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Because of operational constraints, no research studies are performed during return to Earth, when astronauts perform critical operational tasks such as piloting and egressing the vehicle. The objective of this study was to interview Space Shuttle crewmembers to collect a description of post-flight perception of self-motion and self-performance from the astronauts during reentry and immediately after landing. Thirty-four Space Shuttle crewmembers were interviewed immediately after they returned from space. Transcripts of the interviews recount the crewmembers' experiences associated with head movements during reentry, during egressing the vehicle, and shortly after landing. Head movements made during reentry and immediately after return to Earth caused an increase sensation of self-motion, which affected their balance and gait. Pitch and roll head movements provoked the largest effects. Crewmembers also reported a lag in motion perception after the movement had stopped. More than one-third of crewmembers thought they would be unable to egress the Space Shuttle cabin unaided during an emergency. A clinical otoneurological examination of the crewmembers immediately after landing is needed to better understand the extent of vestibular deficits and track recovery.

A compilation of foraminiferal stable isotope measurements from southern high latitude (SHL) deep-sea sites provides a novel perspective important for understanding Earth's paleotemperature and paleoceanographic changes across the rise and fall of the Cretaceous Hot Greenhouse climate and the subsequent Paleogene climatic optimum. Both new and previously published results are placed within an improved chronostratigraphic framework for southern South Atlantic and southern Indian Ocean sites. Sites studied were located between 58° and 65°S paleolatitude and were deposited at middle to upper bathyal paleodepths. Oxygen isotope records suggest similar trends in both bottom and surface water temperatures in the southern sectors of the South Atlantic and in the Indian Ocean basins. Warm conditions were present throughout the Albian, extreme warmth existed during the Cretaceous Thermal Maximum (early-mid-Turonian) through late Santonian, and long-term cooling began in the Campanian and culminated in Cretaceous temperature minima during the Maastrichtian. Gradients between surface and seafloor δ18O and δ13C values were unusually high throughout the 11.5 m.y. of extreme warmth during the Turonian-early Campanian, but these vertical gradients nearly disappeared by the early Maastrichtian. In absolute terms, paleotemperature estimates that use standard assumptions for pre-glacial seawater suggest sub-Antarctic bottom waters were ≥21 °C and sub-Antarctic surface waters were ≥27 °C during the Turonian, values warmer than published climate models support. Alternatively, estimated temperatures can be reduced to the upper limits of model results through freshening of high latitude waters but only if there were enhanced precipitation of water with quite low δ18O values. Regardless, Turonian planktonic δ18O values are ~1.5‰ lower than minimum values reported for the Paleocene-Eocene Thermal Maximum (PETM) from the same region, a difference which corresponds to Turonian surface temperatures ~6 °C warmer than peak PETM temperatures if Turonian and Paleocene temperatures are estimated using the same assumptions. It is likely that warm oceans surrounding and penetrating interior Antarctica (given higher relative sea level) prevented growth of Antarctic ice sheets at all but the highest elevations from the late Aptian through late Campanian; however, Maastrichtian temperatures may have been cool enough to allow growth of small, ephemeral ice sheets. The standard explanation for the sustained warmth during Cretaceous Hot Greenhouse climate invokes higher atmospheric CO2 levels from volcanic outgassing, but correlation among temperature estimates, proxy estimates of pCO2, and intervals of high fluxes of both mafic and silicic volcanism are mostly poor. This comparison demonstrates that the relative timing between events and their putative consequences need to be better constrained to test and more fully understand relationships among volcanism, pCO2, temperature ocean circulation, Earth's biota and the carbon cycle.

