Elastic Constants Of Material Research Articles

Neural networks determination of material elastic constants and structures in nematic complex fluids

Supervised machine learning and artificial neural network approaches can allow for the determination of selected material parameters or structures from a measurable signal without knowing the exact mathematical relationship between them. Here, we demonstrate that material nematic elastic constants and the initial structural material configuration can be found using sequential neural networks applied to the transmmited time-dependent light intensity through the nematic liquid crystal (NLC) sample under crossed polarizers. Specifically, we simulate multiple times the relaxation of the NLC from a random (qeunched) initial state to the equilibirum for random values of elastic constants and, simultaneously, the transmittance of the sample for monochromatic polarized light. The obtained time-dependent light transmittances and the corresponding elastic constants form a training data set on which the neural network is trained, which allows for the determination of the elastic constants, as well as the initial state of the director. Finally, we demonstrate that the neural network trained on numerically generated examples can also be used to determine elastic constants from experimentally measured data, finding good agreement between experiments and neural network predictions.

A first-principles method to calculate fourth-order elastic constants of solid materials

A first-principles method is presented to calculate elastic constants up to the fourth order of crystals with the cubic and hexagonal symmetries. The method relies on the numerical differentiation of the second Piola-Kirchhoff stress tensor and a density functional theory approach to calculate the Cauchy stress tensor for a list of deformed configurations of a reference state. The number of strained configurations required to calculate the independent elastic constants of the second, third, and fourth order is 24 and 37 for crystals with the cubic and hexagonal symmetries, respectively. Here, we present conceptual aspects of our method, we provide technical details of its implementation and use, we assess its accuracy, and we discuss several applications. In particular, this method is applied to five crystalline materials with the cubic symmetry (diamond, silicon, aluminum, silver, and gold) and two metals with the hexagonal close packing structure (beryllium and magnesium). Our results are compared to available experimental data and previous computational studies. Calculated linear and nonlinear elastic constants are also used in the context of nonlinear elasticity theory to predict values of volume and bulk modulus over an interval of pressures. These predictions are compared to results obtained from density functional theory calculations to assess the reliability of our method.

First-principles calculations to investigate structural, elastic and thermodynamic properties of new M2ScSnC2 (M=V or Nb) quaternary compounds for 312 MAX phases

In this research, the approach of FP-LAPW (full potential linearized augmented plane wave) is employed within WIEN2K for the investigations of structural, thermodynamic, electronic, and mechanical properties of the V2ScSnC2 and Nb2ScSnC2 MAX-phases quaternary compounds. The V2ScSnC2 and Nb2ScSnC2 compounds exist in “α” and “β” polymorph structures. The formation energies (Eform) investigated insure that the α-polymorph is more stable than the β one. As it happens, Nb2ScSnC2 is more stable than V2ScSnC2. The Nb2ScSnC2 has an enhanced mechanical property compared to the V2ScSnC2 compound. The elastic constants (ECs) of interested materials fulfill all the conditions of mechanical stability and revealed a ductile nature. The predicted Cauchy's pressure and Poisson's ratio possess positive values signifying the ionic character of the V2ScSnC2 compound. The quaternary Nb2ScSnC2 compound exists as amalgamation of covalent and ionic bonds with a predominance of the ionic bonding character. The high melting temperature and high Debye temperature of V2ScSnC2 and Nb2ScSnC2 make them suitable for use in harsh environments. Furthermore, they exhibit potential as a promising material for thermal barrier coatings (TBCs). Electronic structure analysis confirm the metallic character of the two interested compounds. At high temperatures and pressures the thermodynamic properties including the Cv (Heat capacity) and ƟD(Debye temperature) are explored. We deem that this study of quaternary MAX-phase compounds will bring new insight for the experimentalists to employ for their future applications.

Thermo-acoustoelastic effect of Rayleigh wave: Theory and experimental verification

Previous studies showed that the thermally-induced ultrasonic bulk wave velocity change could be used to measure acoustoelastic coefficients and third-order elastic constants of elastic materials. This method is naturally immune from the ambient temperature effect and has improved sensitivity and a simpler test setup than the conventional acoustoelastic test. However, Rayleigh wave is preferred for thick components or structures with only one accessible surface. In this work, the thermo-hyperelastic constitutive equation, along with acoustoelastic theory, is used to derive the expression of the thermo-acoustoelastic coefficient (TAEC) of Rayleigh wave. The numerical relationship between the TAEC of Rayleigh wave and Murnaghan constants (l, m and n) are given for common metals. The TAEC expressions for Rayleigh wave and shear wave are similar, and both are dominated by the constant m. The TAEC of Rayleigh wave was measured on an aluminum 6061 specimen using the thermal modulation experiment in a temperature range of 22 ∼35 °C. The measured TAEC shows good agreement with the theoretical calculation. Then the third-order elastic constants were calculated based on TAECs of bulk waves and Rayleigh wave.

