Elastic Flexure Research Articles

Testing the cryovolcanism and plate bending hypotheses for Charon's smooth plains

Topographic moats are found at the edges of Charon's Vulcan Planitia, both where the plains meet the higher elevation terrain in Oz Terra, and surrounding isolated mountains within the smooth plains. The curved edges of the moats have been hypothesized to represent either the front of a cryolava flow from the emplacement of the plains material, or the result of elastic flexure of the plains surface due to the load of adjacent mountains or sinking crustal blocks. We tested both of these hypotheses by taking topographic profiles across the moats and comparing the observations to theoretical predictions from two lava flow models and two plate bending models. The algorithm we used returns a correlation coefficient as well as the parameter values for the theoretical model necessary to match the topography. Our results show that the plate bending models provided the best fits for the topography, though the lava flow models provided good matches for a few profiles. Our results for elastic thickness of ~1 km for a continuous plate or ~3 km for a broken plate are similar to results previously derived at Serenity Chasma. The values obtained for Bingham yield strength of ~10 kPa are also consistent with previous results from hypothesized cryovolcanic material on Ariel and Charon.

Geometry of Flexural Uplift by Continental Rifting in Corinth, Greece

AbstractUnderstanding early rifting of continental lithosphere requires accurate descriptions of up‐bended rift margins and footwalls that ought to correlate in space and time with the elastic flexural uplift that produces them. Here we characterize the geometry of elastic flexural uplift by continental rifting at its spatiotemporal scale in nature (tens of kilometers; 104–106 years) using geomorphic evidence along the uplifting margin of the Corinth Rift, Greece. Our geomorphic analyses of space‐borne topography novelly outline the coherent elastic flexure of continental lithosphere along and across the rift margin and throughout faulting (~106 years), as defined by the distribution of footwall uplift south of the active bounding fault. Topography and river drainages outline an elastic flexure signal that increases exponentially toward the bounding fault across the footwall for >50 km and changes in amplitude along the footwall following a parabola that decays from the rift center and has a >60‐km wavelength that correlates with rift length. This continental lithosphere up‐bend correlates with the scale of the rift, and appears maximum in the center of the rift, where drainage reversal of large catchments suggests rapid slip rates at the bounding fault. This is consistent with the growth of a new, rift‐scale, high‐angle normal fault. The coherency of elastic flexure in space and time implies highly localized strain in the rift‐bounding fault and suggests that the fault transects continental lithosphere with long‐term strength. The unparalleled record of flexural uplift and highly localized strain in the landscape of Corinth suggest these processes are intrinsic to early continental rifting elsewhere.

Uplift of Trail Ridge, Florida, by Karst Dissolution, Glacial Isostatic Adjustment, and Dynamic Topography

AbstractThe present elevation of Trail Ridge, a purported Pleistocene paleoshoreline (2.21 ± 0.38 Ma) up to ~70 m high, is attributed to isostatic uplift from karst‐induced mass loss of the underlying Florida Platform. However, glacial isostatic adjustment, dynamic topography (DT), and elastic flexure also contribute to the observed topography. We investigated the combined contribution of these geophysical processes to the elevation of Trail Ridge by adapting a numerical model of karst‐induced Airy isostatic uplift that is driven by sea level change since ~3 Ma with a gravitationally self‐consistent glacial isostatic adjustment model. We treat DT as a free parameter and explore a spectrum of scenarios, from dynamic subsidence (−25 m/Myr) to dynamic uplift (+25 m/Myr), with values consistent with mantle convection simulations for the region. We demonstrate a trade‐off between the age of Trail Ridge, karstification efficiency, and DT rate that necessitates robust estimates of two of these variables when solving for the third. For example, adopting spring‐efflux‐derived estimates of subsurface carbonate dissolution (1 m/38,000 yr) and a 10 m/Myr dynamic topographic uplift for the northern Florida Platform predicts an age of ~2.1 Ma for a model 70 m elevation marker, consistent with the bounds of the electron spin resonance optical dating geochronology. In contrast, by assuming a more rapid carbonate dissolution efficiency (1 m/11,000 yr) and dynamic subsidence of −15 m/Myr predicts a similar age. A refined karst‐induced isostatic uplift model age for Trail Ridge requires both improved rates of regional karst dissolution, dynamic topographic change, and elastic flexure.