A high-resolution multibeam echosounder (MBES) dataset covering over 279,000 km2 was acquired in the southeastern Indian Ocean to assist the search for Malaysia Airlines Flight 370 (MH370) that disappeared on 8 March 2014. The data provided an essential geospatial framework for the search and is the first large-scale coverage of MBES data in this region. Here we report on geomorphic analyses of the new MBES data, including a comparison with the Global Seafloor Geomorphic Features Map (GSFM) that is based on coarser resolution satellite altimetry data, and the insights the new data provide into geological processes that have formed and are currently shaping this remote deepsea area. Our comparison between the new MBES bathymetric model and the latest global topographic/bathymetric model (SRTM15_plus) reveals that 62% of the satellite-derived data points for the study area are comparable with MBES measurements within the estimated vertical uncertainty of the SRTM15_plus model (± 100 m). However, > 38% of the SRTM15_plus depth estimates disagree with the MBES data by > 100 m, in places by up to 1900 m. The new MBES data show that abyssal plains and basins in the study area are significantly more rugged than their representation in the GSFM, with a 20% increase in the extent of hills and mountains. The new model also reveals four times more seamounts than presented in the GSFM, suggesting more of these features than previously estimated for the broader region. This is important considering the ecological significance of high-relief structures on the seabed, such as hosting high levels of biodiversity. Analyses of the new data also enabled sea knolls, fans, valleys, canyons, troughs, and holes to be identified, doubling the number of discrete features mapped. Importantly, mapping the study area using MBES data improves our understanding of the geological evolution of the region and reveals a range of modern sedimentary processes. For example, a large series of ridges extending over approximately 20% of the mapped area, in places capped by sea knolls, highlight the preserved seafloor spreading fabric and provide valuable insights into Southeast Indian Ridge seafloor spreading processes, especially volcanism. Rifting is also recorded along the Broken Ridge – Diamantina Escarpment, with rift blocks and well-bedded sedimentary bedrock outcrops discernible down to 2400 m water depth. Modern ocean floor sedimentary processes are documented by sediment mass transport features, especially along the northern margin of Broken Ridge, and in pockmarks (the finest-scale features mapped), which are numerous south of Diamantina Trench and appear to record gas and/or fluid discharge from underlying marine sediments. The new MBES data highlight the complexity of the search area and serve to demonstrate how little we know about the vast areas of the ocean that have not been mapped with MBES. The availability of high-resolution and accurate maps of the ocean floor can clearly provide new insights into the Earth's geological evolution, modern ocean floor processes, and the location of sites that are likely to have relatively high biodiversity.

Impairments in balance control are inevitable following exposure to microgravity. However, the role of particular sensory system in postural disorders at different stages of the exposure to microgravity still remains unknown. We used a method called Dry Immersion (DI), as a ground-based model of microgravity, to elucidate the effects of 6-h of load-related afferent inputs on kinematic characteristics of postural corrective responses evoked by pushes to the chest of different intensities during upright standing. The structure of postural corrective responses was altered following exposure to DI, which was manifested by: (1) an increase of the ankle and knee flexion during perturbations of medium intensity, (2) the lack of the compensatory hip extension, as well as diminished knee and ankle flexion with a further increase of the perturbation intensity to submaximal level. We suggest that the lack of weight-bearing increases the reactivity of the balance control system, whereas the ability to scale the responses proportionally to the perturbation intensity decreases. Disrupted neuromuscular coordination of postural corrective responses following DI can be attributed to adaptive neural modifications on the spinal and cortical levels. The present study provides evidence that even a short-term lack of load-related afferent inputs alters kinematic patterns of postural corrective responses, and can result in decreased balance control. Because vestibular input is not primarily affected during the DI exposure, our results indicate that activity and the state of the load-related afferents play critical roles in balance control following real or simulated microgravity.

The undamped, finite amplitude horizontal motion of a load supported symmetrically between identical incompressible, isotropic hyperelastic springs, each subjected to an initial finite uniaxial static stretch, is formulated in general terms. The small amplitude motion of the load about the deformed static state is discussed; and the periodicity of the arbitrary finite amplitude motion is established for all such elastic materials for which certain conditions on the engineering stress and the strain energy function hold. The exact solution for the finite vibration of the load is then derived for the classical neo-Hookean model. The vibrational period is obtained in terms of the complete Heuman lambda-function whose properties are well-known. Dependence of the period and hence the frequency on the physical parameters of the system is investigated and the results are displayed graphically.

