Anisotropic Elastic Properties Research Articles

Elastic constants of biogenic calcium carbonate

Living organisms form complex mineralized composite architectures that perform a variety of essential functions. These materials are commonly utilized for load-bearing purposes such as structural stability and mechanical strength in combination with high toughness and deformability, which are well demonstrated in various highly mineralized molluscan shell ultrastructures. Here, the mineral components provide the general stiffness to the composites, and the organic interfaces play a key role in providing these biogenic architectures with mechanical superiority. Although numerous studies employed state-of-the-art methods to measure and/or model and/or simulate the mechanical behavior of molluscan shells, our understanding of their performance is limited. This is partially due to the lack the most fundamental knowledge of their mechanical characteristics, particularly, the anisotropic elastic properties of the mineral components and of the tissues they form. In fact, elastic constants of biogenic calcium carbonate, one of the most common biominerals in nature, is unknown for any organism. In this work, we employ the ultrasonic Pulse-Echo method to report the elasticity tensor of two common ultrastructural motifs in molluscan shells: the prismatic and the nacreous architectures made of biogenic calcite and aragonite, respectively. The outcome of this research not only provides information necessary for fundamental understanding of biological materials formation and performance, but also generates textbook knowledge on biogenic calcium carbonate required for future structural/crystallographic, theoretical and computational studies.

Active vibration suppression of tetrachiral auxetic core sandwich panel with CFRP skin: An RVE homogenization-assisted finite element approach

Free vibration as well as the controlled dynamic response of moderately-thick smart sandwich panel are numerically explored considering the size effect of chiral unit cells at the microscopic level, with the help of RVE-assisted-finite element (FE) approach. In this scientific article, the authors have made a debut attempt to analyse the smart damping behaviour of a tetrachiral-type auxetic core sandwich panel (with carbon/epoxy skin) deploying a real-time based constant velocity feedback controller in a closed loop configuration. Effective anisotropic elastic properties as well as the reduced stiffness matrix of the cellular core layer have been determined by using RVE-FE based full-scale homogenization technique in ANSYS® platform. Dynamic equation of motion governing the plate structure, has been derived using an energy-based variational principle, and further solved with the help of a quadratic interpolation based finite element method. The mid-plane kinematics of the plate structure are assumed to follow first order shear deformation theory (FSDT). A number of numerical examples have been solved and compared with previously published literature to ensure the consistency of the present homogenization-cum-numerical approach. From the observation it is found that, the natural frequency and the controlled dynamic response of tetrachiral-type sandwich structure are very much sensitive towards the geometry (cell wall thickness, ligament length etc.) and architecture of the unit cell of the auxetic core. Also, a comparison study has been performed between tetrachiral auxetic smart sandwich and regular hexagonal honeycomb smart sandwich plate, which confirms about the mechanical advantage of the former over the later configuration, due to the existence of out-of-plane negative Poisson's ratio (NPR) and axial-shear coupling stiffness. Afterwards, a few additional numerical examples have been solved by changing different influencing parameters of the auxetic core sandwich plate and important results are reported in the article.

Distribution of gas hydrate in fractured reservoirs: implications from anisotropic elastic and electrical numerical simulations

SUMMARY Fractured hydrate-bearing reservoirs are extensively discovered worldwide and show notable anisotropic geophysical properties. Hydrate distribution in fractures significantly affects the anisotropic properties, and hence plays an important role in the accurate assessment of hydrate resources. However, the knowledge about how the hydrate distribution impacts the anisotropic geophysical properties of fractured reservoirs, which is the premise for the identification and quantification of hydrate in fractured reservoirs, is still poorly understood. To obtain such knowledge, we forward study the effects of various hydrate distribution (including floating, bridging and evolving hydrate distribution) in aligned fractures on the anisotropic elastic, electrical and joint elastic–electrical properties of a digital core using validated numerical methods. We show that for all the hydrate distribution, the anisotropic velocities increase, while the conductivities decrease with increasing hydrate saturation, with the effects of the floating and bridging distribution being the least and greatest, respectively. We also show that the anisotropic velocities and conductivities for the floating and bridging distribution vary approximately linearly with hydrate saturation, leading to linear correlations between the elastic and electrical properties. Further investigation illustrates that the difference in the slopes of the linear joint correlations between the two distribution is significantly greater than that of the individual properties as a function of hydrate saturation. The results have revealed the distinct effects of hydrate distribution on the anisotropic elastic and electrical properties of fractured reservoirs, and have confirmed the superiority of the joint elastic–electrical properties for the distinguishment of hydrate distribution in fractures over individual physical properties.