The Gravitational Signature of Martian Volcanoes

AbstractBy modeling the elastic flexure of the Martian lithosphere under imposed loads, we provide a systematic study of the old and low‐relief volcanoes (>3.2 Ga, 0.5 to 7.4 km) and the younger and larger prominent constructs within the Tharsis and Elysium provinces (<3 Ga, 5.8 to 21.9 km). We fit the theoretical gravitational signal to observations in order to place constraints on 18 volcanic structures. Inverted parameters include the bulk density of the load, the elastic thickness required to support the volcanic edifice at the time it was emplaced (Te), the heat flow, the volume of extruded lava, and the ratio of volcanic products that form within (Vi) and above the preexisting surface (Ve). The bulk density of the volcanic structures is found to have a mean value of 3,206±190 kg/m3, which is representative of iron‐rich basalts as sampled by the Martian basaltic meteorites. Te beneath the small volcanoes is found to be small, less than 15 km, which implies that the lithosphere was weak and hot when these volcanoes formed. Conversely, most large volcanoes display higher values of Te, which is consistent with the bulk of their emplacement occurring later in geologic history, when the elastic lithosphere was colder and thicker. Our estimates for the volumes of volcanic edifices are about 10 times larger than those that neglect the flexure of the lithosphere. Constraints on the magnitude of subsurface loads imply that the ratio Vi/Ve is generally 3:5, which is smaller than for the Hawaiian volcanoes on Earth.

The design and development of Branch Bot: a branch-crawling, caterpillar-inspired, soft robot

A soft climbing robot has the potential to access locations such as wiring ducts and tree canopies that are unreachable by humans and traditional rigid robots. In addition, a soft robot is robust and can fall without damaging itself or its environment. We present a soft, branch-crawling robot that is inspired by the passive gripping mechanisms used by caterpillars. The conformability of the robot’s soft body makes it uniquely suited to move in a complex 3D environment. A key innovation is that grip release is actively controlled and coordinated with propulsion generated by stored elastic energy. The robot is molded from silicone rubber and actuated using remote motor-tendons coupled to the structure through Bowden cables. Grip is achieved passively through an elastic flexure that pushes a compliant finger against the dowel. Experimental results show that the gripper is easily able to support the weight of the robot, and that the body structure allows the robot to crawl horizontally, vertically, and along branches. This robot demonstrates some key advantages of a soft robotic platform over traditional rigid robots.

Lithospheric flexure and rheology determined by climate cycle markers in the Corinth Rift

Geomorphic strain markers accumulating the effects of many earthquake cycles help to constrain the mechanical behaviour of continental rift systems as well as the related seismic hazards. In the Corinth Rift (Greece), the unique record of onshore and offshore markers of Pleistocene ~100-ka climate cycles provides an outstanding possibility to constrain rift mechanics over a range of timescales. Here we use high-resolution topography to analyse the 3D geometry of a sequence of Pleistocene emerged marine terraces associated with flexural rift-flank uplift. We integrate this onshore dataset with offshore seismic data to provide a synoptic view of the flexural deformation across the rift. This allows us to derive an average slip rate of 4.5–9.0 mm·yr−1 on the master fault over the past ~610 ka and an uplift/subsidence ratio of 1:1.1–2.4. We reproduce the observed flexure patterns, using 3 and 5-layered lithospheric scale finite element models. Modelling results imply that the observed elastic flexure is produced by coseismic slip along 40–60° planar normal faults in the elastic upper crust, followed by postseismic viscous relaxation occurring within the basal lower crust or upper mantle. We suggest that such a mechanism may typify rapid localised extension of continental lithosphere.