We present initial isotopic ratios of lead for Early Cretaceous (Barremian–Aptian) sections from Shatsky Rise (Pacific) and Gorgo a Cerbara (Italy). Our Pb isotopic data track an interval representing Oceanic Anoxic Event (OAE)-1a, which is characterized by quasi-global deposition of organic carbon-rich black shale. Pb isotopic compositions of sediments from Shatsky Rise decrease at the end of Barremian time, from radiogenic continental values to unradiogenic values, and subsequently remained less radiogenic until the end of early Aptian time. We explain the isotopic shift by a significant increase in supply rate of unradiogenic Pb, most likely due to massive volcanism. In contrast, the Pb isotopic compositions from the Italian section, which was situated at the western end of Tethys, are mostly identical to those of upper continental crust, showing no significant change in supply rate of unradiogenic Pb. The discrepancy between two sites is attributed to quiescent deep-submarine eruptions of Pacific large igneous provinces (LIPs) such as the Ontong Java Plateau (OJP), which severely limited dispersion of Pb-carrying particles out of the Pacific Ocean. Published Os isotopic data from the Italian section indicate two episodes of massive eruptions of OJP or contemporaneous Manihiki and Hikurangi plateaus starting from earliest Aptian time, slightly later than that indicated by the sedimentary Pb isotopic record from Shatsky Rise. Differences in isotopic variations between Pb and Os likely reflect differences in their chemical behaviors in the oceans, i.e., Pb isotopic compositions would have varied in response to local or regional changes in sediment provenances, whereas large-scale changes in Os inputs are required to explain variations in seawater Os isotopic compositions. Our Pb isotopic data, together with the published Os isotopic record, provide new evidence for the eruptive history of OJP together with contemporaneous Pacific plateaus and its environmental consequences, starting from end-Barremian time and extending through early Aptian time.

The purpose of the study was to explore the effects of long-duration space flight on the acquisition of specific visual targets in the horizontal plane. Seven cosmonauts (4 high performance pilots and 3 non-pilots) who had flown between 186–198 days on Mir served as subjects. Baseline testing was performed 4 times prior to launch and 4 times following landing at different intervals totrack recovery. During testing the subjects were required to acquire targets that were randomly presented with both a head and eye movement using a time optimal strategy. Prior to flight two unique head movement strategies, related primarily to piloting experience, were used for target acquisition. Non-pilots employed a Type-I strategy consisting of high velocity head movements with large peak amplitudes, while high performance pilots used primarily low velocity, small amplitude head movements (Type-II) to acquire the targets (p

We present 40Ar/39Ar age and geochemical (major and trace element and Sr–Nd–Hf–Pb isotope) data from submarine samples recovered from the basement of the Manihiki Plateau during the R/V Sonne research expedition SO193. The samples, predominately tholeiites, with minor occurrences of basaltic andesites and hawaiites, give a mean age of 124.6 ± 1.6 Ma from four different localities on the plateau. Based on TiO2 content, we define two groups of volcanic rocks that differ in trace element and isotopic compositions. Partial melting modeling suggests that the low-Ti group lavas were derived through large degrees of melting (c. 30%) of a peridotitic source at mantle potential melting temperatures of c. Tp = 1510 °C, more than 100 °C above the ambient mantle potential melting temperature. Since the primary water contents of both groups of lavas are low (0.1–0.3g wt.%) and the source is peridotitic, excess temperature is most likely the reason for the large degrees of melting producing the large volume of plateau basalts, consistent with the involvement of a mantle plume. The incompatible element contents of the low-Ti group lavas show a multistage history with enrichment in the most incompatible elements of a previously highly depleted source. They have isotopic compositions similar to enriched mid-ocean-ridge basalt (EMORB) and similar to the common focal zone (FOZO) component. The high-Ti group lavas have more enriched incompatible element compositions overall. Their isotopic compositions tend towards an enriched mantle (EMI)-type endmember, similar, although less extreme, than lavas from the Pitcairn Islands. The geochemistry of the Manihiki Plateau can best be explained by a plume containing three components: 1) a dominant peridotitic FOZO-type component, 2) delaminated EMI-type subcontinental lithospheric mantle (SCLM), and 3) a HIMU (recycled oceanic crustal)-type component possibly in the form of eclogite/pyroxenite. The similarity in age and geochemical composition of Manihiki, Hikurangi and Ontong Java basement lavas, including volcanism in some adjacent basins, suggests that the Greater Ontong Java Volcanic Event covered c. 1% of the Earth's surface with volcanism.

