In-plane Pressure Research Articles

Dilatometric Studies on Single Crystalline Barlowite – A Structurally Perfect Spin-1/2 Kagome System

We present results of high-resolution thermal expansion measurements on single crystalline barlowite – a structurally perfect spin-1/2 kagome system. The data reveal strongly pronounced and anisotropic second-order phase transition anomalies at the Néel transition at TN = 16K. From these data, together with literature results on the specific heat, the uniaxial-pressure dependences of TN are derived. We find a rather large positive pressure coefficient for uniaxial pressure along the hexagonal c axis of ∂TN/∂pc = (2.3 ± 0.2) K/GPa and smaller negative in-plane pressure coefficient of ∂TN/∂pin-plane = -(0.6 ± 0.03) K/GPa. These effects result in a small positive pressure coefficient under hydrostatic-pressure conditions of ∂TN/∂phydr = (1.1 ± 0.2) K/GPa. Bond-lengths considerations indicate that inter-layer Cu-O bonds, being larger than those typically found in stable Cu-O complexes, are responsible for this behavior.

Exceptionally stiff two-dimensional molecular crystal by substrate-confinement.

We demonstrated an approach to effectively apply in-plane pressures to molecular layers by utilizing the substrate confinement effect. The compressed crystal structure and mechanical behaviors of carbon monoxide (CO) monolayer subjected to the confinement of Cu(100) substrate were jointly investigated by low temperature scanning tunneling microscopy experiments and first-principles density functional theory calculations. By increasing molecular coverage, an exceptionally large Young's modulus of 33 GPa was derived for the constrained CO monolayer film. This extreme in-plane pressure leads to site-specific tilting geometries, polymeric-like electronic states, and vibrational behaviors of CO molecules in the compressed phases. These results provide an extended understanding of the physical and chemical properties of intermolecular interactions in this fundamental system.

In-plane chemical pressure in (U1−yCey)O2 studied by Raman spectroscopy

We investigate the nature of bonding and charge states in (U1−yCey)O2 (y=0.0, 0.2, 0.4, 0.6, 0.8 and 1.0) by Raman spectroscopy. Raman spectrum of UO2 exhibits two prominent bands below 1000cm−1, a F2g mode at 446cm−1 and a F1u LO mode at 578cm−1. As y is increased from 0 to 0.6, the F1u exhibits a large blue shift of 90cm−1, and from y=0.6 to 1.0, a red shift of 54cm−1. We show that our results can be interpreted as arising from anisotropic compression/relaxation of the lattice under Ce substitution and this can give an indication of its charge states. Alternate interpretations have been given in the literature on the effect of substituents and dopants to the Raman spectra of UO2 and CeO2. The present interpretation of chemical stress effects can be taken as another plausible explanation.

Experimental studies on stiffened plates under in-plane load and lateral pressure

An experimental study on stiffened plates subjected to combined action of in-plane load and lateral pressure is described in the paper. Details of the experiments and finite element analyses of the specimens tested are presented along with the results. Measurements of initial imperfection in the specimens have been made and included in the analyses. Results show that lateral load carrying capacity of stiffened plate drops with increase in axial load and vice-versa. It is found that plate slenderness ratio has significant influence on the ultimate load capacity of stiffened plates subjected to both in-plane load and lateral pressure. Increase of plate slenderness ratio results in a decrease of ultimate load capacity of stiffened plate. The accuracy of the finite element modelling is established by comparing the results with the corresponding experimental values.

Rotational Capacitive Micromachined Ultrasonic Transducers (cMUTs)

A rotational capacitive micromachined ultrasonic transducer is introduced. Two pressure-sensitive diaphragms atop vacuum-sealed cavities are mechanically coupled via a rocking beam structure. The rocking structure is designed to reduce deflection of the vacuum-sealed diaphragms under atmospheric pressure while introducing ideally zero rotational stiffness to differential diaphragm pressure. The rocking structure responds to in-plane pressure gradients and is therefore anticipated to have dipole-type directivity to ultrasound. Prototypes employing 200 μm diameter polysilicon diaphragms are presented with a fundamental resonance frequency of 250 kHz.