CRSS determination combining ab-initio framework and Surrogate Neural Networks

Critical Resolved Shear Stress (CRSS), fundamentally linked to the dislocation glide stress, is a crucial measure in dictating plastic deformation in metallic materials. A recent ab-initio predictive model for dislocation glide stress in Face-Centered Cubic (FCC) materials is developed which accurately predicts available experimental data, considering the anisotropic continuum energy, the atomistic misfit energy, and the minimum energy path for the intermittent motion of Shockley partials. The CRSS of a material is predominantly controlled by six parameters, namely, lattice constant, unstable/stable stacking-fault energies, and three anisotropic elastic constants for cubic materials, which are inputs to the predictive model. In this work, a large material dataset is produced incorporating properties of real materials and generating hypothetical combinations, subsequently calculating the CRSS for each combination using the predictive model. The hypothetical combinations of properties are employed to train a machine learning-based Surrogate Neural Network (SNN), and the ones of real materials are utilized to validate the SNN model yielding a 94% accuracy for 1,033 materials. The generated dataset is used to unravel the sensitivity of each material parameter to the predicted CRSS establishing a general trend for the FCC materials for the first time guiding the field in achieving superior mechanical properties.

On the Phase Space of Fourth-Order Fiber-Orientation Tensors

Fiber-orientation tensors describe the relevant features of the fiber-orientation distribution compactly and are thus ubiquitous in injection-molding simulations and subsequent mechanical analyses. In engineering applications to date, the second-order fiber-orientation tensor is the basic quantity of interest, and the fourth-order fiber-orientation tensor is obtained via a closure approximation. Unfortunately, such a description limits the predictive capabilities of the modeling process significantly, because the wealth of possible fourth-order fiber-orientation tensors is not exploited by such closures, and the restriction to second-order fiber-orientation tensors implies artifacts. Closures based on the second-order fiber-orientation tensor face a fundamental problem – which fourth-order fiber-orientation tensors can be realized? In the literature, only necessary conditions for a fiber-orientation tensor to be connected to a fiber-orientation distribution are found. In this article, we show that the typically considered necessary conditions, positive semidefiniteness and a trace condition, are also sufficient for being a fourth-order fiber-orientation tensor in the physically relevant case of two and three spatial dimensions. Moreover, we show that these conditions are not sufficient in higher dimensions. The argument is based on convex duality and a celebrated theorem of D. Hilbert (1888) on the decomposability of positive and homogeneous polynomials of degree four. The result has numerous implications for modeling the flow and the resulting microstructures of fiber-reinforced composites, in particular for the effective elastic constants of such materials. Based on our findings, we show how to connect optimization problems on fourth-order fiber-orientation tensors to semi-definite programming. The proposed formulation permits to encode symmetries of the fiber-orientation tensor naturally. As an application, we look at the differences between orthotropic and general, i.e., triclinic, fiber-orientation tensors of fourth order in two and three spatial dimensions, revealing the severe limitations inherent to orthotropic closure approximations.

THREE-DIMENSIONAL STRAIN/STRESS FIELDS IN BERKOVICH/VICKERS INDENTATION: COMPARISONS WITH THIN FILM DELAMINATION AND SHEAR BAND FORMATION

Starting from the simple assumption that the displacement field underneath a pyramidal (Berkovich/Vickers) tip for very shallow indents is described by the Boussinesq solution, while for deeper ones is dictated by the tip's specific geometry, a combination of the two leads to a combined displacement field for the material at contact with the tip. Continuum mechanics is then utilized for the calculation of the strain tensor, while gradient elasticity theory is adopted for the determination of the stress tensor underneath the tip. Gradient elasticity was assumed in order for the gradient term to be able to model, in this case, the inhomogeneously applied load due to the specific tip geometry, which is different than a flat punch. The thus calculated stress component along the loading (vertical) direction is a parametric function of the material's elastic constants (Poisson's ratio, Lame constants), as well as of the maximum elastic deformation and the gradient coefficient. By appropriately modifying these parameters, the proposed formulation seems to be able to predict the mechanical response of the material underneath the indenter for the specific pyramidal tip geometry (Berkovich or Vickers), without any approximations or empirical relations. The validity of the proposed formulation's predictions was checked against thin film delamination and shear band formation AFM/SEM micrographs, which showed a very good qualitative as well as quantitative comparison with the theoretical predictions.