The small amplitude, free longitudinal vibrational motion of a load supported above by an incompressible, isotropic and homogeneous rubberlike spring is studied for a general class of materials having limited extensibility. First, a simple general frequency equation for small motions about a static equilibrium state is derived without specification of the constitutive nature of the spring. The normalized oscillational frequency of the small superimposed motion of the load is then determined for all materials in a broad class of limited elastic materials. This frequency depends on the limiting extensibility constant and the static stretch, but it is independent of any other physical properties of the spring. It is shown that, for the same static stretch, the normalized vibrational frequency of a load on a neo-Hookean support is a lower bound for its normalized vibrational frequency on any limited elastic spring in the general constitutive class. Specific equations for the Gent and Puso limited elastic models are derived, the frequency for the latter being smaller than that for the former under the same static conditions. The effects of their limited extensibility are described both analytically and graphically, and their connection with experiments on certain rubber materials and biological tissue is noted.

The application of the elliptic balance method to the solution of undamped, two degree of freedom homogeneous nonlinear systems is described. This method uses Jacobian elliptic functions in the balance and is based on the concept of averaging with respect to complete elliptic integrals of the first kind. To assess the accuracy of the approximate solution thus obtained, we consider the motion of a linear vibration absorber attached to a rigid body that is supported symmetrically by incompressible, homogeneous and isotropic hyperelastic shear blocks. It is shown that the amplitude–time response of the model system is well predicted by the elliptic balance method solution even for relatively large parameter values.

Oceanic Anoxic Events (OAEs) are geological time intervals characterized by extremely high burial rates of organic carbon that led to deposition of organic-rich “black shales” in the global ocean. It has been proposed that oceanic anoxic events are ultimately caused by massive volcanism associated with formation of large igneous provinces (LIPs) because of chronological similarities, but no general consensus has developed yet. To investigate the possibility of LIP volcanism instigating OAEs, we measured stable isotopic compositions of bulk organic carbon (δ13Corg) and lead (Pb) isotopic compositions in the silicate sediment fraction across the Bonarelli black shale (Italy), a type stratigraphic section for the end-Cenomanian OAE (OAE-2; 94 Ma). Ultra-high-resolution δ13Corg records determined every 1.5 mm capture a 3‰ sharp negative shift at the base of the Bonarelli. At the same stratigraphic level, Pb isotopic compositions in the silicate sediment fraction exhibit significant shifts toward characteristic values of volcanic rocks from contemporaneous LIPs (Caribbean and Madagascar flood basalts). These data suggest a rapid, substantial increase in the relative supply of silicate minerals from the two LIPs. Massive subaerial volcanism associated with LIP formation provides a simple explanation for these two isotopic geochemical signals via release of a huge amount of carbon dioxide (∼ 105 Gt CO2) and particulate materials into the atmosphere, which resulted in a rapid negative shift of δ13C in sea water and changes in Pb isotopic compositions in the silicate sediment fraction, respectively. We interpret that massive volcanism triggered significant climatic changes, inducing biotic crises and oceanic anoxia.

