Anisotropic Elastic Properties Research Articles

Digital rock physics: Calculation of effective elastic properties of heterogeneous materials using graphical processing units (GPUs)

An application based on graphical processing units (GPUs) applied to 3-D digital images is described for computing the linear anisotropic elastic properties of heterogeneous materials. The application can also retrieve the property contribution tensors of individual inclusions of any shape. The code can be executed on professional GPUs as well as on a basic laptop or personal computer Nvidia GPUs. The application is extremely fast: a calculation of the effective elastic properties of volumes consisting of about 7 million voxel elements (1913) takes less than 4 s of computational time using a single A100 GPU; 3 min for 100 million voxel elements (4793) using a single A100 GPU; 14 min for 350 million voxel elements (7033) using a single A100 GPU. Several comparisons against analytical solutions are provided. In addition, an evaluation of the anisotropic effective elastic properties of a 3-D digital image of a cracked Carrara marble sample is presented. The software can be downloaded from a permanent repository Zenodo, the link with a doi is given in the manuscript.

A novel Taguchi-based approach for optimizing neural network architectures: application to elastic short fiber composites

This study presents an innovative application of the Taguchi design of experiment method to optimize the structure of an Artificial Neural Network (ANN) model for the prediction of elastic properties of short fiber reinforced composites. The main goal is to minimize the computational effort required for hyperparameter optimization while enhancing the prediction accuracy. By utilizing a robust experimental design framework, the structure of an ANN model is optimized. This approach involves identifying a combination of hyperparameters that provides optimal predictive accuracy with the fewest algorithmic runs, thereby significantly reducing the required computational effort. The results suggested that the Taguchi-based developed ANN model with three hidden layers, 20 neurons in each hidden layer, elu activation function, Adam optimizer, and a learning rate of 0.001 can predict the anisotropic elastic properties of short fiber reinforced composites with a prediction accuracy of 97.71%. Then, external validation of the proposed ANN model was done using experimental data, and differences of less than 10% were obtained, indicating an appropriate predictive performance of the proposed ANN algorithm. Our findings demonstrate that the Taguchi method not only streamlines the hyperparameter tuning process but also substantially improves the algorithm's performance. These results highlight the potential of the Taguchi method as a powerful tool for optimizing machine learning algorithms, especially in scenarios where computational resources are limited. The implications of this study are far-reaching, offering insights for future research in the optimization of different algorithms for improved accuracies and computational efficiencies.

TESTING OF ROCK SAMPLES FROM OIL AND GAS FIELDS TO DETERMINE THEIR PHYSICAL AND MECHANICAL CHARACTERISTICS

Determination of the physical and mechanical properties of anisotropic limestone rocks is an important and urgent task, since carbonate deposits are very often found in oil and gas fields of the Mangistau region. The data show that limestone creates from 70% to 90% of all problems related to the stability of wells, which is due to the peculiarities of their physical and mechanical properties. Experimental studies of the physical and mechanical properties of limestone have features both in terms of monolith selection and in terms of preparation of samples for research, and in the methods of conducting and processing experiments. These features are due to extremely low permeability, anisotropy of elastic and strength properties due to their layered structure. The experience of testing core samples of layered limestone is considered, tests are carried out on equipment under the program of consolidated-undrained loading in accordance with the standards. As a result of experiments on core samples cut at an angle, along and across the layering, the anisotropic elastic properties of rocks, as well as their dependencies on geophysical parameters, were studied. The anisotropy of elastic properties has a significant effect both on the stress-strain state when solving specific problems of continuum mechanics and on the design values of the initial stress field as a whole. Taking into account the anisotropy parameters obtained in this paper will make it possible to solve Geomechanics problems in relation to layered limestones of the Sarmatian stage.