Dynamic Analysis of a 5-DOF Flexure-Based Nanopositioning Stage

A multibody dynamic model is developed for dynamic analysis of a 5-DOF flexure-based nanopositioning stage in the projection optical system of the semiconductor lithography in this paper. The 5-DOF stage is considered as an assembly of rigid bodies interconnected by elastic flexure hinges. Considering the length effects of flexure hinges, multibody dynamic equations are established according to spatial motions of rigid bodies by using Lagrangian method. The shear effects and the torsional compliances of the commonly used circular flexure hinges are considered to enhance the modeling accuracy. The accuracies of various out-of-plane compliance formulas are also discussed. To verify the developed dynamic model, the finite element analyses (FEA) by using ANSYS and modal hammer experimental tests of the primary flexure-based composition structures and the integral 5-DOF stage are performed. The analytical modal frequencies are well in agreement with FEA and experimental test. The results are significant to analyze and optimize the 5-DOF flexure-based nanopositioning stage.

Spatial variation in Late Ordovician glacioeustatic sea-level change

Mass extinction of Late Ordovician marine fauna closely coincided with southern hemisphere glaciation. The sequence stratigraphic architecture of shallow marine deposits informs estimates of glacioeustatic sea-level change at sites both proximal and distal to the reconstructed Ordovician ice sheet(s) and contemporaneous changes in ice volume. A recent correlation framework for the stratigraphic architectures of one near and one far field Late Ordovician margin concluded that the Late Ordovician glaciation encompassed multiple long-term cycles of ice volume growth and retreat with superimposed higher frequency cycles. Here we posit that—similar to Cenozoic glacial cycles—glacial isostatic adjustment can preclude synchronous and similar magnitude (or directional) changes in Late Ordovician sea level between ice proximal and ice distal locations and, hence, distort a globally correlative sequence stratigraphy. We explored whether long-duration (i.e., million year) Late Ordovician glacial cycles should produce a globally coherent, eustatic record of sea-level change between ice proximal and ice distal margins using a gravitationally self-consistent theory that accounts for the deformational, gravitational and rotational perturbations to sea level on a viscoelastic Earth model. We adopted a Late Ordovician paleogeography and a synthetic continental ice-sheet distribution and volume informed by the areal extent of glaciogenic deposits and geochemical records, respectively. We demonstrate that modeled million year Late Ordovician glacial cycles produce sea-level histories on near and far field margins that differ from eustasy, and from one another, due primarily to elastic flexure and associated gravitational effects. While predicted far-field sea-level histories faithfully preserve the temporal structure of modeled glacioeustasy, their amplitude may differ from eustasy by as much as 30–40%. The impact of glacial isostatic adjustment is largest at the margins of glaciated continents, and these effects can be of the same order of magnitude as the eustatic, and even induce a local sea-level rise during an episode of ice growth and eustatic sea-level fall, and vice versa. In this regard, stratal surfaces of maximum regression and flooding expressed at near-field margins need not reflect global (‘eustatic’) trends in ice sheet growth and decay, respectively, and thus may not provide chronostratigraphic horizons for correlation with far-field sequence stratigraphic architectures.

Elastoplastic Flexure of Round Steel Beams. 1. Springback Coefficient

Round steel beams are widely used in metallurgy, manufacturing, and construction. It is often irreplaceable in the production of machines and mechanical equipment on account of its excellent corrosion resistance and remarkable strength. Cylindrical springs for road and railroad vehicles are manufactured from round beams by means of special bending machines. Round beams also serve as blanks in the production of seamless pipe for the oil and gas industry. Stepped round beams are used as rollers in rolling and straightening mills. Steel rebar is manufactured from round beams of similar size. Outside Russia, the main producers of continuous-casting machines for the production of round billet are SMS Demag (Germany), Danieli (Italy), SMS Concast (Switzerland), and Siemens VAI (Austria). Russian producers include AO Chusovskii Metallurgicheskii Zavod, PAO Chelyabinskii Metallurgicheskii Kombinat, AO Volzhskii Trunbnyi Zavod, OAO Nizhneserginskii Metizno-Metallurgicheskii Zavod, AO Chepetskii Mekhanicheskii Zavod, PAO Severskii Trubnyi Zavod, and PAO Taganrogskii Metallurgicheskii Zavod. In the manufacture of parts from round beams and their use, they often experience elastic or elastoplastic flexure or complex torsion and flexure. In the present work, we propose an analytical method of calculating the residual curvature of round steel beams in elastoplastic flexure. In the calculations, the residual curvature of the round beam after flexure and the bending moments of the beam cross section in flexure are determined as a function of the beam radius, the Young’s modulus, the yield point, and the hardening modulus of the steel. The results may be widely used at manufacturing and metallurgical plants.