The finite amplitude, free radial oscillations of a thick-walled circular cylindrical tube are studied for an arbitrary incompressible, isotropic and homogeneous rubber-like material having limiting molecular chain extensibility. First, based on classical results for hyperelastic tubes, some results for thick-walled Mooney-Rivlin tubes are described graphically in the phase plane. Then the periodicity of the finite amplitude, free oscillations of a general limited elastic, thick-walled tube is studied; and some analytical results for the Gent model are illustrated in several numerical examples. Results for thick-walled Gent tubes are compared with those for corresponding Mooney-Rivlin tubes; and the motion of thin-walled Gent tubes is illustrated in the phase plane. Physical conclusions are presented. The period of small amplitude oscillations of an arbitrary elastic or limited elastic tube is derived from relations obtained by a linearization of a general class of equations of which the tube problem is a special case. Classical results of the linear theory are thereby recovered and compared with results for Mooney-Rivlin and Gent tubes.

To better understand the effects of varying head movement frequencies on human balance control, 12 healthy adult humans were studied during static and dynamic (0.14, 0.33, 0.6 Hz) head tilts of +/- 30 degrees in the pitch and roll planes. Postural sway was measured during upright stance with eyes closed and altered somatosensory inputs provided by a computerized dynamic posturography (CDP) system. Subjects were able to maintain upright stance with static head tilts, although postural sway was increased during neck extension. Postural stability was decreased during dynamic head tilts, and the degree of destabilization varied directly with increasing frequency of head tilt. In the absence of vision and accurate foot support surface inputs, postural stability may be compromised during dynamic head tilts due to a decreased ability of the vestibular system to discern the orientation of gravity. This instability may compound the risk of falling following recovery from balance disorders or adaptation to altered gravity conditions such as space flight. Thus, dynamic head tilts may improve the diagnostic sensitivity of computerized dynamic posturography, particularly for healthy subjects recovering from temporary balance control deficits.

Systematic analysis of a grid of 3450 km of multichannel seismic reflection lines from the Solomon Islands constrains the late Tertiary sedimentary and tectonic history of the Solomon Island arc and its convergent interaction with the Cretaceous Ontong Java oceanic plateau (OJP). The OJP, the largest oceanic plateau on Earth, subducted beneath the northern edge of the Solomon arc in the late Neogene, but the timing and consequences of this obliquely convergent event and its role in the subduction polarity reversal process remain poorly constrained. The Central Solomon intra-arc basin (CSB), which developed in Oligocene to Recent time above the Solomon arc, provides a valuable record of the tectonic environment prior to and accompanying the OJP convergent event and the subsequent arc polarity reversal. Recognition of regionally extensive stratigraphic sequences—whose ages can be inferred from marine sedimentary sections exposed onland in the Solomon Islands—indicate four distinct tectonic phases affecting the Solomon Island arc. Phase 1: Late Oligocene–Late Miocene rifting of the northeast-facing Solomon Island arc produced basal, normal-fault-controlled, asymmetrical sequences of the CSB; the proto-North Solomon trench was probably much closer to the CSB and is inferred to coincide with the trace of the present-day Kia-Kaipito-Korigole (KKK) fault zone; this protracted period of intra-arc extension shows no evidence for interruption by an early Miocene period of convergent “soft docking” of the Ontong Java Plateau as proposed by previous workers. Phase 2: Late Miocene–Pliocene oblique convergence of the Ontong Java Plateau at the proto-North Solomon trench (KKK fault zone) and folding of the CSB and formation of the Malaita accretionary prism (MAP); the highly oblique and diachronous convergence between the Ontong Java plateau and the Solomon arc terminates intra-arc extension first in the southeast (Russell subbasin of the CSB) during the Late Miocene and later during the Pliocene in the northwest (Shortland subbasin of the CSB); folds in the CSB form by inversion of normal faults formed during Phase 1; Phinney et al. [Sequence stratigraphy, structural style, and age of deformation of the Malaita accretionary prism (Solomon arc-Ontong Java Plateau convergent zone)] show a coeval pattern of southeast to northwest younging in folding and faulting of the MAP. Phase 3: Late Pliocene–early Pleistocene arc polarity reversal and subduction initiation at the San Cristobal trench. Effects of this event in the CSB include the formation of a chain of volcanoes above the subducting Australia plate at the San Cristobal trench, the formation of the broad synclinal structure of the CSB with evidence for truncation at the uplifted flanks, and widespread occurrence of slides and “seismites” (deposits formed by seismic shaking). Phase 4: Pleistocene to Recent continued shortening and synclinal subsidence of the CSB. Continued Australia-Pacific oblique plate convergence has led to deepening of the submarine, elongate basin axis of the synclinal CSB and uplift of the dual chain of the islands on its flanks.