Anisotropic uniaxial pressure response of the Mott insulator Ca2RuO4

We have investigated the in-plane uniaxial pressure effect on the antiferromagnetic Mott insulator Ca${}_{2}$RuO${}_{4}$ from resistivity and magnetization measurements. We succeeded in inducing the ferromagnetic metallic phase at lower critical pressure than by hydrostatic pressure, indicating that the flattening distortion of the RuO${}_{6}$ octahedra is more easily released under in-plane uniaxial pressure. We also found a striking in-plane anisotropy in the pressure responses of various magnetic phases: although the magnetization increases monotonically with pressure diagonal to the orthorhombic principal axes, the magnetization exhibits peculiar dependence on pressure along the in-plane orthorhombic principal axes. This peculiar dependence can be explained by a qualitative difference between the uniaxial pressure effects along the orthorhombic $a$ and $b$ axes, as well as by the presence of twin domain structures.

Design optimization of a piezoelectric microphone with in-plane directivity

A piezoelectric micromachined microphone with in-plane directivity has been recently introduced [Appl. Phys. Lett. 102, 054109 (2013)]. The work is inspired by a design introduced by Miles et al. [J. Acoust. Soc. Am. 125(4), 2009], which was, in-turn, inspired by the hearing mechanism of a particular type of parasitoid fly. A rocking structure pivots about a rotational hinge in response to in-plane pressure gradients, and the rocking motion is read by springs attached to the end of the rocking ‘teeter-totter’ structure, with the springs themselves employing thin piezoelectric films, which operate in a 3-1 mode. Prototypes have been fabricated that employ rocking structures 1 mm x 2 mm in size and functionality has been verified via directivity measurements performed in an anechoic chamber. This presentation will focus on exploring the design space of this sensor, which is accomplished with a hybrid model based on FEA and network models. Designs which maximize SNR are presented, and anticipated microfabrication challenges of these designs are highlighted.

A first-principles study of the mechanical properties of g-GeC

We investigate the mechanical properties of graphene-like hexagonal germanium carbide monolayers (g-GeC) using first-principles calculations based on density-functional theory. Compared to graphene, g-GeC is much softer, with 41% in-plane stiffness, 44%,42% and 37% ultimate strengths in armchair, zigzag, and biaxial strains respectively, as well as smaller ultimate strains. However, g-GeC has a larger Poisson’s ratio, 0.28, about 1.5 times that of graphene. We obtained the second, third, fourth, and fifth order elastic constants for a rigorous continuum description of the elastic response of g-GeC. The second order elastic constants, including in-plane stiffness, are predicted to monotonically increase with pressure while the Poisson’s ratio monotonically decreases with increasing pressure. The sound velocity of a compressional wave has a minima at an in-plane pressure of −7GPa while that of a shear wave monotonically with pressure.

Stress Concentration Calculation of Silo Wall Opening Subjected to In-Plane Tension or Pressure

In this paper, by using complex variable function and conformal mapping technique, the author studies the stress concentration intensities of silo wall opening through predigesting the stress calculation of silo wall opening as a problem of plane calculation and obtains the stress concentration factor of opening. When simplified silo wall is subjected to in-plane tension or pressure, maximal stress concentration point around opening is at the corner of opening. this paper may provide some referenced value to the designers.

Accurate absorbing boundary conditions for anisotropic elastic media. Part 1: Elliptic anisotropy

With the ultimate goal of devising effective absorbing boundary conditions (ABCs) for heterogeneous anisotropic elastic media, we investigate the accuracy aspects of local ABCs designed for tilted elliptic anisotropy in the frequency domain (time-harmonic case). Such media support both anti-plane and in-plane wavemodes with opposing signs of phase and group velocities (cpxcgx<0) that have long posed a significant challenge to the design of accurate (and stable) local ABCs. By first considering the simpler case of scalar anti-plane waves, we show that it is possible to overcome the challenges posed by cpxcgx<0 by simply utilizing the inevitable reflections occurring at the truncation boundaries. This understanding helps us to explain the ability of a recently developed local ABC – the perfectly matched discrete layer (PMDL) – to handle the challenges posed by cpxcgx<0without the need of intervening space–time transformations. PMDL is a simple variant of perfectly matched layers (PML) that is also equivalent to rational approximation-based local ABCs (rational ABCs); it inherits the straightforward approximation properties of rational ABCs along with the versatility of PML. The approximation properties of PMDL quantified through its reflection matrix is used to derive simple bounds on the PMDL parameters necessary for the accurate absorption of all outgoing anti-plane and in-plane wavemodes – including those with cpxcgx<0. Beyond the previously derived bound on the real parameters of PMDL sufficient for the absorption of outgoing propagating anti-plane wavemodes, we present bounds on the complex parameters of PMDL necessary for the absorption of outgoing propagating and evanescent wavemodes for both anti-plane and coupled in-plane pressure and shear waves. The validity of this work is demonstrated through a series of numerical experiments.

