Anisotropic Elastic Properties Research Articles

Numerical local upscaling of elastic geomechanical properties for heterogeneous continua

An efficient, numerical local upscaling technique for estimating elastic geomechanical properties in heterogeneous continua is proposed. The upscaled anisotropic elastic properties are solved locally with various boundary conditions and reproduce the anisotropic geomechanical response of fine-scale simulations of sand–shale sequence models with horizontal and inclined shale bedding planes. The algorithm is automated in a parallel program and can be used to determine optimum upscaling ratios in different regions of the reservoir. The successful application of the proposed upscaling method in a field-scale coupled reservoir–geomechanics simulation demonstrates an improvement in overall computational efficiency while maintaining accuracy in the geomechanical response and reservoir performance.

The effect of anisotropy of elastic properties of GFRP reinforcement on strength of compressed concrete structural elements

Introduction. Despite the growing interest to the use of GFRP reinforcement in various concrete structures, its use in the concrete compressed zone is not investigated sufficiently. The use of GFRP reinforcement in compressed concrete elements is limited by a combination of low value of its modulus of elasticity and small ultimate deformation of concrete during compression. A number of researchers suggest solving this problem by means of increase the ultimate concrete deformation due to lateral reinforcement. However, unlike steel reinforcement, the elastic properties of composite reinforcement depend on the stress direction, which is due to the significant difference between the moduli of elasticity of the fibre glass and the binder. Consequently, the stress-deformation state of compressed concrete elements with longitudinal GFRP reinforcement and close-set lateral reinforcement will differ from the stress-deformation state of steel-reinforced concrete elements. Materials and methods. To clarify the effect of the anisotropy of fibre-glass reinforcement elastic properties on its work in the concrete compressed zone, a physical experiment and numerical simulation using the LIRA-SAPR software were carried out. Physical nonlinearity of materials was not taken into account in the model. Results. An assessment of the effect of anisotropy of elastic properties of fibre-glass reinforced plastic (GFRP) reinforcement on the strength of compressed concrete elements was accomplished for longitudinal reinforcement. The experiment showed that the location of the longitudinal GFRP reinforcement in the concrete compressed zone in the absence of lateral reinforcement led to a decrease in the average strength of the tested samples by 9.2 %, while the fracture nature of GFRP-reinforced samples differed from the fracture nature of control samples. As a result of the numerical simulation, it was revealed that the cause of the strength reduction is the anisotropy of the elastic properties of GFRP reinforcement, which affects the stress-deformation state of compressed concrete. Conclusions. The analysis of the results of experiment and numerical simulation showed that the reason for the decrease in strength is the low modulus of elasticity of GFRP when compressed in the lateral direction as compared with the similar characteristic of concrete. The degree of strength reduction will also depend on the relation between the moduli of elasticity of concrete and GFRP when compressed in the longitudinal direction.

Anisotropic Elasticity of APS and HVOF CoNiCrAlY Coatings Studied by Resonant Ultrasound Spectroscopy with Laser Doppler Interferometry

The splat-based layered structure of thermal spray coatings leads to elastic anisotropy; however, elucidating the anisotropic elastic properties of such coatings is a challenging subject because of the limited sample size and microstructural factors such as high defect level. The objective of this study is to investigate the anisotropic elasticity of the as-sprayed and heat-treated CoNiCrAlY coatings prepared by atmospheric plasma spraying (APS) and high-velocity oxygen fuel (HVOF) spraying. For this purpose, we measure all five elastic constants accurately using resonant ultrasound spectroscopy with laser Doppler interferometry. This approach realizes the correct mode identification of the measured resonance frequencies, even for coatings with high internal friction by comparing the measured and calculated displacement distributions, providing a precise determination of the elastic constants with inverse calculation. We determined that an oriented array of defects causes a significantly low Young’s modulus along the spraying direction in both the as-sprayed coatings. Our measurements on the heat-treated coatings revealed that thermal treatment makes the APS coating stiffer than the HVOF coating, whereas the stiffness anisotropy of the APS coating remains stronger compared to the HVOF coating, even after heating. This phenomenon is consistently explained by focusing on the oxides in the coatings.

