclusions of constant volume fraction and constant radii ratios of the constituent phases. Cauchy equilibrium equations and compatibility conditions are made use of to frame the relation between the variables at the constituents’ interface, while Eshelby’s energy equivalence is applied for solution. Validation is done by following an indirect approach, according to which the characteristic constituents of RAC – the old ITZ and old matrix – are forced to take relatively negligible values and by comparing the predicted values with those of experiments corresponding to normal aggregate concrete. Further, a parametric study is carried out for quantification of the effect of attached mortar (includes old matrix and old ITZ) and new ITZ on the elastic properties of RAC. This first attempt on analytical prediction of the effective elastic properties of RAC yields enough information to make judicious decision on the means – either remove attached mortar or improve new ITZ – to arrive at a design mix of RAC.

In-plane anisotropy of selective laser-melted stainless steel: The importance of the rotation angle increment and the limitation window

The thorough description of the influence of the process conduct in powder-bed-based additive manufacturing on the mechanical properties of the fabricated components represents an ongoing challenge. A recent investigation highlighted that a minor safety feature, such as limiting the range of possible laser beam movements, to avoid interactions between the irradiation and emerging smoke and weld splashes, can cause a noteworthy alteration of the mechanical properties. In this study, the tensile characteristics of selective laser-melted stainless steel (1.4404, 316L) fabricated with two different process conducts were investigated, both of which yielded similar relative densities and surface hardness values. It was found that, besides these two characteristics, the tensile strength (yield and ultimate tensile strength) remained stable, whereas the linear elastic properties, as well as the breaking elongation, exhibited great fluctuations. The Young's modulus in the build-plane ranged from 151 to 208 GPa, and the breaking elongation ranged, respectively, from 33% to 43%. Furthermore, it has been found that this anisotropy is an adjustable characteristic and can be modified via two parameters, the rotation angle increment of the irradiation pathways between successive layers and their total admissible range, also referred to as the limitation window.

Comparative study of the effects of three tunneling methods on ground movements in stiff clay

This paper interprets ground movements induced by tunnel construction, by comparing monitoring data with analytical and numerical predictions based on an assumed set of deformation parameters at the cavity boundary. By minimizing differences between the computed and measured ground movements, optimal cavity deformation parameters can then be used to characterize the performance of the tunneling process. We compare the performance of three tunnel construction methods in stiff clay: (i) closed-face excavation using an Earth Pressure Balance (EPB) tunnel boring machine; (ii) open-face shield excavation; and (iii) sequential construction using the New Austrian Tunneling Method (NATM). The measured data were obtained from three projects in London each involving different tunnel size and depth, but all excavated through deep units of stiff London clay. The measured performance in each case is evaluated using analytical solutions, that assume linear elastic properties for an elastic half-space, and numerical simulations that use an effective stress soil model, MIT-S1, with input parameters calibrated to elemental behavior of the London Clay. Although the numerical analyses achieve better agreement with the measured data, the analytical solutions perform well and could be used in future studies. The results indicate that the closed-face tunneling provided the best control of volume loss, while open-face shield excavation caused the largest ovalization of the tunnel cavity. The proposed methodology offers a practical framework for cataloging and comparing tunnel performance in future projects.

High concentration ratio approximation of linear effectiveproperties of materials with cubic inclusions

This paper establish a high concentration ratio approximation of linear elastic properties of materials with periodic microstructure with cubic inclusions. The approximation is derived using first few terms of power series expansion of the solution of the equivalent eigenstrain problem with a homogeneous eigenstrain approximation. Viability of the approximation at high concentration ratios is proved by comparison with a numerical solution of the homogenization problem. To this end some theoretical result of symmetry properties of the homogenization problem are given. Using these results efficient numerical computation on a reduced computational domain is presented.

Linear and nonlinear elastic properties of isostatic graphite and graphite of MPG-7 brand

The paper presents the results of experimental studies of linear and nonlinear elastic properties of isostatic graphite and graphite of MPG-7 brand. In samples of isotropic structural graphite having the shape of a rectangular parallelepiped, the velocities of longitudinal and shear elastic waves and their dependence on the uniaxial compression of the sample under study were measured. Based on the results of these measurements, independent components of the second-order elasticity tensor in the samples were determined. The acoustoelastic effect in structural graphite was studied. The Thurston-Brugger method was used to calculate the independent components of the third-order elasticity tensor in samples of isostatic graphite and graphite of MPG-7 brand.

