Transverse Isotropic Properties Research Articles

Magnetic field sensing elements based on Ni80Fe20 2D magnetoplasmonic crystals

Here we demonstrate the fabrication of magnetic field sensing elements based on 2D magnetoplasmonic crystals prepared using e-beam lithography and magnetron sputtering methods. The magnetoplasmonic crystals consist of square lattice diffraction gratings with varying filling factors layered with Ag, Ni80Fe20, and Si3N4 layers. Based on the magnetic, optical, and magneto-optical studies, the magnetoplasmonic crystal that allows for both high transverse Kerr effect and isotropic in-plane magnetic properties along the diffraction grating vectors was determined. The sensitivity and measuring range of this sample provide a perspective for measuring several components of an external magnetic field.

Multiscale analysis for characterization of tensile properties in extrusion-based 3D printed carbon nanocomposites

In this study, we proposed a multiscale modeling methodology to predict tensile properties of carbon-based nanocomposites produced through extrusion-based 3D printing. This stepwise method integrates results across scales, from the nanoscale to the macroscale. The stochastic continuum model, informed by molecular dynamics, captures the direction-dependent stiffness of nanocomposites at the atomic level, integrating the transverse isotropic properties and morphological variations, along with process-induced uncertainties in a microscale domain. Considering the variable periodic layered filament shape determined by the printing conditions, we defined the geometry of the representative volume element and derived its homogenized equivalent effective properties. We validated the results of our model by comparing them with experimental stress-strain curves. Using this approach, we simulated the nonlinear response and analyzed the off-axis tensile characteristics of the specimens under various printing conditions. The alignment and orientation of the graphene flakes played pivotal roles in determining the mechanical properties of the nanocomposites. The proposed approach effectively assessed the overall behavior of nanocomposites produced using an extrusion-based 3D printing process, helping to accurately predict the mechanical properties and investigate the effects of the parameters on the macroscopic nonlinear response in applications using 3D printed nanocomposites.

Transverse isotropic compression behavior of aligned steel fiber UHPC produced by electromagnetic field

Aligned steel fiber ultra-high performance concrete (ASF-UHPC) demonstrates transverse isotropic mechanical properties. Specifically, when subjected to compressive stress perpendicular to the fiber orientation, surface cracks emerge proximate to the fiber tips, resulting in a significant enhancement of the material's compressive strength. Conversely, under compressive stress applied parallel to the fiber direction, fissures manifest along the fiber orientation, leading to a notable reduction in compressive strength. Consequently, the primary contributory factor underlying augmented compressive strength is the lateral restraint effectuated by the fibers. The optimization of fiber distribution for the aim of altering compressive strength is subject to the influence of the qualities of the UHPC matrix. Moreover, a comprehensive analysis extends to the examination of pertinent parameters, encompassing fiber volume fractions, fiber lengths, and fiber shapes. Investigation of these facets reveals an optimal range of fiber volume fraction, approximately 1.0% to 1.5%, which imparts maximal compressive strength in ASF-UHPC subjected to compressive stress perpendicular to the fiber orientation. When forces are applied parallel to the fiber direction, the incorporation of longer fibers or hooked-end fibers mitigates the reduction in compressive strength perpendicular to the applied stress. The consideration of the transverse mechanical attributes exhibited by aligned steel fibers, coupled with the optimization of fiber distribution characteristics, not only attenuates steel fiber consumption but also underscores a sustainable approach by curtailing CO2 emissions.

Mechanical properties of 3D auxetic structure: Emergence of transverse isotropy

The 3D auxetic structure (3D-AS) is designed, whose transverse isotropy at small deformations depends strongly on certain geometric parameters. Poisson's ratio and Young's modulus of the 3D-AS in each loading direction are calculated by using the energy method based on the periodic boundary condition at small deformations, and parametric analysis is performed. The effects of θ, t, and b on Poisson's ratio and Young's modulus of the 3D-AS are determined by theoretical analysis, experiments, and numerical simulations. The results show that θ and t are important factors affecting the Poisson's ratio and Young's modulus of 3D-AS, and that b mainly affects Young's modulus. In particular, the transverse isotropy of 3D-AS is analyzed in detail. Through numerical simulations, it is proved that the 3D-AS exhibits transverse isotropic elasticity within a certain parameter range. The 3D-AS exhibits transverse isotropic elasticity in the XY plane when θ ≥ 55°, t ≤ 0.7 mm, or b ≥ 3 mm. The transverse isotropic effective elastic properties can be largely adjusted by modifying the structural geometry. The more desired transverse isotropic elastic properties can be obtained by changing the parameters θ, t, or b of the unit cell. The experimental results agree well with the theoretical analysis and numerical simulations, and prove their accuracy.