Microstructure and mechanical properties of Mo-ZrC-Cu composites synthesized by reactive melt infiltration of Zr-Cu melt into porous Mo2C preforms at 1300 °C

Mo-ZrC-Cu composites have been synthesized by reactive melt infiltration of Zr-Cu binary alloys into porous Mo2C preforms at 1300 °C for 10 min in argon. The influence of Zr content in the Zr-Cu infiltrator on microstructure and mechanical properties of Mo-ZrC-Cu composites are investigated. The as-synthesized composites consist of three major phases of Mo, ZrC and Cu, after a complete reaction of Mo2C(s) + Zr-Cu(l) → Mo(s) + ZrC(s) + Cu(l). Mo2Zr phase is formed when Zr content exceeds 50 at% in the Zr-Cu infiltrator. The formed ZrC grains have sizes less than 1 μm with Mo solid solute inside. Meanwhile, nanoscale zones enriched in Cu and C are also detected in ZrC grains. The angular ZrC particles and rounded Mo grains become larger with increasing Zr content in the Zr-Cu infiltrator. With decreasing Cu content from 43.5 to 31 vol% in Mo-ZrC-Cu composites, the elastic modulus and flexure strength increase from 146 to 156 GPa and from 542 to 569 MPa, respectively.

Effect of Disinfectants on Elastic Modulus, Flexural Strength and Color Stability of Denture Base Resins

Objective: Infection control protocols dictate the disinfection of dentures. There are no products available which are designed for the specific use of disinfecting dentures. The objective of this study was to investigate the impact of chemical disinfectants on elastic modulus, flexural strength and color stability of denture base resins. Methods: 256 specimens from four acrylic denture base resins were manufactured. Two cold-curing denture base resins: PalaXpress (Heraeus Kulzer, Hanau, Germany), Futura Gen (Schuetz Dental, Rosbach, Germany) and two heat-curing denture base resins: Paladon 65 (Heraeus Kulzer, Hanau, Germany), FuturAcryl 2000 (Schuetz Dental, Rosbach, Germany) were used. Three chemical disinfecting agents were tested: Impresept, D050 Instru-Gen, Stammopur DR. Specimens were stored in distilled water and in chemical disinfecting agents. They were divided randomly into groups. E-Modulus and flexural strength were measured using the three-point bending test. Color changes (ΔE) were determined spectrophotometrically. Results: The disinfection agents showed no significant influence on the E-modulus compared to distilled water (Acrylic vs. distilled water from (Futura Gen) 2688.80 ± 230.78 vs. 2766.60 ± 91.22 MPa to (PalaXpress) 3004.20 ± 26.40 vs. 2851.00 ± 95.23 MPa). Flexural strength after storage in distilled water and disinfection did not differ significantly (Acrylic vs. distilled water from (Paladon65) 27.28 ± 1.30 vs. 28.42 ± 0.84 N/mm2, (p > 0.05) to (PalaXpress) 30.88 ± 0.25 vs. 29.68 ± 0.79 N/mm2, p Conclusions: The investigated disinfection agents did not influence elastic modulus and flexural strength of denture base resins negatively. ΔE-values were in a range of 1 to 2. Thus, the detected color changes may be marginal. Clinical relevance: Single use disinfections are feasible for acrylic dentures regarding to elastic modulus and flexural strength.