Derivation of closed-form solution for linear elastic properties of swollen elastomers

Derivation of closed-form solution for linear elastic properties of swollen elastomers

Mechanical behavior of ballasted railway track stabilized with polyurethane: A finite element analysis

Analysis of mechanical behavior of ballast shoulder of railway track reinforced by polyurethane binding agent has been performed by the method of finite-element simulation Limitation of the model of linear-elastic properties of geocomposite has been displayed. Dependence of elasticity modulus of geocomposite on deformation value has been suggested. Influence of penetration depth of polyurethane binding agent on behavior of railway track construction under different train loads has been studied.

Mean and full field homogenization of artificial long fiber reinforced thermoset polymers

AbstractBased on two artificial microstructures representing a long fiber reinforced thermoset material, the effective linear elastic material properties are calculated by both a mean and a full field homogenization method. Concerning the mean field method, the effective elastic material properties are approximated using the homogenization scheme by Mori and Tanaka, formulated explicitly in terms of orientation averages. This allows to use orienation tensors of 2nd and 4th order describing the orientation information on the micro level. The full field method is based on the fast Fourier transformation (FFT), for which the effective material properties are determined by volume averaging. The comparison between both methods show good agreements, the deviations are in the range between 2% and 12%. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A 3D finite element modelling of crystalline anisotropy in rolling contact fatigue

Rolling contact fatigue (RCF) is one of the primary modes of failure in bearings and in this study it is hypothesized and demonstrated that RCF is strongly influenced by inhomogeneity in polycrystalline material microstructure. This paper presents a three-dimensional modeling approach to include the effects of microstructure topology and material anisotropy in a polycrystalline microstructural bearing steel subject to RCF loading. A randomly generated 3D Voronoi tessellation is used to represent the microstructural topology of the material. A cubic material definition with random spatial orientation is specified for the material grains to simulate the polycrystalline anisotropy. The size of the RVE was chosen such that it represented the macroscopic linear elastic material properties of a polycrystalline aggregate. The semi-infinite domain is then subjected to a moving Hertzian pressure to simulate a load cycle. Due to inhomogeneity in the polycrystalline material local stress risers occur at the grain boundaries, however, in general, the locations of the maximum shear stresses compare well to the experimental RCF results readily available in literature. Elemental shear stresses averaging scheme was employed to illustrate that the finite element model is mesh independent. The estimated fatigue life scatter obtained from the inhomogeneous polycrystalline material model corroborates well with the fatigue life scatter obtained from the RCF experiments.

The Construction of Nonlinear Elasticity Tensors for Crystals and Quasicrystals

The problem of construction of constitutive relations in nonlinear elasticity theory for crystals and quasicrystals is associated with finding the construction of the structure of tensors of elastic modules of 2nd and 3rd orders. In the case of linear constitutive relations, the problem is entirely solved for crystals and some quasicrystals. In the case of nonlinear relations, the quantity of nonzero elastic modules of the 3rd order is known only for some classes of crystals. The problem of construction of nonlinear constitutive relations for quasicrystal materials has not been considered. In this article, representations of linear and nonlinear elastic properties of crystals and quasicrystals in the form of decompositions by special invariant tensor bases are considered. This allows us to concretize constitutive relations for icosahedral and axial quasicrystals. It is shown that axial quasicrystals’ behavior towards elastic properties coincides with transversal-isotropic materials. Icosahedral quasicrystals’ behavior matches with the isotropic materials’ one. On the basis of the obtained decompositions of nonlinear elasticity tensors for axial quasicrystals having a symmetry plane and for graphene films with and without defects, the analysis of their mechanical behavior at some types of loading is fulfilled. It is shown that differences in the behavior of these materials appear only in the second order effects.

Mechanical response of SiC sheet under strain

The effect of biaxial strain on crystallographic structure, band gap, polarization, linear and non linear elastic properties of 2D SiC hybrid are studied using ab-initio calculations. The determination of the two critical strain points reveals an elastic region just a little smaller than that of graphene. With load, charge distributions vary and electronic states CBM and VBM undergo a location change. Consequently, enlarging strain reduces the band gap monotonically leading to a semiconductor–metal transition. Debye temperature 407.81K intermediates between the ones of silicene and germanene. Planar SiC shows a piezoelectric response comparable to 2D buckled compounds materials. The negative sign of the effective non linear modulus reveals an hyperelastic softening behavior of SiC. Under pressure, second order elastic constants show a small anisotropie. The results show that tailoring physical properties of SiC under strain reveals its great potential in the electronic and mechanical devices.