Anisotropic elasticity, electronic structure and thermodynamic properties of Al-Fe-Si intermetallic compounds from first principles calculations

In this paper, structural stability, elastic properties, electronic structure and thermodynamic properties of Al-Fe-Si compounds are systematically investigated by first-principles calculations. The negative formation enthalpy indicates that all Al-Fe-Si compounds are thermodynamically stable, and the Al-Fe-Si compounds are determined to be mechanically stable by the stability criteria. The bulk, shear and Young's moduli as well as Poisson's ratio of Al-Fe-Si compounds are also calculated. The results show that Al2Fe3Si3 has the highest shear modulus and Young's modulus, which leads to stronger shear deformation resistance and stiffness. The elastic anisotropy and shear anisotropic factors of Al-Fe-Si compounds are analyzed in this study, and the anisotropy of Al3Fe2Si3 is the greatest among them. Al3Fe2Si3 and Al2Fe3Si4 show metallic character and Al2Fe3Si3 is classified as direct band gap semiconductors. The DOS of Al-Fe-Si compounds are found mainly from Al 3p, Si 3p and Fe 4d states and the Fe-Al/Si bonding is much stronger than that of Al-Si. According to the results, Al2Fe3Si3 has the highest Debye temperature, indicating strong chemical bonding and higher thermal conductivity, which are consistent with the results of Young's modulus and minimum thermal conductivity.

An experimental study on the fracture of a unidirectional carbon fiber-reinforced composite under quasistatic torsion

Carbon fiber-reinforced composites exhibit excellent mechanical properties for a variety of applications. Using the spirally notched specimens, we demonstrate how unidirectional carbon fiber-reinforced polymeric composite specimens with different fiber orientations fail under quasistatic torsion. By collecting data at 200,000 points per second, type I specimens exhibited limited fluctuations at the fiber-matrix interfaces before the catastrophic failure, whereas type II specimens exhibited stepwise failure after the peak loads with torque avalanches described by Gaussian models. Distinctive crack-tip stress contours and energy release rates were obtained through the finite element modeling using anisotropic elastic properties of the unidirectional composite. The fractographic characterization showed that the primary failure of type I specimens occurred along fiber-matrix interfaces, whereas circular cracks switched between polymeric matrices and fiber-matrix interfaces when type II specimens failed progressively. Our findings could help further insights on the mechanical behavior of different fiber-reinforced composites.

Investigation of structural, electronic and lattice dynamical properties of XNiH3 (X = Li, Na and K) perovskite type hydrides and their hydrogen storage applications

XNiH3 (X = Li, Na, and K) perovskite type hydrides have been studied by using Density Functional Theory (DFT) and these materials are found to be stable and synthesizable. The X-ray diffraction patterns have been obtained and they indicate that all materials have the polycrystalline structure. The electronic properties have been investigated and it has been found that these structures show metallic character. The Bader partial charge analysis has also been performed. In addition, the elastic constants have been calculated and these materials are found to be mechanically stable. Using these elastic constants, the mechanical properties such as bulk modulus, shear modulus, Poisson's ratio have been obtained. Moreover, the Debye temperatures and thermal conductivities have been studied. The anisotropic elastic properties have been visualized in three dimensions (3D) for Young's modulus, linear compressibility, shear modulus and Poisson's ratio as well as with the calculation of the anisotropic factors. Additionally, the dynamical stability has been investigated and obtained phonon dispersion curves show that these materials are dynamically stable. Also, the thermal properties including free energy, enthalpy, entropy and heat capacity have been studied. The hydrogen storage properties have been examined and the gravimetric hydrogen storage capacities have been calculated as 4.40 wt%, 3.57 wt% and 3.30 wt% for LiNiH3, NaNiH3 and KNiH3, respectively. Furthermore, the hydrogen desorption temperatures have been obtained as 446.3 K, 419.5 K and 367.5 K for LiNiH3, NaNiH3 and KNiH3, respectively.