Karst‐driven flexural isostasy in North‐Central Florida

AbstractDeformed marine terraces can be used to explore a region's uplift history. Trail Ridge is a marine terrace in north Florida that is nearly 80 m above modern sea level and contains Quaternary marine fossils, a fact that is inconsistent with estimates of paleo‐sea level history since the early Pleistocene. This implies that the terrace has experienced uplift since its formation, as well as nonuniform deformation recorded by the warping of its previously horizontal state. The Florida carbonate platform, located on the passive margin of eastern North America, is a setting where nontectonic influences (e.g. isostatic adjustment, dynamic topography) can be examined. We present a single‐transect, numerical model of vertical displacement, derived from elastic flexure, to assess the influence of karst‐driven isostatic uplift on present day topography of Trail Ridge in north Florida. Flexural modeling predicts elevations in central Florida not observed today, most likely because surface erosion and karst cavity collapse have obliterated this high topography. Older subsurface stratigraphic units, however, display the arched profile predicted from flexural modeling. Mass loss, calculated by differencing modeled topography and observed topography, was found to be 6.75 kg, since emplacement of Trail Ridge. Uplift rates, assuming karst‐driven flexural isostasy alone, using previously estimated ages of Trail Ridge of 0.125, 1.4, 3, or 3.5 Ma were found to be 0.535, 0.048, 0.022, and 0.019 mm/yr, respectively. A more likely explanation of uplift includes contributions from dynamic topography and glacial isostatic adjustment which should be further explored with more advanced geophysical modeling.

The role of magmatic loads and rift jumps in generating seaward dipping reflectors on volcanic rifted margins

The largest volcanic constructs on Earth are the seismically imaged seaward dipping reflector (SDR) units found offshore of many rifted continental margins, including most that border the Atlantic Ocean. Whether their formation requires large magnitude (i.e. 10 s of km) of normal fault slip or results from the deflection of the lithosphere by the weight of volcanic flows is controversial. Though there is evidence for faulting associated with some SDRs, this paper considers the range of structures that can be produced by magmatic and volcanic loading alone. To do this an idealized mechanical model for the construction of rift-related volcanic flow structures is developed. Dikes open as plates move away from the center of a model rift and volcanic flows fill the depression produced by the load caused by dike solidification. The thin elastic plate flexure approximation allows a closed form description of the shape of both the contacts between flows and between the flows and underlying dikes. The model depends on two independent parameters: the flexure parameter, α, and the maximum isostatically supported extrusive layer thickness, w0. For reasonable values of these parameters the model reproduces the observed down-dip thickening of flows and the range of reflector dip angles. A numerical scheme using the analytic results allows simulation of the effect of temporal changes in the locus of magmatic spreading as well as changes in the amount of volcanic infill. Either jumps in the location of the center of diking or periods with no volcanism result in separate units or “packages” of model SDRs, in which the flow-dike contact dips landward, consistent with observations previously attributed only to listric normal fault offset. When jumps in the spreading center are small (i.e. less than α) they result in thicker, narrower volcanic units on one side of a rift compared to those on the other side. This is similar to the asymmetric distributions of volcanic packages seen across some conjugate margins.

Elastic flexure controls magma trajectories and explains the offset of primary volcanic activity upstream of mantle plume axis at la Réunion and Hawaii hotspot islands

Surface volcanism at la Réunion and Hawaii occurs with an offset of 150–180 km upstream to the plume axis with respect to the plate motion. This striking observation raises questions about the forcing of plume-lithosphere thermo-mechanical interactions on melt trajectories beneath these islands. Based on visco-elasto-plastic numerical models handled at kilometric resolution, we propose to explain this offset by the development of compressional stresses at the base of the lithosphere, that result from elastic plate bending above the upward load exerted by the plume head. This horizontal compression adopts a disc shape centered around the plume axis: (i) it is 20 km thick, (ii) it has a 150 km radius, (iii) it lays at the base of the elastic part of the lithosphere, i.e., around ∼50–70 km depth where the temperature varies from ∼600 °C to ∼750 °C, (iv) it lasts for 5 to 10 My in an oceanic plate of age greater than 70 My, and (vi) it is controlled by the visco-elastic relaxation time at ∼50–70 km depth. This period of time exceeds the time during which both the Somalian/East-African and Pacific plates drift over the Reunion and Hawaii plumes, respectively. This indicates that this basal compression is actually a persistent feature. It is inferred that the buoyant melts percolating in the plume head pond below this zone of compression and eventually spread laterally until the most compressive principal elastic stresses reverse to the vertical, i.e., ∼150 km away from the plume head. There, melts propagate through dikes upwards to ∼35 km depth, where the plate curvature reverses and ambient compression diminishes. This 30–35 km depth may thus host a magmatic reservoir where melts transported by dykes pond. Only after further magmatic differentiation can dykes resume their ascension up to the surface and begin forming a volcanic edifice. As the volcano grows because of melt accumulation at the top of the plate, the lithosphere is flexed downwards, inducing extra tensile stress at 30–35 km depth and compression at ∼15 km depth (induced by the edifice load). It implies that now the melts pond at ∼15 km and form another magmatic reservoir lying just underneath the crust. These processes explain the ponding of primary (shield) melts at ∼35 km and ∼15 km depths as recorded below La Reunion, Mauritius or Hawaii volcanoes, all shifted by ∼150 km with respect to the plume axis.