Mechanical properties of the human spinal cord under the compressive loading

The spinal cord as the most complex and critical part of the human body is responsible for the transmission of both motor and sensory impulses between the body and the brain. Due to its pivotal role any types of physical injury in that disrupts its function following by shortfalls, including the minor motor and sensory malfunctions as well as complicate quadriplegia and lifelong ventilator dependency. In order to shed light on the injuries to the spinal cord, the application of the computational models to simulate the trauma impact loading to that are deemed required. Nonetheless, it has not been fulfilled since there is a paucity of knowledge about the mechanical properties of the spinal cord, especially the cervical one, under the compressive loading on the grounds of the difficulty in obtaining this tissue from the human body. This study was aimed at experimentally measuring the mechanical properties of the human cervical spinal cord of 24 isolated fresh samples under the unconfined compressive loading at a relatively low strain rate. The stress-strain data revealed the elastic modulus and maximum/failure stress of 40.12±6.90 and 62.26±5.02kPa, respectively. Owing to the nonlinear response of the spinal cord, the Yeoh, Ogden, and Mooney-Rivlin hyperelastic material models have also been employed. The results may have implications not only for understanding the linear elastic and nonlinear hyperelastic mechanical properties of the cervical spinal cord under the compressive loading, but also for providing a raw data for investigating the injury as a result of the trauma thru the numerical simulations.

A multiscale microstructure model of cement paste sulfate attack by crystallization pressure

A recent microstructural model of near-surface external sulfate attack on cement paste is modified to incorporate diffusive ionic transport between the surface and interior of a macroscopic specimen that has been hydrated for 100 d prior to exposure to sulfates. The model estimates the driving force for local expansive growth of the -tri (AFt) phase in terms of crystallization pressure, and the strain and stress fields are tracked within the microstructure with micrometer-scale resolution using a linear elastic finite element model. Damage induced by expansion modifies both the local effective transport properties and linear elastic properties of the local microstructure at different depths, and thereby potentially alters the rates of sulfate ingress and expansion. Therefore, the progress of phase transformations and expansion from the surface to the interior of the porous material is dictated by the rate of ingress of concentration fronts of both sulfate ions and pH, which do not necessarily coincide. The model is used to relate microscopic changes in the structure of cement paste, induced by ingress of sodium sulfate solutions of different concentrations, to the macroscopic expansion, and the results are compared with previous models and published experimental data. The model demonstrates what has previously been assumed in sulfate-attack models, namely that volumetric expansion of macroscopic paste samples in the early stages of sulfate attack is a linear function of the mass of AFt phase precipitated. In addition, the model captures the main features of the evolution of local elastic and transport properties within a macroscopic paste sample, showing an apparently parabolic dependence on depth of the local Young’s modulus and local formation factor.

Prediction of the structural response of the femoral shaft under dynamic loading using subject-specific finite element models

The goal of this study was to predict the structural response of the femoral shaft under dynamic loading conditions using subject-specific finite element (SS-FE) models and to evaluate the prediction accuracy of the models in relation to the model complexity. In total, SS-FE models of 31 femur specimens were developed. Using those models, dynamic three-point bending and combined loading tests (bending with four different levels of axial compression) of bare femurs were simulated, and the prediction capabilities of five different levels of model complexity were evaluated based on the impact force time histories: baseline, mass-based scaled, structure-based scaled, geometric SS-FE, and heterogenized SS-FE models. Among the five levels of model complexity, the geometric SS-FE and the heterogenized SS-FE models showed statistically significant improvement on response prediction capability compared to the other model formulations whereas the difference between two SS-FE models was negligible. This result indicated the geometric SS-FE models, containing detailed geometric information from CT images with homogeneous linear isotropic elastic material properties, would be an optimal model complexity for prediction of structural response of the femoral shafts under the dynamic loading conditions. The average and the standard deviation of the RMS errors of the geometric SS-FE models for all the 31 cases was 0.46 kN and 0.66 kN, respectively. This study highlights the contribution of geometric variability on the structural response variation of the femoral shafts subjected to dynamic loading condition and the potential of geometric SS-FE models to capture the structural response variation of the femoral shafts.

Investigation on statistical characteristics of asphalt concrete dynamic moduli with random aggregate distribution model

Finite element models generating the random aggregate have been used to predict the dynamic moduli of the asphalt concrete materials. The asphalt concrete is modeled as a triphasic medium composed of granular inclusions with linear elastic properties, interfacial transition zone (ITZ) with linear elastic properties, and a porous matrix of bituminous mastics exhibiting linear viscoelastic behavior at small strain level. The predicted complex moduli of asphalt mixes from numerical approach are found close to that from the dynamic modulus tests, resulting in a good agreement. Meanwhile, the size effort of dynamic modulus for asphalt concrete material is investigated through nearly 30,000 times numerical examples, and a theoretical statistic formula for describing the size effort of dynamic modulus is proposed. The simulation results reveal that the theoretical statistic formula provides a suitable description for the size effort of dynamic modulus for asphalt concrete.

Development and validation of a subject-specific finite element model of the functional spinal unit to predict vertebral strength.