Measurement of the anisotropic elastic properties of shale: uncertainty analysis and water effect

The static anisotropic elastic properties of shales can be measured by performing uniaxial compression on core specimens with bedding planes of different inclination angles (or anisotropy angles). However, these measurements differ when different numbers of specimens are tested, mainly because of the heterogeneity of shales. This study aimed to quantify the uncertainties of the anisotropic elastic properties of a shale when testing different numbers of specimens with distinct anisotropic angles. Three sets of room-dried core samples were prepared, and each set consisted of seven specimens with incremental anisotropic angles of 15°. Uniaxial compression measurements were used to determine the anisotropic elastic properties for a given number (2–7) of specimens in each set. The results indicated that the uncertainties of the determined anisotropic elastic properties decreased monotonically as the number of measurements was increased. The results also suggested that at least five specimens with different anisotropic angles should be tested in order to obtain accurate elastic properties (uncertainty <10%). An additional set of wet specimens of the same shale were also tested and analyzed. It was found that water absorption significantly decreased Young’s moduli, increased Poisson’s ratios, and had a limited effect on the shear modulus. The wet specimens also displayed a slightly stronger anisotropic ratio of the elastic moduli compared to the room-dried specimens. Finally, the alteration of the anisotropic elastic properties of shales upon water absorption was tentatively related to the mineralogy and microstructure heterogeneity. The findings of this study have major implications for many geoengineering operations where the anisotropic elastic properties of shales must be considered.

Effect of Microstructure and Texture Evolution During Variable Gauge Rolling on Mechanical Properties of Tailor Rolled Blanks

In this study, anisotropic elastic and plastic mechanical properties of a tailor rolled blank (TRB) with thickness ratio of 0.52 (1 mm/1.9 mm), have been fully studied. To gain a deeper insight into anisotropic mechanical behavior of the studied TRB, continuous changes in microstructure and crystallographic texture of a dual phase steel caused by variable gauge rolling (VGR) were investigated on several points (on RD–ND plane) along longitudinal direction with the aid of EBSD observations. Analysis of grain boundary (GB) maps revealed that ferrite grain refinement is occurred during VGR so that the average ferrite grain size decreases from 4.1 µm for the thicker side to 2.2 µm for the thinner side. Furthermore, it was found out that substructure density is more intense within smaller ferrite grains. Evaluation of inverse pole figures as well as orientation distribution function maps showed that texture of thicker side comprises {001}〈110〉 and {112}〈110〉 components along $$ \alpha $$ -fiber. In addition, it was revealed that orientations of {111}〈110〉 and {111}〈112〉 along $$ \gamma $$ -fiber strengthen along VGR direction by further increase in thickness reduction near thinner side. Accordingly, unprecedented gradual changes in mechanical properties with respect to these changes in microstructure and texture, were obtained. Finally, the correlation between in-plane anisotropic mechanical properties [Young’s modulus (E), yield stress (YS), ultimate tensile stress (UTS) and total elongation] of the studied tailor rolled blank with microstructure and deformation texture was interpreted.

First principles study on new half-metallic ferromagnetic ternary zinc-based sulfide and telluride (Zn3VS4 and Zn3VTe4)

In this resear, we have investigated electronic and magnetic behavior and also some mechanical properties of ternary zinc-based chalcogenides Zn3VCh4 (Ch = S and Te) conform to space group with 215 space number, which have simple cubic (SC) crystal structure, by spin-polarized Generalized Gradient Approximation (GGA) within Density Functional Theory (DFT). To make extensive study within ab initio methods, after the optimization process to get optimal structural parameters in most suitable magnetic phase, the electronic band structures with the total density of electronic states and second order elastic constants to predict some thermal and elastic features have been calculated. The calculated negative formation enthalpy values indicate that, our materials are thermodynamically stable and structurally synthesizable. The observed minority (down) band gaps in the calculated electronic band structures, Eg = 2.62 eV for Zn3VS4 and Eg = 1.75 eV for Zn3VTe4, show that our crystal systems have half-metallic character. Also, the calculated elastic constants prove that our compounds are mechanically stable due to satisfy the Born-Huang criteria. Moreover, the anisotropic elastic properties have been visualized in two-dimensional (2D) and three-dimensional (3D) surfaces for Young’s modulus, linear compressibility, shear modulus and Poisson’s ratio as well as with the calculation of the anisotropic factors.