Comparison of Characterization Methods for Assessing the Temperature Dependencies of Elastic and Piezoelectric Constants of Piezoelectric Materials

Comparison of Characterization Methods for Assessing the Temperature Dependencies of Elastic and Piezoelectric Constants of Piezoelectric Materials

Interpreting ultrasonic pulse velocities and elastic properties of lac du bonnet granite under compression

The measurement of ultrasonic velocities in rock core is a straightforward, non-destructive, economic method to estimate rock material properties conducted by emitting high frequency acoustic waves through the rock core. The velocities of compressional and shear waves (P- and S-waves, respectively) are influenced by the unique microstructural characteristics of the rock. Once wave velocities and bulk density for each sample have been determined, the dynamic elastic material constants such as Young’s modulus, Poisson’s ratio, and shear modulus can be calculated. In theory, it is expected that the dynamic properties would be similar to the static properties calculated in uniaxial compression strength (UCS) tests. In UCS tests, elastic parameters are estimated using stress-strain relationships at approximately 50% of the peak strength. However, dynamic properties from the UPV method often do not match static properties. In this study, dynamic testing of the rock core is completed under two broad stress conditions: no compression and axial compression (UCS). This allows for a direct comparison between dynamic UPV testing data, and static data, and should produce a closer match between the dynamic and static testing data when dynamic UPV testing is conducted under stress conditions similar to the static testing stress state.

Assessment of the concentration of wear products of bearing elements

The article presented by the author considers the greatest wear along the arc of the contact of the bearing ring with the ball is observed on the surface where there is more slippage, i.e. on the face of the groove of the rings. The problem often lies in the low durability of the bearing supports. The authors of this article are invited to analytically evaluate the durability of the bearing with additional consideration of the regularity of changes in the concentration of wear products in the oil of the unit. Uneven load distributions and different elastic constants of materials used for the outer ring and balls, and further with the subsequent improved correction of the resource, which are carried out in accordance with modern requirements. Such a correction involves not only taking into account the impact of lubrication conditions and oil contamination on the bearing life, but also modifying the resource in relation to the fatigue stress limit to the dynamic equivalent load, taking into account many factors of influence.

Computing Elastic Moduli of Igneous Rocks Using Modal Composition and Effective Medium Theory

Elastic constants of rock materials are the basic parameters required for modeling the response of rock materials under mechanical loads. Experimental tests for determining these properties are expensive, time-consuming and suffer from a high uncertainty due to both experimental limitations and the heterogeneous nature of rock materials. To avoid such experimental difficulties, in this paper a method is suggested for determining elastic constants of rock materials by determining their porosity and modal composition and employing effective medium theory. The Voigt–Reuss–Hill average is used to determine effective elastic constants of the studied igneous rocks according to the elastic moduli of their mineral constituents. Then, the effect of porosity has been taken into account by considering rock as a two-phase material, and the Kuster–Toksoz formulation is used for providing a close estimation of different moduli. The solutions are provided for different isotropic igneous rocks. This sustainable method avoids destructive tests and the usage of energy for performing time-consuming and expensive tests and requires simple equipment.

Determination of Some Elastic Constants of Materials Using Impact Analysis

Determination of Some Elastic Constants of Materials Using Impact Analysis

High-temperature elastic moduli: A tool for understanding chemical bonding in thermoelectric materials

In the study of thermoelectric materials, the elastic moduli are valuable for predicting and interpreting trends in lattice thermal conductivity and some aspects of electronic conductivity (e.g., electron-phonon interactions). Because elastic moduli are highly sensitive to the details of chemical bonding, they can also be used to detect subtle changes in crystal symmetry or site-disorder due to phase transitions. Consequently, measurements of elastic moduli are of fundamental value in the development of structure-property relationships in thermoelectric materials. However, experimental reports of the elastic constants of functional materials are relatively sparse, and temperature-dependent data is even less common. Further, unlike most types of functional materials, thermoelectric materials are used over an extremely wide temperature range (up to 1300 K in some cases). In our lab, we measure the elastic constants of polycrystalline and single crystalline thermoelectric materials across a wide temperature range (250–1300 K) using resonant ultrasound spectroscopy with Al2O3 buffer rods to separate the transducers from the hot zone. In this talk, I will discuss the high-temperature elastic properties of several classes of thermoelectric materials, including Mg3Sb2 and GeSe-AgBiSe2 alloys, emphasizing the role that such data can play in interpreting composition- and temperature-dependent trends in lattice thermal conductivity.

