Elastic Constants Of Material Research Articles

Systematic investigation of physical properties of Mg3XO4 (X = Cr, Mn, Fe, Co, Ni); a computational approach

Material development is primarily dependent on their design and theoretical exploration. Density functional theory is a great tool to achieve this goal. Here, Mg3XO4 (X = Cr, Mn, Fe, Co, Ni) are considered in order to reveal their full characteristics using density functional theory. Mg3XO4 (X = Cr, Mn, Fe, Co, Ni) are investigated in terms of their structural, elastic, mechanical, thermodynamic, electronic, and dynamic properties. The formation energies for Mg3XO4 (X = Cr, Mn, Fe, Co, Ni) are found to be negative implying synthesisability and dynamic stability of these materials. The evolution of elastic constants of materials demonstrates that all materials satisfy the Born stability criterion, hence Mg3XO4 (X = Cr, Mn, Fe, Co, Ni) are mechanically stable. Several polycrystalline parameters are derived by using elastic constants and evaluated. All materials are found be brittle, hard (Vickers hardness) and magnetic. They exhibit some degree of anisotropy in Young/Shear modulus and Poisson’s ratio. The electronic band structures for Mg3CrO4, Mg3MnO4 and Mg3FeO4 indicated a semi-metallic nature whereas for Mg3CoO4 and Mg3NiO4 indicated metallic nature because both the majority and minority energy bands cut the Fermi level. The phonon modes are found to be in positive frequencies that confirms dynamical stability. The materials’ free energy, entropy, specific heat capacity, Debye and melting temperatures, minimum thermal conductivity and Grüneisen parameters are also obtained and discussed.

Group-random algorithm to generate representative volume element models for composites

One of the most commonly used methods for characterizing the mechanical properties of discontinuous fiber reinforced composites (DFRC) is to establish a Representative Volume Element (RVE) model and perform finite element (FE) analysis. However, FE analysis on RVE models established by traditional sampling algorithms is often computationally expensive due to the large size of RVE that is required to be statistically representative of the composite. To address this issue, this paper proposes a new approach for constructing RVE models with more accurate description of fiber orientation, aiming to make the FE modelling more efficient by using an RVE with small size. When establishing RVE models with given target fiber orientation tensor, it is very challenging to accurately capture the orientation of fibers. In order to mitigate the error between the orientation tensor reconstructed by fibers generated in the RVE and the target orientation tensor, a group-random algorithm is proposed in the current work to generate RVE models. Unlike the traditional algorithm, in which fibers are sampled one by one in the RVE, the group-random algorithm samples a group of four fibers at one time in order to eliminate the error of the off-diagonal components of the reconstructed orientation tensor in the principal coordinate system. Then a modification tensor is further introduced to mitigate the error of the diagonal components of the reconstructed orientation tensor. Simulation results show that the orientation tensor error could be significantly reduced by the group-random algorithm even for the RVE with low number of fibers. The merits of the group-random algorithm are also witnessed by the stability and accuracy of predicting the elastic constants of composite materials through RVE modeling. It is thus concluded that the major advantage of this work is to provide an alternatively feasible strategy to substantially improve computational efficiency of RVE modelling.

First principles exploration of structural, mechanical, thermodynamic, optic, electronic and dynamic properties of MgNiX (X=Bi, Ge, Sb) for energy storage applications