Algorithmic aspects and finite element solutions for advanced phase field approach to martensitic phase transformation under large strains

A new problem formulation and numerical algorithm for an advanced phase-field approach (PFA) to martensitic phase transformation (PT) are presented. Finite elastic and transformational strains are considered using a fully geometrically-nonlinear formulation, which includes different anisotropic elastic properties of phases. The requirements for the thermodynamic potentials and transformation deformation gradient tensor are advanced to reproduce crystal lattice instability conditions under a general stress tensor obtained by molecular dynamics (MD) simulations. The PFA parameters are calibrated, in particular, based on the results of MD simulations for PTs between semiconducting Si I and metallic Si II phases under complex action of all six components of the stress tensor (Levitas et al. in Phys Rev Lett 118:025701, 2017a; Phys Rev B 96:054118, 2017b). The independence of the PFA instability conditions of the prescribed stress measure is demonstrated numerically for the initiation of the PT. However, it is observed that the PT cannot be completed unless the stress exceeds the stress peak points that depend on which stress measure is prescribed. Various 3D problems on lattice instability and following nanostructure evolution in single-crystal Si are solved. The effect of stress hysteresis on the nanostructure evolution is studied through analysis of the local driving force and stress fields. It is demonstrated that variation of internal stress fields due to differing boundary conditions may lead to completely different PT mechanisms.

Anisotropic Elastic and Lattice Dynamical Properties of Cr2AB MAX Phases Compounds

The structural, mechanical and lattice dynamical properties of the MAX Phase borides compounds Cr 2 AB (A= Al, P, Si) have been investigated using the first principles calculations with the generalized gradient approximation (GGA) based on Density Functional Theory (DFT). The obtained negative formation energies of Cr 2 AB indicate that these compounds are stable and could be synthesized. Some basic physical parameters such as lattice constants, elastic constants, bulk modulus, Shear modulus, Young’s modulus, and Poison’s ratio have been calculated. Ionic character has been found for Cr 2 AB compounds. Also, Cr 2 AlB is a brittle material while Cr 2 SiB and Cr 2 PB are ductile materials. In addition, the elastic anisotropy has been visualized in detail by plotting the directional dependence of linear compressibility, Poisson ratio, Young’s and Shear moduli. Furthermore, electronic band structures and corresponding partial density of stated have been examined and it has been found that these compounds have metallic character. Moreover, the phonon dispersion curves as well as corresponding phonon partial density of states (PDOS) have been obtained. This study is the first investigation of the MAX Phase borides compounds Cr 2 AB (A= Al, P, Si) and could lead to the future studies.

Anisotropic elastic properties of human femoral cortical bone and relationships with composition and microstructure in elderly

The strong dependence between cortical bone elasticity at the millimetre-scale (mesoscale) and cortical porosity has been evidenced by previous studies. However, bone is an anisotropic composite material made by mineral, proteins and water assembled in a hierarchical structure. Whether the variations of structural and compositional properties of bone affect the different elastic coefficients at the mesoscale is not clear. Aiming to understand the relationships between bone elastic properties and compositions and microstructure, we applied state-of-the-art experimental modalities to assess these aspects of bone characteristics. All elastic coefficients (stiffness tensor of the transverse isotropic bone material), structure of the vascular pore network, collagen and mineral properties were measured in 52 specimens from the femoral diaphysis of 26 elderly donors. Statistical analyses and micromechanical modeling showed that vascular pore volume fraction and the degree of mineralization of bone are the most important determinants of cortical bone anisotropic mesoscopic elasticity. Though significant correlations were observed between collagen properties and elasticity, their effects in bone mesoscopic elasticity were minor in our data. This work also provides a unique set of data exhibiting a range of variations of compositional and microstructural cortical bone properties in the elderly and gives strong experimental evidence and basis for further development of biomechanical models for human cortical bone. Statement of SignificanceThis study reports the relationships between microstructure, composition and the mesoscale anisotropic elastic properties of human femoral cortical bone in elderly. For the first time, we provide data covering the complete anisotropic elastic tensor, the microstructure of cortical vascular porosity, mineral and collagen characteristics obtained from the same or adjacent samples in each donor. The results revealed that cortical vascular porosity and degree of mineralization of bone are the most important determinants of bone anisotropic stiffness at the mesoscale. The presented data gives strong experimental evidence and basis for further development of biomechanical models for human cortical bone.