Mechanical properties of graphene and boronitrene

We present an equation of state (EOS) that describes how the hydrostatic change in surface area is related to two-dimensional in-plane pressure ($\mathcal{F}$) and yields the measure of a material's resilience to isotropic stretching (the layer modulus $\ensuremath{\gamma}$) as one of its fit parameters. We give results for the monolayer systems of graphene and boronitrene, and we also include results for Si, Ge, GeC, and SiC in the isostructural honeycomb structure for comparison. Our results show that, of the honeycomb structures, graphene is the most resilient to stretching with a value of ${\ensuremath{\gamma}}_{\text{C}}$ = $206.6$ N m${}^{\ensuremath{-}1}$, second is boronitrene with ${\ensuremath{\gamma}}_{\text{BN}}$ = $177.0$ N m${}^{\ensuremath{-}1}$, followed by ${\ensuremath{\gamma}}_{\text{SiC}}$ = 116.5 N m${}^{\ensuremath{-}1}$, ${\ensuremath{\gamma}}_{\text{GeC}}$ = 101.0 N m${}^{\ensuremath{-}1}$, ${\ensuremath{\gamma}}_{\text{Si}}$ = 44.5 N m${}^{\ensuremath{-}1}$, and ${\ensuremath{\gamma}}_{\text{Ge}}$ = 29.6 N m${}^{\ensuremath{-}1}$. We calculate the Young's and shear moduli from the elastic constants and find that, in general, they rank according to the layer modulus. We also find that the calculated layer modulus matches the one obtained from the EOS. We use the EOS to predict the isotropic intrinsic strength of the various systems and find that, in general, the intrinsic stresses also rank according to the layer modulus. Graphene and boronitrene have comparable strengths with intrinsic stresses of 29.4 and 26.0 N m${}^{\ensuremath{-}1}$, respectively. We considered four graphene allotropes including pentaheptite and graphdiyne and find that pentaheptite has a value for $\ensuremath{\gamma}$ comparable to graphene. We find a phase transition from graphene to graphdiyne at $\mathcal{F}$ = $\ensuremath{-}7.0$ N m${}^{\ensuremath{-}1}$. We also consider bilayer, trilayer, and four-layered graphene and find that the addition of extra layers results in a linear dependence of $\ensuremath{\gamma}$ with $\mathcal{F}$.

Reducing the data: Analysis of the role of vascular geometry on blood flow patterns in curved vessels

Three-dimensional simulations of blood flow usually produce such large quantities of data that they are unlikely to be of clinical use unless methods are available to simplify our understanding of the flow dynamics. We present a new method to investigate the mechanisms by which vascular curvature and torsion affect blood flow, and we apply it to the steady-state flow in single bends, helices, double bends, and a rabbit thoracic aorta based on image data. By calculating forces and accelerations in an orthogonal coordinate system following the centreline of each vessel, we obtain the inertial forces (centrifugal, Coriolis, and torsional) explicitly, which directly depend on vascular curvature and torsion. We then analyse the individual roles of the inertial, pressure gradient, and viscous forces on the patterns of primary and secondary velocities, vortical structures, and wall stresses in each cross section. We also consider cross-sectional averages of the in-plane components of these forces, which can be thought of as reducing the dynamics of secondary flows onto the vessel centreline. At Reynolds numbers between 50 and 500, secondary motions in the directions of the local normals and binormals behave as two underdamped oscillators. These oscillate around the fully developed state and are coupled by torsional forces that break the symmetry of the flow. Secondary flows are driven by the centrifugal and torsional forces, and these are counterbalanced by the in-plane pressure gradients generated by the wall reaction. The viscous force primarily opposes the pressure gradient, rather than the inertial forces. In the axial direction, and depending on the secondary motion, the curvature-dependent Coriolis force can either enhance or oppose the bulk of the axial flow, and this shapes the velocity profile. For bends with little or no torsion, the Coriolis force tends to restore flow axisymmetry. The maximum circumferential and axial wall shear stresses along the centreline correlate well with the averaged in-plane pressure gradient and the radial displacement of the peak axial velocity, respectively. We conclude with a discussion of the physiological implications of these results.