Thermo-hydro-mechanical behavior of a clayey rock: A constitutive approach and numerical validation

Temperature strongly affects the thermo-hydro-mechanical properties of clayey rocks. Using the Drucker–Prager Cap model and available experimental results, an advanced constitutive model is proposed to describe the influence of temperature on the hydro-mechanical properties of clayey rocks. To replicate the stress-strain behavior of clayey rock under the thermo-hydro-mechanical conditions, transverse isotropic properties are considered in the constitutive model. Attention is particularly focused on the stress-strain behavior of clayey rock at the plastic stage, the evolution laws of cohesion, friction angle, and pre-consolidation pressure are established by introducing factors such as elastic damage, plastic damage and hardening, and thermal damage. A hydraulic conductivity evolution law is presented, accounting for the thermal effect on water properties and porosity. Theoretical studies are implemented in the finite element method software ABAQUS FEA using the subroutine USDFLD. Some theory parameters are verified through back analysis. Finally, the experimental results and numerical simulations are compared, showing the superiority of the established theoretical model.

Determination of transverse isotropic elastic constants of nacre and constituent tablets based on genetic-algorithm-assisted resonant ultrasound spectroscopy

Novel classes of tough composites inspired by natural biological materials like nacre, which possesses a multiscale structure with a lamellar microarchitecture, have attracted significant attention for use in structural and energy-related applications. The current theoretical understanding of the toughening and deformation mechanisms of nacre, which could serve as guidelines for composite development, is based on limited material parameters. Here, we report an experimental and numerical study on the transverse isotropic elastic constants of nacre and its constituent inorganic tablets based on genetic-algorithm-assisted resonant ultrasound spectroscopy. The results show that, among the five elastic constants measured, the out-of-plane and in-plane Young's moduli of nacre sampled from Pinctada martensii were 72.3 ± 1.7 and 74.8 ± 2.0 GPa, respectively. The remaining out-of-plane and in-plane Poisson's ratios and out-of-plane shear modulus were 0.23 ± 0.01, 0.24 ± 0.04, and 21.3 ± 0.9 GPa, respectively. Similar trends were observed for the constituent tablets, however, the Young's moduli were slightly higher at 72.7 and 75.0 GPa, respectively. These results concerning the transverse isotropic elastic properties of nacre and its constituent tablets aid in realizing the bio-duplication of novel nacreous composite materials.

Ultrasonic characterization of complete anisotropic elasticity coefficients of compressed oral solid dosage forms

In compacted materials, elastic anisotropy coupled with residual stresses could play a determining role in the manifestation of various types of defects such as capping and lamination, as it creates shear planes/bands and temporal relaxation. This internal micro-structure leads to time-delayed flaw initiation/formation, crack tip propagation under residual stresses, and ultimately product quality failures. Thus, their accurate characterization and variations are useful for understanding underlying failure mechanisms and to monitor variations in materials, processes and product quality during production prior to onset of failure. The extraction of tablet anisotropic elasticity properties is a challenging task, especially for commercial tablets with complex shapes, as shape often prevents the use of traditional destructive techniques (e.g., diametric compression testers) to produce accurate measurements. This study introduces and applies an ultrasonic approach to extracting the complete transverse isotropic elastic properties of compressed oral solid dosage forms to a commercial tablet product. A complete set of waveforms and the constitutive matrix for the compacted materials are reported. In addition, a perturbation analysis is carried out to analytically relate propagation speeds in various directions to the elastic coefficients. The proposed characterization approach is non-destructive, rapid, easy, and reliable in evaluating tablet anisotropy.