Possibilities for the fate of oceanic plateaus at subduction zones range from complete subduction of the plateau beneath the arc to complete plateau–arc accretion and resulting collisional orogenesis. Deep penetration, multi-channel seismic reflection (MCS) data from the northern flank of the Solomon Islands reveal the sequence stratigraphy, structural style, and age of deformation of an accretionary prism formed during late Neogene (5–0 Ma) convergence between the 33-km-thick crust of the Ontong Java oceanic plateau and the 15-km-thick Solomon island arc. Correlation of MCS data with the satellite-derived, free-air gravity field defines the tectonic boundaries and internal structure of the 800-km-long, 140-km-wide accretionary prism. We name this prism the “Malaita accretionary prism” or “MAP” after Malaita, the largest and best-studied island exposure of the accretionary prism in the Solomon Islands. MCS data, gravity data, and stratigraphic correlations to islands and ODP sites on the Ontong Java Plateau (OJP) reveal that the offshore MAP is composed of folded and thrust faulted sedimentary rocks and upper crystalline crust offscraped from the Solomon the subducting Ontong Java Plateau (Pacific plate) and transferred to the Solomon arc. With the exception of an upper, sequence of Quaternary? island-derived terrigenous sediments, the deformed stratigraphy of the MAP is identical to that of the incoming Ontong Java Plateau in the North Solomon trench.

The ∼120 Ma Ontong Java Plateau and neighboring, contemporaneous Nauru, East Mariana, and (probably) Pigafetta basin flood basalts in the western equatorial Pacific Ocean comprise the Earth’s largest flood basalt province. Geophysical, geochemical, and geodynamic evidence from the province are difficult to reconcile with mantle plume models; absence of an obvious hotspot source or track, minor crustal uplift associated with emplacement, minor total subsidence compared with normal oceanic crust or other oceanic plateaus and submarine ridges, high degrees of melting at shallow, upper mantle depths, low water contents of basalts, enrichment of platinum group elements in basalts, and a ∼300 km deep, seismically slow mantle root are more consistent with the consequences of an impacting bolide. An object ∼20 km in diameter impacting relatively young (∼20 Myr) Pacific lithosphere and penetrating into the uppermost asthenosphere would have initiated massive decompression melting in the upper mantle, and may have resulted in emplacement of the greater Ontong Java Plateau.

The equilibrium (EQ) score commonly used in computerized dynamic posturography is normalized between 0 and 100, with falls assigned a score of 0. The resulting mixed discrete-continuous distribution limits certain statistical analyses and treats all trials with falls equally. We propose a simple modification of the formula in which peak-to-peak sway data from trials with falls is scaled according the percent of the trial completed to derive a continuous equilibrium (cEQ) score. The cEQ scores for trials without falls remain unchanged from the original methodology. The cEQ factors in the time before a fall and results in a continuous variable retaining the central tendencies of the original EQ distribution. A random set of 5315 Sensory Organization Test trials were pooled that included 81 falls. A comparison of the original and cEQ distributions and their rank ordering demonstrated that trials with falls continue to constitute the lower range of scores with the cEQ methodology. The area under the receiver operating characteristic curve (0.997) demonstrates that the cEQ retained near-perfect discrimination between trials with and without falls. We conclude that the cEQ score provides the ability to discriminate between ballistic falls from falls that occur later in the trial. This approach of incorporating time and sway magnitude can be easily extended to enhance other balance tests that include fall data or incomplete trials.