Development of machine learning force field for thermal conductivity analysis in MoAlB: Insights into anisotropic heat transfer mechanisms

The MAB phases have garnered significant attention as a new generation high-temperature structural materials due to their outstanding high-temperature mechanical properties, resistance to oxidation at elevated temperatures, low-temperature synthesis, and machining capabilities. The chemically anisotropic bonding within MAB phases leads to unique anisotropic elastic properties, oxidation behavior, and electrical characteristics, posing challenges in understanding the structure-property relationships.To address this challenge, we leveraged recent advances in machine learning force fields based on quantum mechanics methods. Using ab initio molecular dynamics simulations, we constructed a comprehensive dataset and developed an accurate machine learning force field for the Mo–Cr–Al–B system based on deep neural network. We then employed non-equilibrium molecular dynamics simulations to calculate the phonon thermal conductivity of MoAlB, investigating its temperature dependence and anisotropy. Our analysis includes phonon density of states, phonon participation ratio, and spectral heat flux analysis, shedding light on the temperature-dependent anisotropy of phonon thermal conductivity in MoAlB. This work not only provides a reliable force field for large-scale molecular dynamics simulations but also advances our understanding of the composition-structure-performance relationship in MAB phases.

Effect of indented growth rings on spruce wood mechanical properties and subsequent violin dynamics

Abstract In this study, the influence of “bear claw” or indented growth ring anatomical patterns on the vibro-mechanical behavior of spruce wood have been investigated, particularly in the context of utilizing these singularities/specific features for the construction of violins. By employing vibrometry and modal analysis followed by finite element model updating, the vibro-mechanical properties (specific stiffness in longitudinal (L) and radial (R) directions and shear LR plane, and associated damping) of the indented growth rings spruce were identified and implemented in a numerical model of a violin. Results have revealed a significant increase in specific moduli in R direction and LR plane and decrease in L direction of spruce wood in the presence of indented growth rings, therefore accompanied by a reduction in anisotropic elastic properties, in comparison to spruce without these patterns. These properties led to changes in violin dynamics, globally increasing resonance frequencies and changing the shape of the vibration modes. The simulated frequency response function of the violin at the bridge suggested a global shift of the admittance of the bridge toward higher frequencies. These results suggest a potential impact of indented growth rings of spruce on the acoustic properties of instruments.

Anisotropic elastic and thermal properties and damage tolerance of CrH: A first-principles calculation

The elastic properties, thermal properties, and damage tolerance of one cubic (C-CrH) and two hexagonal (H1-CrH and H2-CrH) CrH hydrides were investigated using first-principles calculation based on density functional theory (DFT). The results showed that C-CrH is brittle, while H1-CrH and H2-CrH are ductile. Compared to the hexagonal CrH, C-CrH has the highest hardness, the largest damage tolerance, and the largest fracture toughness values. Three-dimensional (3D) surface configurations and two-dimensional (2D) planar projections were used to estimate the elastic anisotropy, and the elastic anisotropy is in the order of H2-CrH > C-CrH > H1-CrH. In addition, C-CrH has the highest minimum thermal conductivity among these CrH hydrides. CrH hydrides are anisotropic in minimum thermal conductivity with the order of H1-CrH > C-CrH > H2-CrH.

Novel Design Charts for Anisotropic Effective Elastic Properties of Pyramidal Lattice Materials

Novel design charts for predicting the anisotropic effective elastic properties of pyramidal lattices are proposed for a wide range of relative density and various struts shape through finite element (FE) simulations. Pyramidal lattices are 3D printed using digital light processing (DLP) and are subsequently subjected to uniaxial compression tests to provide a partial experimental validation for the presented design charts. Regarding strut shape, the presented results uncover that using hollow-tapered instead of solid-uniform struts leads significant improvements for effective Young's and shear moduli. In addition, this study has paved the way towards enhancing our understanding of how the anisotropy of pyramidal lattices can be tailored by tuning the relative density and strut architecture. Resorting to an analytical framework, results indicate that controlling the void volume fraction of struts can lead the same effective Young's modulus for all three principal directions of pyramidal lattices with low relative densities.

Deep Learning for Size-Agnostic Inverse Design of Random-Network 3D Printed Mechanical Metamaterials.