Finite element models of an isolated vertebral body cannot accurately predict compressive strength of the spinal column because, in life, compressive load is variably distributed across the vertebral body and neural arch. The purpose of this study was to develop and validate a patient-specific finite element model of a functional spinal unit, and then use the model to predict vertebral strength from medical images. A total of 16 cadaveric functional spinal units were scanned and then tested mechanically in bending and compression to generate a vertebral wedge fracture. Before testing, an image processing and finite element analysis framework (SpineVox-Pro), developed previously in MATLAB using ANSYS APDL, was used to generate a subject-specific finite element model with eight-node hexahedral elements. Transversely isotropic linear-elastic material properties were assigned to vertebrae, and simple homogeneous linear-elastic properties were assigned to the intervertebral disc. Forward bending loading conditions were applied to simulate manual handling. Results showed that vertebral strengths measured by experiment were positively correlated with strengths predicted by the functional spinal unit finite element model with von Mises or Drucker-Prager failure criteria ( R2 = 0.80-0.87), with areal bone mineral density measured by dual-energy X-ray absorptiometry ( R2 = 0.54) and with volumetric bone mineral density from quantitative computed tomography ( R2 = 0.79). Large-displacement non-linear analyses on all specimens did not improve predictions. We conclude that subject-specific finite element models of a functional spinal unit have potential to estimate the vertebral strength better than bone mineral density alone.

Dependence of nonlinear elasticity on filler size in composite polymer systems

Nanosized filler particles enhance the mechanical properties of polymer composites in a size-dependent fashion. This is puzzling, because classical elasticity is inherently scale-free, and models for the elasticity of composite systems never predict a filler-size dependence. Here, we study the industrially important system of silica-filled rubbers, together with a well-characterized model-filled crosslinked gel and show that at high filler content both the linear and nonlinear elastic properties of these systems exhibit a unique scaling proportional to the cube of the volume fraction divided by the particle size. This remarkable behavior makes it possible to predict the full mechanical response of particle-filled rubbers for small but finite deformations based solely on the rheology of the matrix and the size and modulus of the filler particles.

Failure analysis for railroad embankment under heavy haul wagon loads

In this paper, a dynamic three-dimensional finite element model using linear elastic material properties while including wheel-rail friction was developed and used to investigate embankment deviator stress. The effect of train speeds, axle load, and rail roughness on failure of embankment was investigated during repeated train passage. Results indicate that axle load and rail roughness have important effect on foundation failure. Embankment failure occurs first in engineering filler layer instead of gravel layer, and there is a rapidly decrease in foundation life which was determined by fill layer failure as annual tonnage is increased. As annual tonnage is increased beyond 400Mt, the foundation life cannot meet a projected design life of 40 years. DOI: http://dx.doi.org/10.5755/j01.mech.23.2.13911

Nonlinear mechanical behaviour of γ-graphyne through an atomistic finite element model

A non-linear finite element model for the simulation of the mechanical in-plane behaviour of γ-graphyne is presented in this paper. Different types of bonds (Single CC, Aromatic CC, Triple CC) are simulated by means of non-linear springs, which accurately take into account the different behaviour of interatomic forces in tension and compression at 0K temperature. Then, the finite element model is used to conduct six tests (two uniaxial tension–compression tests, one biaxial tension–compression test, two uniaxial shear tests, one biaxial shear test) to evaluate the non-linear mechanical behaviour of γ-graphyne. After that, a set of linear elastic properties (Young’s modulus, Poisson’s ratio, shear modulus, bulk modulus) and non-linear elastic properties (limit of proportionality stress and strain, ultimate stress and strain) is reported and compared with values reported in the literature (mostly linear elastic properties). This validation shows that the developed finite element model is able to predict accurately the linear and non-linear mechanical properties of γ-graphyne (i.e. stiffness and strength). Additionally, some remarks are drawn regarding the anisotropy of γ-graphyne and its distinct behaviour under tension and compression.

Finite Element modeling of Mechanical Loading-Pumpkin Peel and flesh

Abstract Finite element (FE) models of uniaxial loading of pumpkin peel and flesh tissues were developed and validated using experimental results. The tensile model was developed for both linear elastic and plastic material models, the compression model was developed only with the plastic material model. The outcomes of force versus time curves obtained from FE models followed similar pattern to the experimental curves; however the curve resulted with linear elastic material properties had a higher difference with the experimental curves. The values of predicted forces were determined and compared with the experimental curve. An error indicator was introduced and computed for each case and compared. Additionally, Root Mean Square Error (RMSE) values were also calculated for each model and compared. The results of modeling were used to develop material model for peel and flesh tissues in FE modeling of mechanical peeling of tough skin vegetables. The results presented in this paper are a part of a study on mechanical properties of agricultural tissues focusing on mechanical peeling methods using mathematical, experimental and computational modeling.