Energy storage material development is primarily dependent on their design and theoretical exploration. Using density functional theory is a good way to achieve this. To do that, MgNiX (Bi, Ge, Sb) are proposed, and their full characteristics are investigated using density functional theory. MgNiX (Bi, Ge, Sb) are investigated in terms of their structural, mechanical, thermodynamic, optical, electronic, and dynamic properties. The formation energies for MgNiX (Bi, Ge, Sb) are −0.224, −0.258 and −0.421 eV/atom, respectively, implying synthesisability and dynamic stability. The evolution of elastic constants of materials demonstrates that all materials satisfy the Born stability criterion, hence MgNiX (Bi, Ge, Sb) are mechanically stable. Several polycrystalline elastic constants are computed and evaluated. The electronic band structures show that the valence band and conduction band overlaps, indicating the metallic nature of MgNiX (Bi, Ge, Sb) materials which are calculated by using PBE-GGA, PBE+SOC and PBE+U methods. The phonon modes are found to be in positive frequencies that confirms dynamical stability of the materials. The materials' free energy, entropy, specific heat capacity, Debye and melting temperatures and Grüneisen parameters are also obtained and discussed. The maximum optical conductivity is determined in the ultraviolet region for MgNiBi and MgNiSb as 73 at about 5.1 eV and 80 at about 5.50 eV, respectively and it is determined as 62 at 0.65 eV in the infrared region for MgNiGe.

Micro-CT image-based computation of effective thermal and mechanical properties of fibrous porous materials

Fibrous porous materials are extensively employed as heat shielding material for space vehicles and capsules. To predict the performance of these materials using computational modeling at the vehicle/capsule scale, the effective material properties are needed. In this work, the effective thermal conductivity and elastic constants of a carbon fibrous porous material called FiberForm (precursor of PICA) were calculated using a direct image-based approach. In this image-based approach, the microstructures obtained using X-ray computed tomography technique are represented as binary voxel data. Nonlocal interactions are introduced between neighboring voxels. Integro-differential equations, with respect to spatial and temporal dimensions respectively, are developed to govern material thermal and mechanical behaviors. Using this approach, energy-based computational procedures were developed to calculate the effective material properties of fibrous and porous materials irrespective of the periodicity of underlying microstructures. The size of representative volume element was determined by convergence of effective properties with respect to microstructure size.

The Pressure‐Induced Structural Stability, Mechanical, and Optoelectronic Properties of Pb2ScTaO6 Perovskite: a Density Functional Theory Study

This study provides a comprehensive analysis of the cubic double‐perovskite compound Pb2ScTaO6, exploring its structural stability, electronic, optical, and mechanical properties. The material's response to hydrostatic pressure, using density functional theory with the FP‐LAPW approach, is investigated. The analysis, validated by experimental and theoretical data, reveals Pb2ScTaO6's semiconductor nature with a bandgap of 3.129 eV, which decreases under hydrostatic pressure. Furthermore, the assessment of the material's elastic constants confirms its mechanical stability and the optical properties across ultraviolet and infrared spectra suggest potential applications in optoelectronic devices.

Resonant ultrasound spectroscopy for textured materials

Resonant ultrasound spectroscopy (RUS) is a method in which the least-squares fitting of a sample's measured resonance frequencies is used to determine the sample material's elastic constants. Difficulties arise when RUS is applied to textured materials, which are composed of crystallites that are neither completely aligned nor randomly oriented; such materials would have effective elastic tensors with 21 independent elastic constants, and this would overburden the conventional RUS analysis process. In any case, the elastic nature of some textured materials may be represented as the weighted average of the elastic tensors of the constituent crystalline material rotated in the directions of the individual crystallites. The collection of weights is the orientation distribution function (ODF). Now the least-squares fitting of a sample's measured resonance frequencies may be used to determine not the sample's elastic constants but instead its ODF. This is not trivial since the weights must be positive and sum to one, but it may be done with a simple modification of the conventional RUS software.

Exploring the electronic potential of effective tight-binding hamiltonians

The linear combination of atomic orbitals (LCAO) is a standard method for studying solids and molecules, it is also known as the tight-binding (TB) method. In most of the implementations only the basis set and the coupling constants are provided, without the explicit definition of kinetic and potential energy operators. The tight-binding scheme is, nonetheless, capable of providing an accurate description of properties such as the electronic bands and elastic constants for many materials. However, for some applications, the knowledge of the underlying electronic potential associated with the tight-binding hamiltonian might be important to guarantee that the actual physics is preserved by the semiempirical scheme. In this work the electronic potentials that arise from the use of tight-binding effective hamiltonians it is explored. The formalism is applied to the extended Hückel tight-binding (EHTB) hamiltonian, which is a two-center Slater−Koster approach that makes explicit use of the overlap matrix.