Anisotropic swelling due to hydration constrains anisotropic elasticity in biomaterial fibers

Naturally occurring protein fibers often undergo anisotropic swelling when hydrated. Within a tendon, a hydrated collagen fibril’s radius expands by 40% but its length only increases by 5%. The same effect, with a similar relative magnitude, is observed for single hair shafts. Fiber hydration is known to affect elastic properties. Here we show that anisotropic swelling constrains the anisotropic linear elastic properties of fibers. First we show, using data from disparate previously reported studies, that anisotropic swelling can be described as an approximately linear function of water content. Then, under the observation that the elastic energy of swelling can be minimized by the anisotropic shape, we relate swelling anisotropy to elastic anisotropy — assuming radial (transverse) symmetry within a cylindrical geometry. We find an upper bound for the commonly measured axial Poisson ratio νzx<1/2. This is significantly below recently estimated values for collagen fibrils extracted from tissue-level measurements, but is consistent with both single hair shaft and single collagen fibril mechanical and hydration studies. Using νzx, we can then constrain the product γ≡(1−νxy)Ez/Ex — where νxy is the seldom measured transverse Poisson ratio and Ez/Ex is the ratio of axial to radial Young’s moduli.

Unveiling the DFT perspectives on structural, elastic, electronic, optical and thermal properties of XMn2As2 (X = Ca, Sr)

A comprehensive first-principles investigation of XMn2As2 (X = Ca, Sr) materials using Density Functional Theory (DFT) have used in this study. Variety of physical attributes, including thermal, mechanical, electronic, optical and elastic anisotropic properties are explored. Lattice parameters and crystal structures showed excellent agreement with previous experimental data. The findings reveal that CaMn2As2 and SrMn2As2 exhibit notable elastic anisotropy, and satisfy the Born criteria for mechanical stability. The calculated elastic moduli are consistent with previously published values. The metallic nature of these compounds is demonstrated through band structure and density of states (DOS) analyses. Optical property analyses, including energy loss function, electrical conductivity, reflectivity, dielectric constant, refractive index, and absorption coefficient, highlight the potential of these materials for optoelectronic and photovoltaic applications. Notably, SrMn2As2 displays an exceptionally low minimum thermal conductivity compared to CaMn2As2, indicating its potential as a superior Thermal Barrier Coating (TBC) material.

Present-day stress stratification in the lower Palaeozoic shale sequence of the Baltic Basin, northern Poland, inferred from borehole data

We performed an analysis of present-day stress profiles for four wells penetrating the Lower Palaeozoic shale sequence of the Baltic Basin (northern Poland). Breakouts, hydraulic fracturing and leak-off tests were used to calibrate stress models based on anisotropic elastic shale properties. Initial stress models, balancing the lengths of the modelled and observed breakouts, indicated a degradation of the mechanical properties reconstructed from the density and dipole acoustic tool logs. Taking this adverse effect into account, final stress models were calculated which showed a stratification of the stress regime consistent with the lithostratigraphic shale units. A clear dominance of the horizontal stress-generating gravity factor over the horizontal tectonic strain was demonstrated. The obtained values of tectonic strain in the shale sequence compared to the previously determined strain in the crystalline basement of the same study area suggest a significant role of viscoelastic relaxation of the shale sequence.

Experimental study of thermal transport across metal/h-BN interfaces: Comparison with metal/graphite interfaces