Effect of Mn content in Fe(1−x)MnxB (x = 0, 0.25, 0.5, 0.75 and 1) on physical properties - ab initio calculations

Abstract Structural, electronic, intrinsic magnetic, anisotropic elastic properties, sound velocities and Debye temperature of Fe1−xMnx B (x = 0, 0.25, 0.5, 0.75, 1) transition metal monoborides have been studied by first-principles calculations within the method of virtual crystal approximation (VCA) based on density-functional theory (DFT) through generalized gradient approximation (GGA). The average magnetic moment per cell increased with increasing of Mn content, which could be associated with the relationship between the composition and magnetic properties. The observed magnetic behavior of Fe1−xMnx B compounds can be explained by Stoner model. Lattice parameters and Debye temperature agree well with the experimental values. Furthermore, we have plotted three-dimensional (3D) surfaces and planar contours of the directional dependent Young and bulk moduli of the compounds on several crystallographic planes, to reveal their elastic anisotropy versus Mn content (x) in Fe1−xMnx B.

Scattering Radiation Pattern Atlas: What Anisotropic Elastic Properties Can Body Waves Resolve?

AbstractFull‐waveform inversion (FWI) optimizes the subsurface properties of geophysical Earth models in such a way that the modeled data, based on these subsurface properties, match the observed data. The anisotropic properties, whether monoclinic, orthorhombic, triclinic, or vertical transversally isotropic (VTI), of the subsurface, be it a fractured reservoir or the core‐mantle boundary, are necessary to describe the observed wave phenomena. There are no principal limitations on the complexity of the anisotropy that can be inverted using FWI. However, the question remains—what kind of anisotropic descriptions of the elastic properties of the Earth can or cannot be inverted reliably from seismic waveforms? We reveal the resolution that can be achieved through reconstructions of each elastic parameter by building vertical resolution patterns from the scattering radiation patterns of body waves. A visual analysis of these patterns indicates “trade‐offs,” that is, perturbations of parameters that have the same reflection‐based scattering patterns as other perturbations. Each trade‐off leads to an apparent ambiguity in the inversion, which must be addressed by additional assumptions, constraints, or regularizations. For orthorhombic media, we find the exact trade‐offs that exist between parameters. Our parameterization isolates the VTI parameters, and therefore, we also obtain trade‐offs for every scattering mode for VTI media. We discover that only monoclinic parameters are recoverable from the first‐order scattering of monotypic waves. We summarize the trade‐offs in tables for easy reference. This paper is intended to be useful for researchers setting up anisotropic FWI problems, and interpreting or controlling the quality of such inversions.

Effect of Phonon Focusing on the Thermal Conductivity of GaAs/AlGaAs Heterostructures at Low Temperatures

The effect of the anisotropy of elastic properties on the thermal conductivity of GaAs/AlGaAs heterostructures at low temperatures is investigated. The effect of phonon focusing on the anisotropy of the thermal conductivity is analyzed. The parameters of the specular reflection of phonons from the boundaries of the heterostructures, which characterize the heat flux in the Knudsen mode of the phonon gas flow, are determined. The angular dependences of the mean free paths of phonons of different polarizations, which determine the thermal conductivity anisotropy of heterostructures with orientations {100} and {110}, are calculated.