A GENERALIZED FRACTAL-BASED APPROACH FOR STRESS-DEPENDENT PERMEABILITY OF POROUS ROCKS

The pore geometry of porous rocks is fundamental for accurate description of stress dependence of effective permeability, which is an important parameter of mass transfer in porous rocks. An important physical assumption that porous rocks contain numerous elliptical or spherical pores has been shown to be successfully applied to many aspects of hydromechanical coupling properties of porous rocks. To investigate the detailed description of pore structures on the degree of effect on the coupled hydromechanical process, in this work, a generalized stress-dependent model for permeability of porous rocks has been proposed based on fractal geometry theory and mechanics of porous rock. The proposed model is expressed as a nonlinear function of pore structure parameters, such as aspect ratio ([Formula: see text]), the fractal dimensions ([Formula: see text] and [Formula: see text]) for tortuosity, the initial fractal dimension ([Formula: see text]), and initial porosity ([Formula: see text]) as well as matrix elastic constants ([Formula: see text] and [Formula: see text]) of porous rocks without any empirical parameter. The validity of the proposed models is verified by the good agreements between available experimental data and theoretical predictions of stress-dependent permeabilities of porous rocks. Detailed discussions of the essential effects of pore structures parameters and material elastic constants of porous rocks on the dimensionless stress-dependent permeabilities are performed. It is found that the stress parameters ([Formula: see text] and [Formula: see text]) have remarkable effects on the dimensionless stress-dependent permeabilities compared with other parameters ([Formula: see text] and [Formula: see text]). The proposed model may contribute to a better quantitative understanding of the coupled hydromechanical properties of porous rocks.

An innovative quasi-bond approach to bridge continuity, anisotropic damage and macroscopic fracture of solids and structures

Spontaneous formation and evolution of discontinuities in solid media still poses one of the significant challenges in solid mechanics and computational mechanics. To facilitate numerical modeling, a new model called herein ‘quasi-bond’ model is proposed, which redefines the form of local interaction between material particles. Unlike traditional discrete methods that require direct connections between material particles, in this quasi-bond method, only one end of each bond is actually connected to a material particle, rendering great flexibility in describing bond distribution and anisotropic damage by bond breakage. Homogenization of solid body can be performed by an integral over quasi-bonds, while the process of crack nucleation, propagation and coalescence to form fracture is simulated through bond breakage. Especially, the relationship between material elastic constants and bond stiffness parameter is established in both two- and three-dimensional contexts. Furthermore, a smoothed strain-based fracture description is proposed with the ability of eliminating particle density/distribution dependence problems. Finally, several benchmark tests are conducted to demonstrate the efficiency and accuracy of the proposed approach in solving elasticity and fracture problems.

Overall elastic characterization of equivalent FE models for aluminum foams through computational homogenization approach and genetic algorithm optimization

Aluminum foams are gaining increasing interest because of their widespread set of functional attributes combined with highly specific structural properties and affordable manufacturing processes. The finite element analysis of foam materials is typically performed with complex and time-consuming 3D models. Here, a beam FE model strategy is utilized to obtain a precise and time-saving simulation instrument for open-cell aluminum foams. The beam FE modeling is based on the Kelvin cell as a fundamental unit and provides a simplified geometrical description of the intersection node between ligaments whose elastic properties need to be adjusted through a calibration procedure. The beam FE model elastic properties are measured through a homogenization procedure that evaluates the elastic constants of an equivalent material. The issue of model calibration is formulated as an optimization problem exploiting the NSGA-II genetic algorithm. This procedure allows obtaining the full elastic calibration of the beam FE model, reproducing the orthotropic elastic behavior of the aluminum foams with reduced computational efforts.