Practical applications of mechanical metamaterials often involve solving inverse problems aimed at finding microarchitectures that give rise to certain properties. The limited resolution of additive manufacturing techniques often requires solving such inverse problems for specific specimen sizes. Moreover, the candidate microarchitectures should be resistant to fatigue and fracture. Such a multi-objective inverse design problem is formidably difficult to solve but its solution is the key to real-world applications of mechanical metamaterials. Here, a modular approach titled "Deep-DRAM" that combines four decoupled models is proposed, including two deep learning (DL) models, a deep generative model based on conditional variational autoencoders, and direct finite element (FE) simulations. Deep-DRAM integrates these models into a framework capable of finding many solutions to the posed multi-objective inverse design problem based on random-network unit cells. Using an extensive set of simulations as well as experiments performed on 3D printed specimens, it is demonstrate that: 1) the predictions of the DL models are in agreement with FE simulations and experimental observations, 2) an enlarged envelope of achievable elastic properties (e.g., rare combinations of double auxeticity and high stiffness) is realized using the proposed approach, and 3) Deep-DRAM can provide many solutions to the considered multi-objective inverse design problem.

Suspended Black Arsenic Nanoribbons with Anisotropic Elastic Properties for Nanomechanical Devices

Suspended Black Arsenic Nanoribbons with Anisotropic Elastic Properties for Nanomechanical Devices

Data-driven texture design for reducing elastic and plastic anisotropy in titanium alloys

Polycrystalline titanium alloys exhibit anisotropic elastic and plastic properties, which hinder their extensive application as structural components. Overcoming this anisotropy via texture control is challenging due to the anisotropy intrinsic to the titanium single crystal. We propose a theoretical framework to derive textures that minimize anisotropy while maximizing Young’s modulus or flow stress. The workflow integrates data-driven methods, convex optimization theory, and computational crystal plasticity, using measured elastic constants and the alloy’s three slip modes. Optimization constraints are applied to predict textures that satisfy an anisotropy-reducing texture-property relationship. Examples include minimizing both elastic and plastic anisotropy while maximizing stiffness or flow stress, maximizing both stiffness and flow stress, and minimizing the number of distinct orientations. Deformation crystal plasticity simulations of 3D polycrystal microstructure realizations of the example textures demonstrate the achievement of target properties. We show that uniformly distributed (or no) textures or textures designed to purely reduce elastic anisotropy are accompanied by reduced moduli. Counterintuitively, the analysis reveals that appropriate fractions of a relatively small number of select orientations can reduce elastic or plastic anisotropy. Moreover, we derive anisotropy-reducing textures constrained to achieve similarity to those from common metal forming processes like rolling. Finally, we show that anisotropy-reducing textures from this framework can be effectively used for minimizing anisotropy in other Ti alloys, without the need to repeat the data-collection and optimization processes. This study offers new insights into the link between microstructure texture and structural properties, providing a novel approach to designing materials of anisotropic hexagonal close-packed crystals.

Noninvasive identification of directionally-dependent elastic properties of soft tissues using full-field optical data

This paper introduces an innovative approach for elastic property characterization of soft tissues, having directional-dependent material behavior, via their vibration response measurement and interpretation. The full-field time-dependent surface displacements as a result of externally excited soft tissues are collected through digital image correlation (DIC). A developed analytical model, capturing the low-amplitude vibration behavior of anisotropic layered human skin with the incorporation of the influence of subcutaneous elasticity and inertia, is employed to accurately predict its resonant frequencies and pertaining displacement field images. An efficient solution approach for the model is implemented into an inverse algorithm to rapidly characterize the anisotropic elastic properties based on importing the vibration characteristics. To show the merit of the approach, a 3-D finite element (FE) simulation model was used to generate full-field data, detected and matched with a set of specific vibration modes via modal assurance criterion (MAC). The validity of the model implemented into the inverse characterization algorithm is demonstrated through a comparison of predicted vibration frequencies and mode-shapes simulated via the 3-D FE model for different cases with anisotropic elastic properties in different layers of the skin. It is shown that modes are influenced differently when anisotropic properties are introduced to the model. Thus, the established inverse characterization algorithm is capable of rapidly predicting the elastic material properties of anisotropic soft sheets with adequate accuracy.

Anisotropy of Elastic Properties of Inconel 718 Alloy Specimens Obtained by 3D Printing

Anisotropy of Elastic Properties of Inconel 718 Alloy Specimens Obtained by 3D Printing

Uncertain sound transmission loss of composite laminated plates with embedded viscoelastic damping layer