Composite Circular Plates With Residual Tensile Stress Undergoing Large Deflections

Many micromachined electroacoustic devices use thin plates in conjunction with electrical components to measure acoustic signals. Composite layers are needed for electrical passivation, moisture barriers, etc. The layers often contain residual stresses introduced during the fabrication process. Accurate models of the composite plate mechanics are crucial for predicting and optimizing device performance. In this paper, the von Kármán plate theory is implemented for a transversely isotropic, axisymmetric plate with in-plane tensile stress and uniform transverse pressure loading. A numerical solution of the coupled force-displacement nonlinear differential equations is found using an iterative technique. The results are verified using finite element analysis. This paper contains a study of the effects of tensile residual stresses on the displacement field and examines the transition between linear and nonlinear behavior. The results demonstrate that stress stiffening in the composite plate delays the onset of nonlinear deflections and decreases the mechanical sensitivity. In addition, under high stress the plate behavior transitions to that of a membrane and becomes insensitive to the composite nature of the plate. The results suggest a tradeoff between mechanical sensitivity and linearity.

Antiplane Wave Scattering from a Cylindrical Void in a Pre-Stressed Incompressible Neo-Hookean Material

AbstractAn isolated cylindrical void is located inside an incompressible nonlinear-elastic medium whose constitutive behaviour is governed by a neo-Hookean strain energy function. In-plane hydrostatic pressure is applied in the far-field so that the void changes its radius and an inhomogeneous region of deformation arises in the vicinity of the void. We consider scattering from the void in the deformed configuration due to an incident field (of small amplitude) generated by a horizontally polarized shear (SH) line source, a distance r0 (R0) away from the centre of the void in the deformed (undeformed) configuration. We show that the scattering coefficients of this scattered field are unaffected by the pre-stress (initial deformation). In particular, they depend not on the deformed void radius a or distance r0, but instead on the original void size A and original distance R0.

Anisotropic in-plane reversible strain effect inY0.5Gd0.5Ba2Cu3O7 − δ coated conductors**Contribution of NIST, not subject to US copyright.

Recent experiments have shown that reversible effects of strain on the criticalcurrent density and flux pinning strength in the high-temperature superconductorBi2Sr2Ca2Cu3Ox can beexplained entirely by the pressure dependence of its critical temperature. Such a correlation is less simplefor RE–Ba2Cu3O7 − δ (RE = rare earth) superconductors, in part because the in-plane pressure dependence of its critical temperatureis highly anisotropic. Here, we make a qualitative correlation between the uniaxial pressuredependence of the critical temperature and the reversible strain effect on the critical current of RE–Ba2Cu3O7 − δ coated conductors by taking the crystallography and texture of the superconducting filminto account. The strain sensitivity of the critical current is highest when strain is orientedalong the [100] and [010] directions of the superconducting film, whereas the criticalcurrent becomes almost independent of strain when strain is oriented along the[110] direction. The results confirm the important role of the anisotropic pressuredependence of the critical temperature on the reversible strain behavior of RE–Ba2Cu3O7 − δ. The reversiblestrain effect in RE–Ba2Cu3O7 − δ is expected to decrease the performance of the conductor in many applications, such ashigh-field magnets, but the effect may be only minor in coated conductor cables, wherestrain is generally not aligned with the tape axis.

In-plane and tunneling pressure sensors based on graphene/hexagonal boron nitride heterostructures

An in-plane pressure sensor (IPPS) consisting of graphene sandwiched by hexagonal boron nitride (h-BN) and a tunneling pressure sensor (TPS) consisting of h-BN sandwiched by graphene are demonstrated. The responses as function of external pressure are modeled. The current varies by 3 orders of magnitude as pressure increases from 0 to 5 nN/nm2. The IPPS current is negatively correlated to pressure, whereas TPS current exhibits positive correlation to pressure. The IPPS design is insensitive to the number of wrapping h-BN layers, indicating precise process control is unnecessary. The result paves a viable avenue towards realizing of atomic scale pressure sensors.

Assessment of early diastolic strain-velocity temporal relationships using spatial modulation of magnetization with polarity alternating velocity encoding (SPAMM-PAV).