Characterizing Mechanical Properties of Layered Engineered Wood Using Guided Waves and Genetic Algorithm.

This study develops a framework for determining the material parameters of layered engineered wood in a nondestructive manner. The motivation lies in enhancing nondestructive evaluation (NDE) and quality assurance (QA) for engineered wood or mass timber, promising construction materials for sustainable and resilient civil structures. The study employs static compression tests, guided wave measurements, and a genetic algorithm (GA) to solve the inverse problem of determining the mechanical properties of a laminated veneer lumber (LVL) bar. Miniature LVL samples are subjected to compression tests to derive the elastic moduli and Poisson's ratios. Due to the intrinsic heterogeneity, the destructive compression tests yield large coefficients of variances ranging from 2.5 to 73.2%. Dispersion relations are obtained from spatial-temporal sampling of dynamic responses of the LVL bar. The GA pinpoints optimal mechanical properties by updating orthotropic elastic constants of the LVL material, and thereby dispersion curves, in a COMSOL simulation in accordance with experimental dispersion relations. The proposed framework can support estimation accuracy with errors less than 10% for most elastic constants. Focusing on vertical flexural modes, the estimated elastic constants generally resemble reference values from compression tests. This is the first study that evaluates the feasibility of using guided waves and multi-variable optimization to gauge the mechanical traits of LVL and establishes the foundation for further advances in the study of layered engineered wood structures.

Evaluation of elastic constants of particle accelerator cavity materials with Resonant Ultrasound Spectroscopy

European Spallation Source is a multi-nation, interdisciplinary research facility based on the world’s most powerful neutron source that will operate with high standards of availability and reliability minimizing downtime periods. In order to meet these goals, critical component’s performance and ageing need to be constantly monitored and assessed. Resonant Ultrasound Spectroscopy (RUS) is a highly versatile non-destructive technique for the definition of elasticity matrix of materials through the measurement of resonance frequencies. RUS could benefit the characterization of particle accelerator cavity materials exposed to challenging operational environments during project’s design and commissioning phases. This paper demonstrates the methodology and the first results on the implementation of this technique on Radio-Frequency Quadrupole (RFQ) structural copper. Rectangular parallelepiped samples of polycrystal, oxygen free, high purity Cu-OF copper were prepared and RUS measured on a designed experimental set-up. The obtained resonance frequencies were used as an input for the solution of the inverse eigenvalue problem using open-source objective function minimization software. The obtained results are compared with commercially available Finite Element Method (FEM) software defining a repeatable methodology for material property and defect characterization.

Experimental characterization, theoretical modeling and failure analysis of the mechanical behavior of acrylonitrile butadiene styrene parts by fused filament fabrication

PurposeThe purpose of this research is present an experimental and numerical study of the mechanical properties of the acrylonitrile butadiene styrene (ABS) in the additive manufacturing (AM) by fused filament fabrication (FFF). The characterization and mechanical models obtained are used to predict the elastic behavior of a prosthetic foot and the failure of a prosthetic knee manufactured with FFF.Design/methodology/approachTension tests were carried out and the elastic modulus, yield stress and tensile strength were evaluated for different material directions. The material elastic constants were determined and the influence of infill density in the mechanical strength was evaluated. Yield surfaces and failure criteria were generated from the tests. Failures over prosthetic elements in tridimensional stresses were analyzed; the cases were evaluated via finite element method.FindingsThe experimental results show that the material is transversely isotropic. The elasticity modulus, yield stress and ultimate tensile strength vary linearly with the infill density. The stresses and the failure criteria were computed and compared with the experimental tests with good agreement.Practical implicationsThis research can be applied to predict failures and improve reliability in FFF or fused deposition modeling (FDM) products for applications in high-performance industries such as aerospace, automotive and medical.Social implicationsThis research aims to promote its widespread adoption in the industrial and medical sectors by increasing reliability in products manufactured with AM based on the failure criterion.Originality/valueMost of the models studied apply to plane stress situations and standardized specimens of printed material. However, the models applied in this study can be used for functional parts and three-dimensional stress, with accuracy in the range of that obtained by other researchers. The researchers also proposed a method for the mechanical study of fragile materials fabricated by processes of FFF and FDM.