Resonances and mode shape imaging for characterizing the microstructure of complex metals

Resonant Ultrasound Spectroscopy (RUS) is a mature and reliable technique for measuring the elastic stiffness constants of anisotropic materials. In highly processed materials such as additively manufactured metal parts, the anisotropic stiffnesses arrive from microstructures that contain grains with preferred orientations, which can result from directionally dependent thermal or mechanical processes. The connection between elastic stiffnesses and microstructure suggest the potential for RUS being used as a tool to characterize microstructure. This presentation will highlight modeling and experimental measurements in this direction. The RUS model is developed from a micromechanical foundation and includes structure-property linkages between the microstructure’s orientation distribution function and the macroscopic elastic constitutive behavior. The micromechanical basis allows efficient creation of a complete catalog containing all possible resonant behavior (resonant frequencies and mode shapes) of polycrystalline samples as a function of the possible textures. The second part of the presentation will focus on connecting experimentally measured resonances and mode shapes to a particular catalog entry. The inclusion of mode shape imaging in the analysis is expected to offer additional detail and potential for expanded characterization beyond texture and elastic stiffnesses.

MyElas: An automatized tool-kit for high-throughput calculation, post-processing and visualization of elasticity and related properties of solids

Elasticity is one of the most fundamental mechanical properties of solid. In high-throughput design of advanced materials, there is an imperative demand for the capability to quickly calculate and screen a massive pool of candidate structures. A fully automatized pipeline with minimal human intervention is the key to provide high efficiency to achieve the goal. Here, we introduce a tool-kit MyElas that aims to address this problem by forging all pre-processing, elastic constant and other related property calculations, and post-processing into an integrated framework that automatically performs the assigned tasks to drive data flowing through parallelized pipelines from input to output. The core of MyElas is to calculate the second and third order elastic constants of a solid with the energy-strain method from first-principles. MyElas can auto-analyze the elastic constants, to derive other related physical quantities. Furthermore, the tool-kit also integrates a visualization function, which can, for example, plot the spatial anisotropy of elastic modulus and sound velocity of monocrystalline. The validity and efficiency of the toolkit are tested and bench-marked on several typical systems. Program summaryProgram title: MyElasCPC Library link to program files:https://doi.org/10.17632/jbz2s9xsmv.1Code Ocean capsule:https://codeocean.com/capsule/4149434Licensing provisions: GNU General Public License 3Programming language: Python 3.XExternal routines/libraries: Numpy [1], Spglib [2], Matplotlib [3]Nature of problem: Through the first-principal calculation, the second-order and third-order elastic constants of solid materials are automatically calculated, and the post-processing and visualization of single crystal and polycrystalline physical properties are carried out.Solution method: Firstly, the required strain structure is automatically generated through the space group of materials and the corresponding strain matrix. Secondly, the energy of the structure is calculated by first-principles calculation software such as VASP [4]. Thirdly, the relationship between energy and strain is polynomial fitted to deduce the elastic constant of the material. Fourth, automatically derive the relevant physical properties. Finally, the distribution of mechanical modulus and sound velocity in spherical space is visualized.Additional comments including restrictions and unusual features: Many modules of the software can be embedded into other software through simple modification, such as visualization module. The software supports finite temperature calculation with electronic temperature. In addition, the software supports the derivation of corresponding elastic constants from phonon spectrum data generated by Phonopy [5], Alamode [6] and TDEP [7] software through long-wave limit approximation and Christoffel equation.

Model anisotropic materials with ellipsoidal wave surfaces and their application to determination of elastic constants by acoustical methods

A new class of elastic materials with orthorhombic symmetry is introduced. For such materials, group velocity surfaces of quasi-longitudinal waves have ellipsoidal shapes. Relations between elastic constants that guaranty ellipsoidal shapes of the group velocity surfaces are indicated. The model materials are used for approximate determination of effective elastic constants of heterogeneous materials by acoustical methods. Examples of reconstruction of elastic constants from acoustical data are presented, and possible errors of the reconstructions are discussed.