A novel MR imaging technique, spatial modulation of magnetization with polarity alternating velocity encoding (SPAMM-PAV), is presented to simultaneously examine the left ventricular early diastolic temporal relationships between myocardial deformation and intra-cavity hemodynamics with a high temporal resolution of 14 ms. This approach is initially evaluated in a dynamic flow and tissue mimicking phantom. A comparison of regional longitudinal strains and intra-cavity pressure differences (integration of computed in-plane pressure gradients within a selected region) in relation to mitral valve inflow velocities is performed in eight normal volunteers. Our results demonstrate that apical regions have higher strain rates (0.145 ± 0.005 %/ms) during the acceleration period of rapid filling compared to mid-ventricular (0.114 ± 0.007 %/ms) and basal regions (0.088 ± 0.009 %/ms), and apical strain curves plateau at peak mitral inflow velocity. This pattern is reversed during the deceleration period, when the strain-rates in the basal regions are the highest (0.027 ± 0.003 %/ms) due to ongoing basal stretching. A positive base-to-apex gradient in peak pressure difference is observed during acceleration, followed by a negative base-to-apex gradient during deceleration. These studies shed insight into the regional volumetric and pressure difference changes in the left ventricle during early diastolic filling.

Topology Optimization of Composite Structure Using Bi-Directional Evolutionary Structural Optimization Method

This paper deals with topology optimization of composite structure using Bi-directional Evolutional Structural Optimization (BESO) method. By redefining the criteria of the optimization evolution progress, the proposed method is able to extend current BESO method from isotropic material to anisotropic composite material. The initial modification of BESO method is to allow for inefficient Material Element String (MES) to be removed while efficient MES to be added in the thickness direction of a composite structure. This modification can reduce the chance of high stress concentration in a composite structure and also produce the geometry which is easy to fabricate using fabrication techniques currently available. The results of a cantilever composite laminate under uniform inplane pressure are presented, showing that the proposed method can produce shape and topology for composite structures with optimal structure stiffness.

Seismic wave propagation in laterally inhomogeneous poroelastic media via BIEM

SUMMARY This work addresses in-plane pressure P and vertically polarized shear SV seismic wave propagation in a finite, laterally inhomogeneous, multilayered poroelastic geological region resting on the homogeneous elastic half-space. The particular approach followed here is based on a combination of the (i) viscoelastic approximation (isomorphism) to Biot's equations of dynamic poroelasticity and on the (ii) boundary integral equation method (BIEM) using frequency-dependent fundamental solutions of the governing wave equations. The problem is formulated under plane strain conditions and time-harmonic motions are assumed. Validation of the viscoelastic isomorphism and verification of the BIEM is done by solution of benchmark examples. These simulation studies reveal that the proposed methodology is able to depict a sensitivity of the seismic signals recovered to the following parameters: (i) poroelastic properties of fluid saturated layers; (ii) lateral geological inhomogeneity; (iii) surface topography and (iv) frequency content and direction of the incident wave. It is concluded that the combination of viscoelastic isomorphism with BIEM software provides an effective numerical tool for evaluating site-effect phenomena in multilayered, fluid saturated geological regions with complex geometry. The numerical results obtained demonstrate that dynamic poroelasticity interacting with other physical peculiarities of the Earth's surface layers, such as lateral heterogeneity, material properties along the wave path, local geological profile and type of elastic wave, gives rise to complex seismic signals on the free surface at the site of interest. Copyright © 2010 John Wiley & Sons, Ltd.

Optimal Design of Unitized Structures Using Response Surface Approaches

Developments in rapid manufacturing techniques such as electron beam freeform fabrication have made it easier to manufacture objects with complex shapes (like panel with curvilinear stiffeners). In this paper, design optimization of stiffened panels is carried out using different types of response surfaces. Placement and sizing variables are optimized using integrated high-performance, commercially available software. The proposed approach has two optimization loops. The sizing optimization is carried out in the first loop through finite element analysis using gradient-based optimization method for different placement variables. In the second loop, optimal placement of stiffeners is carried out using response surfaces. Because of response surface construction using whole design space, the proposed approach does not suffer from getting trapped in a local minima. The proposed approach is applied to square panels subjected to in-plane biaxial and uniform surface pressure loadings. Panel weight is minimized with buckling, displacements, and stress constraints. An approach to perform both placement and sizing optimization of panels with curvilinear stiffeners is also discussed and a surrogate model is developed for placement and shape optimization of stiffeners.