The continuing miniaturization of layered material electronics highlights the increasingly significant role of interfacial thermal conductance (G) in the efficient nanoscale heat dissipation in these electronics. Despite its importance, the mechanisms of thermal transport across the interfaces of layered materials and the underlying substrate remain unclear. In this work, we comprehensively investigate the interfacial thermal and phonon transport across layered-material interfaces through our ultrafast pump-probe measurements and detailed calculations on G for the interfaces of hexagonal boron nitride (h-BN), one of the most promising layered materials. We first experimentally measure Gc for interfaces between four different metals (Al, Pd, Au and Ti) and h-BN along c-axis using time-domain thermoreflectance (TDTR) from 80 to 300 K. We successfully achieve high accuracy of our measurements with uncertainty <10 % through using the carefully chosen high modulation frequency (15.6 MHz) and relatively large laser spot size (22.5 μm). We find that the measured Gc for interfaces between metals (except Al) and (100) plane of h-BN is lower than that of metal/graphite interfaces, while Gc of Al/h-BN is comparable to that of Al/graphite interfaces. Furthermore, together with our proposed anisotropic model and the diffuse mismatch model (DMM), we determine the transmission probability for the various metal/h-BN interfaces and find that the strong bonding strength enhances the phonon transmission across Ti/h-BN or Ti/graphite interfaces. Finally, we predict the orientation-dependent thermal conductance (i.e., the different interfacial thermal transport along c-axis (Gc) and in-plane (Gab) crystallographic orientations) for both metal/h-BN and metal/graphite. We find Gab between metals and (001) plane is up to 2–3 times higher than Gc. This can be attributed to the highly anisotropic elastic properties in the h-BN and graphite. This work provides important insight into the phonon transmission mechanisms across metal/h-BN interfaces, and thus contributes significantly to the thermal management of layered material electronics.

Anisotropic polymer components with desired elastic properties manufactured through fused filament fabrication additive manufacturing

AbstractFused filament fabrication (FFF) is a popular additive manufacturing (AM) process, primarily used for fabricating polymer components. Optimizing the mechanical properties of FFF components, such as their elastic moduli, is crucial in many applications. This study focuses on adjusting the elastic properties of polymer components manufactured through FFF process by selecting appropriate process parameters. The elastic constants of the anisotropic FFF components are measured by using ultrasonic testing (UT). Response surface methodology (RSM) is employed to determine the optimal settings for these parameters to achieve the desired elastic properties. The effects of layer thickness, printing speed, and raster angle on Young's modulus are explored. Analysis of variance (ANOVA) is used to identify the contributions of each process factor on the output responses. According to ANOVA results, the optimal conditions identified are: a printing speed of 2040 mm/min, a layer thickness of 0.2 mm, and a raster angle of 29°. These conditions collectively achieved the maximum Young's modulus. The differences between the predicted and measured moduli for all responses are less than 5%. The structural factors influencing the results are examined by analyzing the fracture surfaces of the tensile testing (TT) specimens with field emission scanning electron microscopy. Additional measurements of other properties, including ultrasound velocity and wave attenuation, are conducted on the samples. The findings indicate that optimizing the parameters by setting them to their minimum values does not only improve the maximum elastic modulus in specific directions but also reduces attenuation. It is concluded that the desired elastic modulus for a component can be achieved by properly adjusting the process parameters.Highlights Optimizing AM parameters to achieve the desired elastic properties of FFF samples. Examining the effects of each AM parameter by utilizing ANOVA and RSM methods. Measuring the anisotropic elastic properties of AM samples by UT. Verifying UT results through TT and measuring attenuation.

Strong Vertical Piezoelectricity and Broad-pH-Value Photocatalyst in Ferroelastic Y2Se2BrF Monolayer.

With the development of miniaturized devices, there is an increasing demand for 2D multifunctional materials. Six ferroelastic semiconductors, Y2Se2XX' (X, X' = I, Br, Cl, or F; X ≠ X') monolayers, are theoretically predicted here. Their in-plane anisotropic band structure, elastic and piezoelectric properties can be switched by ferroelastic strain. Moderate energy barriers can prevent the undesired ferroelastic switching that minor interferences produce. These monolayers exhibit high carrier mobilities (up to 104 cm2 V-1 s-1) with strong in-plane anisotropy. Furthermore, their wide bandgaps and high potential differences make them broad-pH-value and high-performance photocatalysts at pH value of 0-14. Strikingly, Y2Se2BrF possesses outstanding d33 (d33 = -405.97 pm/V), greatly outperforming CuInP2S6 by 4.26 times. Overall, the nano Y2Se2BrF is a hopeful candidate for multifunctional devices to generate a direct current and achieve solar-free photocatalysis. This work provides a new paradigm for the design of multifunctional energy materials.

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 of 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 yields 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.