Estimation of the elastic modulus of child cortical bone specimens via microindentation

ABSTRACTPurpose: Non-pathological child cortical bone (NPCCB) studies can provide clinicians with vital information and insights. However, assessing the anisotropic elastic properties of NPCCB remains a challenge for the biomechanical engineering community. For the first time, this paper provides elastic moduli values for NPCCB specimens in two perpendicular directions (longitudinal and transverse) and for two different structural components of bone tissue (osteon and interstitial lamellae).Materials and Methods: Microindentation is one of the reference methods used to measure bone stiffness. Here, 8 adult femurs (mean age 82 ± 8.9 years), 3 child femurs (mean age 13.3 ± 2.1 years), and 16 child fibulae (mean age 10.2 ± 3.9 years) were used to assess the elastic moduli of adult and child bones by microindentation.Results: For adult specimens, the mean moduli measured in this study are 18.1 (2.6) GPa for osteons, 21.3 (2.3) GPa for interstitial lamellae, and 13.8 (1.7) GPa in the transverse direction.For child femur specimens, the mean modulus is 14.1 (0.8) GPa for osteons, lower than that for interstitial lamellae: 15.5 (1.5) GPa. The mean modulus is 11.8 (0.7) GPa in the transverse direction. Child fibula specimens show a higher elastic modulus for interstitial lamellae 15.8 (1.5) than for osteons 13.5 (1.6), with 10.2 (1) GPa in the transverse direction.Conclusion: For the first time, NPCCB elastic modulus values are provided in longitudinal and transverse directions at the microscale level.

Orientation dependence of elastic properties in orthorhombic Ca3Mn2O7

Elastic properties are important in fundamental understanding of multiferroic materials. However, up to now, there is no work about anisotropy of elastic properties in orthorhombic Ca3Mn2O7. In this study, using coordinate transformation method, we investigated basic elastic parameters (elastic constants ) and engineering elastic parameters (Youngʼs modulus , Poissonʼs ratio , and the rigidity modulus ) of orthorhombic Ca3Mn2O7 along arbitrary orientations. The detailed anisotropic characteristics of these parameters were presented. The results reveal the orientation related elastic properties in mm2 point group orthorhombic Ca3Mn2O7.

Prediction of the anisotropic mechanical properties of compacted powders

The multi-particle finite element method (MPFEM) was used to test the anisotropic elastic and plastic properties of compacted powders with cohesive contacts. A representative volume element (RVE) of monodisperse, spherical, deformable particles was used to investigate the powder properties after compaction. Efficient periodic boundary conditions and an RVE of only 50 particles allowed extensive parameter studies. During parameter studies the relative density after compaction, the contact cohesion strength and the strain path during compaction were varied. The strain paths were characterized by the ratios of the applied principal strains during compaction that results in different Dirichlet boundary conditions on the RVE. Seven different strain paths were considered including the practically important isostatic and closed die compaction.The outcome of the parameter study were the elastic constants of an orthotropic material model, the uniaxial yield strength for tension and compression, and the yield surfaces for general load cases. No anisotropy was observed for isostatic compaction but increasing anisotropy was observed with increasing ratio of the principal strains during compaction. Regression curves were generated to describe the mechanical properties as a function of the model parameters. In this way, continuous functions were obtained which were capable to describe the distribution of the mechanical material properties in a FEM model of a heterogeneous compacted powder part.

Strain-rate effect on mechanical behavior of unidirectional carbon fiber reinforced plastic

Abstract To form the constitutive equations for a unidirectional carbon fiber reinforced plastic, the hereditary elastic medium constitutive relations, the anisotropic theory of elasticity and the Volterra correspondence principle are used. Based on the proposed model applied to describe the compression stress-strain curves of the unidirectional IM7/8552 composite with various off-axis angles, an attempt is made to take into account the strain rate effect on the stress-strain curves. Experimental data analysis shows that rheological and physically nonlinear properties distinctly appear along with the anisotropy of elastic properties. Computational algorithm implementation becomes possible due to using the relations of the algebra of weakly singular resolvent operators. The experimental data of the unidirectional IM7/8552 and AS4/3501-6 composites under off-axis loading with various strain rates are analyzed.

An inverse method for design and characterisation of acoustic materials

This paper presents applications of an inverse method for the design and characterisation of anisotropic elastic material properties of acoustic porous materials. Full field 3D displacements under static surface loads are used as targets in the inverse estimation to fit a material model of an equivalent solid to the measurement data. Test cases of artificial open-cell foams are used, and the accuracy of the results are verified. The method is shown to be able to successfully characterise both isotropic and anisotropic elastic material properties. The paper demonstrates a way to reduce costs by characterising material properties based on the design model without a need for manufacturing and additional experimental tests.