A dynamic poroelastic model for auxetic polyurethane foams involving viscoelasticity and pneumatic damping effects in the linear regime

This work proposes a new dynamic poroelastic model to describe the vibration transmissibility of auxetic polyurethane (PU) foams. The model includes the pneumatic damping effect provided by the porous structure of the foam, and the viscoelasticity of the PU material. The auxetic foam is manufactured using a simplified and relatively low-cost uniaxially thermoforming compression technique, which allows the production of a foam with transverse isotropic properties. Stress relaxation, quasi-static cyclic compressive-tensile and seismic base vibration tests in the small strains and linear elastic regimes have been performed in this work. The permeability and the viscoelasticity of the auxetic foams with different thermoforming compression ratios along the thermoforming and transverse directions are identified by performing a nonlinear regression from the mechanical and vibration-derived data. The auxetic foams possess lower stiffness along the thermoforming direction and higher modulus along the transverse one. The moduli of different auxetic foams obtained from quasi-static tests are 40%–70% lower than the corresponding dynamic values estimated from the seismic base excitation, while the static loss factors are all around 20%–100% lower than the corresponding dynamic ones. The enhancements of the dynamic stiffness and damping are mainly caused by the pneumatic damping effect and the viscoelasticity of the PU material. The permeability of the auxetic foam loaded along the thermoforming direction is ∼ 2 times larger than the one of the pristine foam, but 50% smaller when the foam is dynamically loaded along the transverse direction, due to the transverse isotropic microstructure of this porous material.

Analysis of dynamic response of two-dimensional orthotropic layered media with imperfect interfaces between layers

Although solving the dynamic response of layered media has always been a major concern in the engineering field, the problem of interlayer contact of layered media has seldom been addressed in the related studies. Thus, this paper proposes an algorithm to analyze the dynamic displacement and stress responses of two-dimensional layered media with imperfect interfaces between layers at an arbitrary point under time-harmonic loads. The Fourier transform was used to convert the dynamic equation of the generalized plane strain problem from the frequency-spatial domain to the frequency-wavenumber domain. In addition, combined with the introduction of dual variables, an integration algorithm with high precision was employed to solve the state equation. Based on the displacement response in the frequency-wavenumber domain, the dynamic displacement and stress responses at an arbitrary point were obtained using the inverse Fourier transform. This algorithm not only considers the transverse isotropic properties of layered media but also considers the contact problem at the interface between the adjacent layers of the layered media with different properties. In addition, the harmonic load can be applied to both the surface and inside of the medium. The accuracy of the proposed algorithm was verified by comparing the calculated data with the numerical results, and the influence of the imperfect interface parameters on the dynamic response of layered media was analyzed in detail. Finally, the mechanism of the impact of the imperfect interface between the layers on the dynamic displacement and stress responses of layered media was examined.

Transverse Isotropic Criterion Based on Generalized Nonlinear Strength

Abstract The geotechnical materials formed by natural deposition usually have transverse isotropic properties, and the transverse isotropic properties not only have a direct influence on the deform...

Axially- and torsionally-polarized radially converging shear wave MRE in an anisotropic phantom made via Embedded Direct Ink Writing

Magnetic Resonance Elastography (MRE) is a non-invasive imaging method to quantitatively map the shear viscoelastic properties of soft tissues. In this study, Embedded Direct Ink Writing is used to fabricate a muscle mimicking anisotropic phantom that may serve as a standard for imaging studies of anisotropic materials. The technique allowed us to obtain a long shelf life silicone-based phantom expressing transverse isotropic mechanical properties. Another goal of the present investigation is to introduce a torsionally-polarized, radially-converging shear wave actuation method for MRE. The implemented design for this novel setup was first validated via its application to isotropic and homogeneous gelatin phantoms. Then, a comparison of the resulting complex wave images from axially- and torsionally-polarized MRE on the developed anisotropic phantom and on a skeletal muscle murine sample is presented, highlighting the value of using multiple actuation and motion encoding polarization directions when studying anisotropic materials.