Applications of Stretching Technique and Time Window Effects on Ultrasonic Velocity Monitoring in Concrete

Coda wave interferometry (CWI) has been used to measure the relative wave-velocity change (dV/V) caused by small changes in materials. This study uses the stretching processing technique which has been used for CWI analysis to investigate velocity changes of direct longitudinal (P) wave, direct shear (S) wave, and coda wave in concrete by choosing different time windows of ultrasonic signals. It is found that the obtained wave-velocity change depends on the time window position, because the relative contribution of P wave and S wave is different in each signal window. This paper presents three experimental scenarios of velocity change in concrete: early-age hydration, temperature change, and uniaxial loading. In early-age concrete, the S wave has a larger relative velocity change than the P wave, which is consistent with the microstructure development due to the hydration process. Temperature change causes a larger dV/V on the P wave than on the S wave, and the difference between P and S wave-velocity changes may be used to determine nonlinear elastic constants of materials. In the uniaxial loading experiment, analysis of the direct P wave can distinguish the acoustoelastic effects in the stress direction and the non-stress direction, which may potentially be used for stress evaluation in prestressed structures. However, the coda wave does not show this directional property to stress due to multiple scattering in the medium.

Applications of a micro-structured brittle damage model to laboratory tests on rocks

A multiscale microstructured brittle damage model is used to describe the behavior of confined rock materials. Plane strain and triaxial tests conducted at the laboratory scale are simulated in terms of boundary value problems. Simulations reveal good predictive qualities of the model to describe the macroscopic features of specimens at failure. The microstructures, oriented in different directions, allow the localization of the macroscopic strain along straight lines, emerging at the macroscale in the form of shear bands. The microstructured material model, characterized by recursive equidistant parallel cohesive-frictional faults, is fully defined by six elastic and inelastic material constants. The model was originally developed in a finite kinematics framework to simulate the dynamic behavior of confined brittle materials (Pandolfi et al. in J Mech Phys Solids 54:1972–2003, 2006). In linearized form, it has been extended and used for the simulation of in-field excavations (De Bellis et al. in: Eng Geol 215:10–24, 2016). The performance of the model in predicting the behavior of small scale rock tests in the laboratory, the object of the present study, has never been investigated. Numerical simulations show that the model is able to capture several important features observed in rocks, in particular the reduction of the overall stiffness for increasing deterioration of the material, fragile to ductile transition, strain localization, shear band formation, and more general size-effect.

Response of rigid circular plate in a functionally graded transversely isotropic, half-space under horizontal steady-state excitation

In this paper, a theoretical formulation for lateral translation and impedance function of a rigid foundation in a transversely isotropic functionally graded (TIFG) half-space is presented. Accordingly, the medium is considered linear elastic and the elastic constants of materials vary exponentially along the depth for considering the effect of elastic non-homogeneities. The relax treatment of mixed boundary value problem is formulated by integrating the transformed kernels of Green’s functions over the foundation area with unknown surface traction function, which can be reduced into a Fredholm integral equation. The results represent the impact and treatment of frequency and material anisotropy through the medium. In addition, static and dynamic distribution of tangential shear stress over the foundation for surface and embedded disk extracted and the cutoff frequency is found out explicitly. The proposed solution gives exact concurrence with accessible literature.

Theoretical and experimental investigation of circumferential guided waves in orthotropic annuli

The fiber composite materials fabricated by stacking the lamina structure obtain increasing attention in the industry, and at the same time, damage analysis is essential for safe operation. A proposed way to detect defects such as debonding and delamination is to induce circumferential guided waves. Accurate determination of the dispersion characteristics and wave fields is a prerequisite for using acoustic guided waves. The aim of this work is to provide such an accurate dispersion results in an arbitrarily thick cylindrically orthotropic homogeneous cylindrical shell of uniform thickness. Compared with the traditional SAFE method, the proposed method, which combines the two numerical methods, namely Floquet Boundary Condition (Floquet BC) Method and Sweeping Frequency Finite Element Modeling (SFFEM) method has obvious advantages. Through Floquet BC method, a theoretical result can be easily obtained without tedious code writing. Then SFFEM helps to verify the theoretical result in an experimental way. Besides, the slight gap between the theoretical and experimental results works as a basis for calibrating the elastic constants of composite materials provided in the manual. Simulations in COMSOL Multiphysics FE software supported by both methods and experiments by the latter have been carried out in this work. The calculated phase velocity dispersion curves demonstrated the efficiency of those two methods. The developed method can be adapted to other complex pipeline structures to extract circumferential guided wave dispersion characteristics by both simulation and experimental measurements.