Investigating elastic constants across diverse strain-matrix sets

Elastic constants and mechanical properties play a pivotal role across multiple disciplines and engineering applications. We introduced the optimized high-efficient strain-matrix set (OHESS) that determines the second-order elastic constants of materials using the stress–strain method. Herein, we systematically investigate the computational efficiency of OHESS across a broad range of crystal systems and compare it with other notable stress–strain approaches, such as the single-element strain-matrix sets and the universal linear-independent coupling strains. Notably, our data affirm the superior efficacy of OHESS among the strain-matrix sets under consideration. We believe OHESS will markedly improve computational efficiency in determining the elastic constants and mechanical properties, becoming an indispensable tool for material research, design, and high-throughput screening.

The dependence of X-ray elastic constants with respect to the penetration depth.

X-ray diffraction techniques are widely used to estimate stresses within polycrystalline materials. The application of these techniques requires the knowledge of the X-ray elastic constants relating the lattice strains to the stress state. Different analytical methods have been proposed to evaluate the X-ray elastic constants from the single-crystal elastic constants. For a given material, such methods provide the bulk X-ray elastic constants but they do not consider the role of free surfaces. However, for many practical applications of X-ray diffraction techniques, the penetration depth of X-rays is the same order of magnitude as the grain size, which means that the influence of the free surface on X-ray elastic constants cannot be excluded. In the present work, a numerical procedure is proposed to evaluate the surface and bulk X-ray elastic constants of polycrystalline materials. While the former correspond to the situation where the penetration is infinitely small in comparison with the grain size, the latter are representative of an infinite penetration depth with no free-surface effect. According to numerical results, the difference between surface and bulk X-ray elastic constants is important for strongly anisotropic crystals. Also, it is possible to propose a relation that allows evaluating X-ray elastic constants as a function of the ratio between the penetration depth and the average grain size. The corresponding parameters of such a relation are provided here for many engineering materials.

Determining the Elastic Constants of Isotropic Materials by Measuring the Phase Velocities of the A0 and S0 Modes of Lamb Waves.

In this study, a new method for determining the elastic constants of isotropic plates using Lamb wave fundamental modes is presented. This method solves the inverse problem, where the elastic constants (Young's modulus and Poisson's ratio) of the plate were estimated by measuring the phase velocities of the Lamb wave using the Rayleigh-Lamb equations to find the solution and determining the phase velocities of the A0 and S0 modes using a new method. The suitability of the proposed method for determining the elastic constants was evaluated using simulated and experimental signals propagating on an aluminum plate. The theoretical modeling on the aluminum 7075-T6 plate shows that the proposed method allows the determination of the Poisson ratio with a relative error not exceeding 2% and Young's modulus with a relative error not exceeding 0.5%. The experimental measurements of an aluminum plate of known thickness (2 mm) and density (2685 kg/m3) confirmed the suitability of the proposed method for the measurements of elastic constants. In the proposed method, the processing of ultrasonic signals can be performed in real-time, and the values of the elastic constants can be obtained immediately after scanning the required distance.

Cross-modulation in guided wave propagation: how does it relate to the Luxemburg-Gorky effect?