Laminated composite structures have been widely applied in the engineering field due to their excellent capacities such as high specific stiffness, high specific strengths and tailorable anisotropic elastic properties. Embedding the viscoelastic damping layers into the laminated composites to construct co-cured composite damping structures provides an effective way to improve the sound insulation capability. In this paper, a semi-analytical model is proposed to investigate the sound transmission loss (STL) of composite laminated structure with embedded viscoelastic damping layer considering its frequency-dependent characteristic. Furthermore, Polynomial Chaos Expansion (PCE) method in conjunction with the semi-analytical model is employed for uncertainty propagation analysis of sound transmission loss of the composite laminated plates subjected to uncertain parameters of frequency-dependent interleaved viscoelastic damping layer. Moreover, numerical simulations are conducted to demonstrate the impacts of the uncertain parameters of the embedded viscoelastic damping layer on the STL of the composite laminated plate. Finally, experiments are carried out to investigate the uncertain acoustic insulation performance of composite laminated plates with embedded damping layer. Key words: Laminated composite structure; Sound transmission loss; Uncertainty analysis; Damping layer; Frequency-dependent properties

Velocity anisotropy measured on the spherical specimens: History and applications

The anisotropy of elastic properties, including seismic velocities, has already been investigated in the lab over past seven decades. Here, we present a review related to the development of a unique apparatus for the detailed measurement of seismic velocity anisotropy. Its originality lies in measuring velocities on spherical specimens, which allows for determination of the velocity anisotropy as a function of confining pressure loading with high resolution. The 132 directions, covering the sphere in a regular 15° net of meridians and parallels, have proven to be optimal with respect to common heterogeneities of investigated rocks. The device was designed and the first measurements were performed by a research team of the Institute of Geophysics in Prague (Babuška, Pros and Klíma) in 1968, shortly following many pioneer velocity anisotropy studies. Since then, almost 100 papers have been published using the velocity anisotropy measured with this unique device. The review consists of three separate but mutually interconnected parts: (i) historical development; (ii) microstructural insights from an ultrasonic velocity measurement perspective; (iii) macroscale applications to practical problems in geophysics, structural geology and rock mechanics.

Experimental Observation of Highly Anisotropic Elastic Properties of Two-Dimensional Black Arsenic.

Anisotropic two-dimensional layered materials with low-symmetry lattices have attracted increasing attention due to their unique orientation-dependent mechanical properties. Black arsenic (b-As), with the puckered structure, exhibits extreme in-plane anisotropy in optical, electrical, and thermal properties. However, experimental research on mechanical properties of b-As is very rare, although theoretical calculations predicted the exotic elastic properties of b-As, such as the anisotropic Young's modulus and negative Poisson's ratio. Herein, experimental observations on highly anisotropic elastic properties of b-As were demonstrated using our developed in situ tensile straining setup based on the effective microelectromechanical system. The cyclic and repeatable load-displacement curves proved that Young's modulus along the zigzag direction was ∼1.6 times greater than that along the armchair direction, while the anisotropic ratio of ultimate strain reached ∼2.5, attributed to the hinge structure in the armchair direction. This study could provide significant insights into the design of novel anisotropic materials and explore their potential applications in nanomechanics and nanodevices.

Molecular dynamic simulation of the influence of layer charge characteristics on the anisotropic elastic properties of hydrated montmorillonites

Montmorillonites are commonly existing in shales and understanding the anisotropic elastic properties of montmorillonite is very crucial because they provide important geomechanical information for the discovery and development of shale gas. Layer charges with varying densities and locations are naturally associated with montmorillonites and it has been demonstrated that these layer charge characteristics can dramatically influence the anisotropic elastic properties of dry montmorillonites. However, montmorillonites are generally hydrated by water under reservoir conditions and whether the existence of water will impact the effect of the layer charge characteristics on the anisotropic elastic properties is still poorly understood. To gain such knowledge, this paper investigated the anisotropic elastic parameters of hydrated montmorillonites with various layer charge characteristics via molecular dynamic (MD) simulations. The results demonstrated that the existence of water reduces all the elastic factors of montmorillonites, and weakens the variation of the elastic factors with different layer charge locations (LCLs), in comparison with dry montmorillonites. It was also found that when hydrated, the influence of layer charge density (LCD) on the in-plane compressional factors tends to be diminished, and the out-of-plane compressional and shear factors tend to increase consistently with increasing LCD, whereas their dependence on the LCD can be disordered in different dry montmorillonite models. The variations in the basal spacing and the interactions between the atoms caused by different layer charge characteristics when water is present were found to plausibly explain and interpret the simulation results. The results not only illustrate the link between the anisotropic elastic properties and layer charge characteristics in hydrated montmorillonites but also provide crucial geomechanical information to help the successful discovery and development of shale gas reservoirs containing hydrated montmorillonite.