Closed form second order energy release rate in a cracked elastic beam

This study presents a closed form, second order, Mode-I fracture mechanics solution for a cracked elastic beam subject to axial compressive load. The solution considers a crack with a symmetric parabolic geometric imperfection in the beam and provides the strain energy release rate (SERR) as a continuous function of the axial load level. The effect of the elastic interface is considered by means of an additional equivalent beam length determined from a Winkler beam model. The closed form solution is corroborated through numerical non-linear fracture analyses for different geometries with isotropic and transverse isotropic material properties. The results show that the analytical models provide accurate predictions with an accuracy ranging between 2% and 4%. It is analytically adduced that the second order SERR in a cracked beam subject to axial loading is stable inasmuch the SERR decreases with increasing crack length. Moreover, the results show a significant influence of the elastic interface on the SERR.

Biomechanical Study of Proximal Femur for Designing Stems for Total Hip Replacement

Innovative hip implants should be designed in accordance with biomechanical models of the proximal femur and take into account both body weight and muscle action in order to improve usability and biomimetic performance. This article proposes a finite element analysis of the proximal femur using both cortical and trabecular regions and employing transverse isotropic properties with standardized loads taken from active and young patients. Maximum principal stresses are plotted to show the mechanical behavior of the femur and grouped to evaluate stress shielding. Tsai–Wu and the maximum principal stress fields are useful for finding the areas more prone to failure and analyzing the influence of the stems on femoral mechanics. Other parameters, such as the stem material, absence of neck and osteotomy level, are explained. This paper is expected to provide a guide for designers and surgeons of femoral stems for assessing qualitatively and quantitatively the risks of stress shielding.

Mechanics of tissue rupture during needle insertion in transverse isotropic soft tissue

During robot-assisted percutaneous puncture surgery, a bevel-tipped needle is inserted into a fiber-structured soft tissue, which has transverse isotropic mechanical properties. Tissue rupture may lead to needle bending and insertion error. Therefore, analysis of the mechanics of rupture events in transverse isotropic space is essential for the precise control of needle motion. We analyzed the needle stiffness force and the cutting force, both related to rupture events, which are caused by contact deformation and tissue cutting, respectively. A modified model based on a homogeneous elastic half-space contact force model was used to describe the variation in the stiffness force of the needle. An energy-based maximum stiffness force model was proposed to predict the surface rupture for a needle that is inserted at different orientations. A model for the cutting force was presented based on a solid mechanics theory of unidirectional fiber-reinforced composite material to analyze the effect of the needle tip pose on the cutting force. Experiments on porcine muscle confirmed that the stiffness force and the cutting force were clearly influenced by the insertion orientation angle. The developed models could predict the stiffness force and the cutting force during needle insertion into the transverse isotropic tissue. This method provides a foundation for predicting needle deflection in the transverse isotropic space. Graphical abstract Force modeling for needle insertion in transverse isotropic soft tissue.

Analytical solution for converging elliptic shear wave in a bounded transverse isotropic viscoelastic material with nonhomogeneous outer boundary.

Dynamic elastography methods-based on optical, ultrasonic, or magnetic resonance imaging-are being developed for quantitatively mapping the shear viscoelastic properties of biological tissues, which are often altered by disease and injury. These diagnostic imaging methods involve analysis of shear wave motion in order to estimate or reconstruct the tissue's shear viscoelastic properties. Most reconstruction methods to date have assumed isotropic tissue properties. However, application to tissues like skeletal muscle and brain white matter with aligned fibrous structure resulting in local transverse isotropic mechanical properties would benefit from analysis that takes into consideration anisotropy. A theoretical approach is developed for the elliptic shear wave pattern observed in transverse isotropic materials subjected to axisymmetric excitation creating radially converging shear waves normal to the fiber axis. This approach, utilizing Mathieu functions, is enabled via a transformation to an elliptic coordinate system with isotropic properties and a ratio of minor and major axes matching the ratio of shear wavelengths perpendicular and parallel to the plane of isotropy in the transverse isotropic material. The approach is validated via numerical finite element analysis case studies. This strategy of coordinate transformation to equivalent isotropic systems could aid in analysis of other anisotropic tissue structures.