The well-known Luxemburg-Gorky effect in radio waves has also been observed in elastic waves recently, which points to new possibilities for incipient damage detection. However, how the cross-modulation phenomenon of guided waves in a weakly nonlinear medium is related to the Luxemburg-Gorky effect remains an open question. This issue is investigated in this paper. Considering the third-order nonlinear elasticity of a plate waveguide, a theoretical framework is proposed to analyze the influence of the mode combination and mixing direction of a pair of single-frequency and modulated waves on the cross-modulated component generation. In particular, a codirectional shear-horizontal wave mixing scheme is highlighted which enables the generation of internally-resonant cross-modulated components at all frequencies. After verification by finite element simulation, mechanisms underpinning the cross-modulated components in the codirectional shear-horizontal wave mixing scheme are revealed through tactical tuning of the higher-order material elastic constants. Experiments are conducted to further confirm the phenomena and substantiate their relevance to the Luxemburg-Gorky effect. It is established that the cross-modulated components of guided waves can be generated and practically measured in a weakly nonlinear plate via both pure and mixed mechanisms as a result of the cubic nonlinearity instead of the quadratic nonlinearity. Compared with the conventional two-wave mixing methods based on quadratic nonlinearity, the cross-modulated components exhibit higher sensitivity to material microstructural changes, which is conducive to incipient damage detection. Although the observed nonlinear cross-modulation in guided waves shows similarities with the Luxemburg-Gorky effect, they stem from different mechanisms: the former from nonlinear elasticity and the latter nonlinear dissipation.

Microstructure of macrointerfaces in shape-memory alloys

Shape-memory alloys exhibit a rich microstructure, characterized by large regions containing relatively regular laminates mixing different martensitic variants. Macrointerfaces separate these regions, and are often composed of arrays of needle-shaped martensitic domains. We formulate a model for the geometry of arrays of needles and present numerical simulations, appropriate for two compound twinned variants of martensite in a plane stress setting. One important ingredient is a new class of polyconvex energy densities with cubic symmetry, that is able to reproduce the austenitic elastic constants of the relevant materials. The energy-minimizing needle geometry is determined with tools from shape optimization. Our main finding is the “transparency effect”, which characterizes the effect of needles on domain boundaries located in front of their tip. Our numerical results are in good agreement with experimental observations.

Characterizing elastic constants of anisotropic materials by spherical indentation method

By the theoretical analysis and the finite element (FE) method, a new model for measuring the elastic constants of transversely isotropic materials has been proposed from spherical indentation. A theoretical analysis of the spherical indentationmodulus for the materials is presented. Extensive spherical indentation tests were implemented by three dimensional (3D) FE simulations. By fitting the simulation results, the analytical relationship correlating the elastic parameters with the indentation moduli at three different indentation orientation angles (0°, 45°, and 90°) was set up. The effectiveness of the proposed method was examined by a series of numerical indentation experiments. It is found that the calculated values by the proposed method are well consistent with the input elastic parameters. The sensitivity of the calculated elastic parameters to the experimental data was analyzed. Simultaneously, this method was applied to carbon fiber materials. The results calculated by the method proposed in this paper were compared with results obtained by the theoretical model and experimental measurement to verify the effectiveness of this method. Thus the proposed method is practiced and could be used to identify the elastic properties of transversely isotropic materials.

Elastemp — A workflow to compute the quasi-harmonic temperature dependent elastic constants of materials

Elastic constants characterize the stiffness of a material. A linear relationship between the stress and strain tensors in the limit of infinitesimal deformation is used to define and compute the elastic constants. Typically, this is computed at zero temperature by deforming the simulation box in one of the six directions and computing the stress tensor. Calculating elastic constants at finite temperature is more challenging owing to large fluctuations and thermal noise. Here, we introduce a semi-automated workflow — Elastemp, to obtain the quasi-harmonic elastic constants of materials as a function of temperature. The workflow integrates with electronic structure packages such as VASP and PHONOPY to get the quasi-harmonic energies. The workflow is capable of estimating the zero temperature elastic constants, thermal expansion coefficients of materials and temperature dependent elastic constants. The predictions for a set of representative test cases with different crystal symmetries (Al, Diamond, Titanium nitride (TiN) and α-Ti) are compared with experiments and used to demonstrate the efficacy of our workflow.