Structural, anisotropic elasticity, and thermal properties of TiGe2, Ti5Ge3 and Ti6Ge5, a first-principles prediction

The anisotropic in elastic and thermal properties of C40-, C49-and C54-TiGe2, Ti5Ge3 and Ti6Ge5 were calculated by first-principles. The elastic properties of C40-, C49-and C54-TiGe2, Ti5Ge3 and Ti6Ge5 were obtained by Voigt-Reuss-Hill method. According to obtained elastic modulus, Vickers hardness HV of TiGe2, Ti5Ge3 and Ti6Ge5 were calculated. The elastic anisotropies of TiGe2, Ti5Ge3 and Ti6Ge5 were characterized by elastic anisotropic indexes (AU, AB, AG, A1, A2 and A3), three-dimensional(3D) constructions and projections of bulk and Young's moduli. In addition, the Debye temperature and sound velocity were obtained according to the elastic modulus. Finally, the directional sound velocities were also calculated and analyzed.

Physical Properties and Effect of Helium-Vacancy Pair on Tungsten/Graphene Composite as Plasma-Facing Materials from First Principles

Tungsten/graphene composite was developed and demonstrated to have good mechanical and thermal properties. Density functional theory calculations were performed to investigate elastic constants, elastic anisotropies and isotropic elastic moduli, thermodynamic properties and minimum thermal conductivity of tungsten/graphene with and without a helium-vacancy pair, and tungsten/graphane and tungsten/ditungsten carbide (tungsten/W2C) composites. The results show that tungsten/graphene composite has more toughness when compared with pure tungsten metal. It is noticed that the minimum thermal conductivity of tungsten/graphene composite is higher, introducing a potential application in heat dissipation at high temperatures. We give an honest appraisal of the anisotropic and isotropic (polycrystalline) elastic properties of tungsten/graphene, tungsten/graphane, and tungsten/W2C carbide composites. In addition, the results show that the graphene layer is a strong trap for the He atom, while He affinity to the graphene layer is weaker to a single vacancy. The formation of the He-vacancy pair due to trapping effects near the W/graphene interface will help to reduce the concentration of impurities and defects in the tungsten matrix and maintain the inherent heat dissipation properties under irradiation.

Deep material network via a quilting strategy: visualization for explainability and recursive training for improved accuracy

Recent developments integrating micromechanics and neural networks offer promising paths for rapid predictions of the response of heterogeneous materials with similar accuracy as direct numerical simulations. The deep material network is one such approaches, featuring a multi-layer network and micromechanics building blocks trained on anisotropic linear elastic properties. Once trained, the network acts as a reduced-order model, which can extrapolate the material’s behavior to more general constitutive laws, including nonlinear behaviors, without the need to be retrained. However, current training methods initialize network parameters randomly, incurring inevitable training and calibration errors. Here, we introduce a way to visualize the network parameters as an analogous unit cell and use this visualization to “quilt” patches of shallower networks to initialize deeper networks for a recursive training strategy. The result is an improvement in the accuracy and calibration performance of the network and an intuitive visual representation of the network for better explainability.

Image Processing-Based Method of Evaluation of Stress from Grain Structures of Through Silicon Via (TSV)

Visualization of material composition across numerous grains and complicated networks of grain boundaries using image processing techniques can reveal fresh insights into the material’s structural evolution and upcoming functional capabilities for a variety of applications. Three-dimensional integrated circuits (3D IC) are the most practical technology for increasing transistor density in future semiconductor applications. One of the key benefits of 3D IC is heterogeneous integration, which results in shorter interconnections due to vertical stacking. However, one of the most significant challenges in building higher-density microelectronics devices is the stress generated by material mismatches in the coefficient of thermal expansion (CTE). The purpose of this study is to analyze grain boundary migration caused by variations in strain energy density using image processing methods for 3D grain continuum modeling. Temperature changes in polycrystalline structures generate stresses and strain energy densities, which may be calculated using FEM software. Single crystal Cu’s anisotropic elastic properties are twisted to suit grain orientation in space and each grain is treated as a single crystal. Grain boundary speeds are calculated using a simple model that relates grain boundary mobility to variations in strain energy density on both sides of grain boundaries. Using the grain continuum model, researchers will be able to investigate the effect of thermally generated stresses on grain boundary motion caused by atomic flux driven by strain energy. Using finite-element modeling of the grain structure in a Through Silicon Via, the stress effect on grain boundaries caused by grain rotation due to CTE mismatch was investigated (TSV). The structure must be modeled using a scanning electron microscopes Electron Backscatter Diffraction (EBSD) image (SEM). Grain growth and subsequent grain boundary rotation can be performed using the appropriate extrapolation method to measure their influence on stress and, as a result, the TSV’s overall reliability.