Dispersion of High Concentrations of Carbon Nanofibers in Portland Cement Mortars

This research focuses on creating and maintaining a stable dispersion of carbon nanofibers (CNFs) in portland cement based materials. A microfine cement is used in conjunction with an untraditional dispersion method to encourage and stabilize the dispersion of CNFs in concentrations up to 5% by mass of cement. A computational simulation was utilized to examine an effect called geometric clustering on the dispersion of CNFs among Type I/II and microfine cement grains. The geometric clustering simulation revealed a higher achievable dispersion for microfine cement than for Type I/II cement. Scanning electron microscopy (SEM) was used to quantify the dispersion of CNFs among Type I/II and microfine cement grains. SEM image analysis indicated excessive CNF clumping among Type I/II cement grains, while the dispersion of hybrid microfine cement mortar continued to improve as the concentration of CNFs increased up to 5% by mass of cement. Mortar cube elastic stiffness and mortar prism flexure tests revealed that high concentrations of CNFs had detrimental effects in hybrid Type I/II cement mortar, whereas similar concentrations of CNFs had negligible or beneficial effects in hybrid microfine cement mortar.

Interpreting the Coseismic Uplift and Subsidence of the Longmen Shan Foreland Basin System during the Wenchuan Earthquake by a Elastic Flexural Model

AbstractThe coseismic surface uplift of the Longmen Shan (LMS) created an instantaneous topographic load over the western margin of the Sichuan Basin, where surface subsidence, decreasing eastward, has been measured using several methods, such as GPS, SAR and levelling. Using an elastic flexural model, we aim to interpret the coseismic surface uplift and subsidence, and constrain the effective lithospheric elastic thickness (Te) of the Sichuan Basin. Using different effective elastic thickness values for the Sichuan Basin, a series of subsidence curves were computed by the elastic flexure model equation for a broken elastic plate. The curves, produced by models using an effective elastic thickness of 30–40 km, provided the best fit to the general pattern of observed coseismic subsidence of the Sichuan Basin. However, the calculated subsidence (∼40–70 cm) at the front of the LMS is evidently lower than the observed values (∼100 cm), suggesting that the effective elastic thickness therein should be lower. These results indicate that the lithospheric strength may decrease westward from the Sichuan Basin to the LMS.

Evaluation of polymerization shrinkage in dental restorative experimental composites based: BisGMA/TEGDMA, filled with MMT

ABSTRACTThis work concerns to the investigation of the polymerization shrinkage and mechanical properties in dental restoratives experimental composites filled with nano clay Montmorilonite (MMT) Cloisite® 10A nanoparticles, in glycidyl methacrylate resin, using experimental composites filled with silanized Aerosil OX‐50 Silica as a control group. Six formulations with BisGMA/TEGDMA based polymeric matrix (three added with MMT and three added with silanized silica as filler) containing 50, 60, and 70 wt % were investigated. Characterization of the experimental composites was established with the following analyses: Scanning Electron Microscope, (SEM); Thermo‐Mechanical Analysis, (TMA) for Shrinkage Polymerization; Differential Scanning Calorimetry Analysis (DSC); Knoop Micro Hardness analysis; X‐ray Diffraction (XRD); Degree of Conversion (DC); Elastic Modulus and Flexural Strength; Transmission Electron Microscopy (TEM). Statistical Analyses were realized using two‐way ANOVA (type and amount of filler) and Tukey's test. TMA results showed that composites filled with MMT nanoparticle present statistically lower polymerization shrinkage values and statistically high degree of conversion in all formulations tested, when compared to composites filled with silanized silica. XRD and TEM analyses showed evidences of the intercalation phenomenon in the MMT nanoparticles in relation to BisGMA/TEGDMA polymeric matrix. However, for Flexural Strength, groups filled with MMT nanoparticle showed statistically lower values in all concentration tested. At high filler concentration it was observed the appearance of tactoids and functionalization of MMT nanoparticle did not promote a strong interface adhesion between polymeric matrix and filler. In order to adjust the mechanical properties, it would be convenient to promote the concentration optimization of MMT nanoparticles. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 43543.