Analytical solution for elliptic shear standing wave pattern in a bounded transversely isotropic viscoelastic material

Dynamic elastography methods—based on photonic, ultrasonic, or magnetic resonance imaging—are being developed for quantitatively mapping the shear viscoelastic properties of biological tissues, which are often altered by disease and injury. These diagnostic imaging methods involve analysis of shear wave motion in order to estimate or reconstruct the tissue’s shear viscoelastic properties. Most reconstruction methods to date have assumed isotropic tissue properties. But, application to tissues like skeletal muscle and brain white matter with aligned fibrous structure resulting in local transverse isotropic mechanical properties would benefit from analysis that takes into consideration anisotropy. A theoretical approach is developed for the elliptic shear wave pattern observed in transverse isotropic materials subjected to axisymmetric excitation normal to the fiber axis. This approach, utilizing Mathieu functions, is enabled via a transformation to an elliptic coordinate system with isotropic properties and a ratio of minor and major axes matching the ratio of shear wavelengths perpendicular and parallel to the plane of isotropy in the transverse isotropic material. The approach is validated via finite element analysis cases studies. This strategy of coordinate transformation to equivalent isotropic systems could aid in analysis of other anisotropic tissue structures. (Grant support: NIH AR071162.)

Generalized evaluation method for anisotropy of elastic tensor obtained by homogenization method and its application to transverse isotropic material property

Generalized evaluation method for anisotropy of elastic tensor obtained by homogenization method and its application to transverse isotropic material property

Application of Anisotropic Thin Plate Theory for Development of Displacements for Silicon <111> Crystals Plates in Cylindrical Systems

Silicon <111> crystal is one of the crystal orientations, which shows potential for application in micro device developments of pressure diaphragms for measurement purposes. To date, no theoretical basis has been examined to develop the deflections for computational analysis purposes [1]. This paper presents the development of the diaphragm deflections for Silicon <111> Crystal in Cylindrical coordinates system. The Silicon <111> crystal possesses transverse isotropic properties. Thus, an anisotropic thin plate theory is used here to develop the plate deflection. A numerical example is given to compare the theoretical results with Finite Element Analysis (FEA) results.

Pyroelectromagnetic Effects of a Piezocomposite in the Binary Refinement of the Method of Quasi-Periodic Polydisperse Correlation Components

A numerical analysis of two-point correlation functions of correlated quasi-periodic mono- and polydisperse unidirectional fibrous composite structures is carried out. The features of application of an earlier obtained solution of the method of polydisperse correlation components to monodisperse quasi-periodic pyroelectromagneticelastic piezostructures, with the example of numerical calculation of the effective coefficients of pyroelectric and pyromagnetic couplings of a composite whose constituents do not exhibit these effects, are considered. The solution for the required tensors of effective transverse isotropic pyroelectromagnetoelastic properties of a monodisperse quasi-periodic fibrous structure is given as a linear expansion in terms of corresponding known analytical solutions for traditional polydisperse structures by using the correlation coefficients of quasi-periodic mono- and polydisperse structures.

Impact of hydraulic perforation on fracture initiation and propagation in shale rocks

To enhance the oil and gas recovery rate, hydraulic fracturing techniques have been widely adopted for stimulation of low-permeability reservoirs. Pioneering work indicates that hydraulic perforation and layout could significantly affect fracture initiation and propagation in low-permeability reservoir rocks subjected to complex in-situ stresses. This paper reports on a novel numerical method that incorporates fracture mechanics principles and the numerical tools FRANC3D and ANSYS to investigate the three-dimensional initiation and propagation behavior of hydro-fracturing cracks in shale rock. Considering the transverse isotropic property of shale rocks, the mechanical parameters of reservoir rocks attained from laboratory tests were adopted in the simulation. The influence of perforation layouts on the 3D initiation of hydro-fracturing fractures in reservoir rocks under geo-stresses was quantitatively illuminated. The propagation and growth of fractures in three dimensions in different perforating azimuth values were illustrated. The results indicate that: 1) the optimal perforation direction should be parallel to the maximum horizontal principal stress, 2) the crack plane gradually turns toward the direction of the maximum horizontal principal stress when they are not in parallel, 3) compared with the linear and symmetric pattern, the staggered perforation is the optimal one, 4) the proper perforation density is four to six holes per meter, 5) the optimal perforation diameter in this model is 30♣mm, and 6) the influence of the perforation depth on the fracture initiation pressure is low.