Maximum-recorded overland run-ups of major nearfield paleotsunamis during the past 3000 years along the Cascadia margin, USA, and Canada

Maximum-recorded run-up estimates of six major nearfield paleotsunamis, dating from 0.3 to 2.8 ka, are compiled from reported studies at 12 reliable localities distributed over a north–south distance of 1000 km in the Cascadia subduction zone. The run-up estimates are based on surveyed elevations and positions of terminal sand sheet layers that were deposited by the dated paleotsunamis. Maximum terminal deposit elevations from open-coastal sites range from 3 to 12 m NAVD88. Paired proximal and distal run-up sites at four localities demonstrate landward vertical attenuation gradients (−2.5 to −4.2 m km−1) of decreasing terminal sand deposit elevation with increasing distance inland. An averaged attenuation gradient is reversed (3.0 m km−1) to project paleotsunami run-up elevations to adjacent ocean shorelines. The run-up projections are further adjusted by paleotsunami age and relative sea level curves to estimate shoreline inundation elevations under modern sea level conditions. The tsunami shoreline inundation elevations range from 3 ± 2 to 15 ± 2 m NAVD88, with the largest values occurring along the central Cascadia margin and the smallest values occurring in the eastern Juan de Fuca Strait. Contradictory to some numerical tsunami modeling assumptions, there is no apparent correlation between duration of interseismic strain accumulation or estimated upper-plate elastic flexure and corresponding paleotsunami run-up heights on the central Cascadia margin. The short duration since the last Cascadia megathrust rupture (0.3 ka) cannot be used to imply smaller run-up values for a near-future Cascadia tsunami. Coastal communities should plan for the maximum paleotsunami run-ups as recorded at the nearest reliable run-up localities.

An iterative spectral solution method for thin elastic plate flexure with variable rigidity

S U M M A R Y Thin plate flexure theory provides an accurate model for the response of the lithosphere to vertical loads on horizontal length scales ranging from tens to hundreds of kilometres. Examples include flexure at seamounts, fracture zones, sedimentary basins and subduction zones. When applying this theory to real world situations, most studies assume a locally uniform plate thickness to enable simple Fourier transform solutions. However, in cases where the amplitude of the flexure is prominent, such as subduction zones, or there are rapid variations in seafloor age, such as fracture zones, these models are inadequate. Here we present a computationally efficient algorithm for solving the thin plate flexure equation for non-uniform plate thickness and arbitrary vertical load. The iterative scheme takes advantage of the 2-D fast Fourier transform to perform calculations in both the spatial and spectral domains, resulting in an accurate and computationally efficient solution. We illustrate the accuracy of the method through comparisons with known analytic solutions. Finally, we present results from three simple models demonstrating the differences in trench outer rise flexure when 2-D variations in plate rigidity and applied bending moment are taken into account. Although we focus our analysis on ocean trench flexure, the method is applicable to other 2-D flexure problems having spatial rigidity variations such as seamount loading of a thermally eroded lithosphere or flexure across the continental–oceanic crust boundary.

Prescription opioid use is associated with increased mortality in the reasons for geographic and racial differences in stroke study

Porous acicular mullite (ACM) ceramics are known to be mechanically robust even at high porosities. This study was undertaken to better understand what aspects of acicular mullite's needle-like microstructure affect the overall mechanical properties and how the microstructure might be modified to improve mechanical performance. ACMs with a variety of porosities, pore sizes, and needle diameters were produced, and their elastic moduli, flexure strengths, and fracture toughnesses were measured. Three-dimensional image analysis was an invaluable tool in determining the needle diameters of these complex 3D network structures. It was found that porosity was the most dominant factor in determining the mechanical properties of ACM and that its behavior could be described using the Gibson–Ashby foam model.