New constitutive equations based on an amended form of the Kuhn–Grun probability distribution function due to Jernigan and Flory are derived from the standard James–Guth (JG) 3-chain and Arruda–Boyce (AB) 8-chain non-Gaussian molecular network models. The kinematics describing the stretch of a 1-chain model in an affine deformation shows that the relative stretch of a single molecular chain initially oriented along the diagonal of a cube is determined by the first principal invariant of the Cauchy–Green deformation tensor. The Kuhn–Grun probability distribution for a randomly oriented chain and its more general amended form due to Wang and Guth, are functions of only the relative chain stretch. Hence, any non-Gaussian network model for which the configurational entropy of all chains may be uniform is characterized by an elastic response function that depends on only the first principal invariant of the Cauchy–Green deformation tensor. Both the regular and amended AB 8-chain models are characterized by specific response functions in this class; the regular and amended JG 3-chain models, however, are not. An amended form of the phenomenological composite 3-chain/8-chain model suggested by Wu and van der Giessen is introduced. Analytical relations for several kinds of homogeneous deformations of the standard and amended models are compared with a variety of experimental data by others. It is found that results for the amended 3-chain and 8-chain models do not vary significantly from results for the corresponding regular models. The composite model, on the other hand, shows excellent overall agreement with the diverse data, including equibiaxial deformations for which other models show greater variance; but it offers no improvement in comparison with data for plane strain compression. Some remarks relating the chain parameters of the 3-chain and 8-chain network models, and the limiting chain and continuum stretches for these models are discussed in an appendix.

The motion of a homogeneous, thin rigid plate or shell subject to Stokes damping over its entire surface and to any additional system of workless forces, including those that are equipollent to zero, is studied. It is shown that the equation for the single-degree of freedom motion of every thin body having the same mass density per unit area is universal; the result, except for sufficient mathematical smoothness essential to integration over the body, is independent of any other physical features or dimensions of the body. A few examples illustrate the general problem and the universal nature of the equation of motion for thin plates and shells.

A general constitutive theory of stress-softening in isotropic, compressible materials based on a two phase microstructural damage model is presented. Stress-softening induced by an uniaxial stretch of the material is analyzed, and some general analytical results consonant with experimental observations are obtained. It is shown for compressible stress-softening materials that the Poisson function for the elastic stress-softened material generally will differ from that for the virgin material. Some general characteristics of the physical response of equi-Poisson materials are described, and an example of a general class of these materials is presented. It is shown that the physical response of isotropic, compressible stress-softening materials parallels that described in earlier papers on its incompressible counterpart. For illustration, a special subclass of stress-softening hyperelastic parent materials and an exponential softening function are introduced. The general results are then described graphically for uniaxial tension and compression of a special class of Blatz–Ko parent material models developed from experiments on polyurethane foamed rubbers.

A general theory of isotropic stress-softening in incompressible isotropic materials is developed. The principal idea is that a stress-softening material is an inelastic material that has selective memory of only the maximum previous deformation to which it is subjected. This memory dependence is incorporated within general material response functions that are monotone decreasing functions of a stress-softening variable, which is a monotone increasing function of the maximum previous strain experienced by the material. A loading criterion is introduced to identify when the material is loaded along its virgin deformation path where the maximum previous strain is its current value, and to identify when it is unloaded to deform subsequently as an ideal isotropic elastic material in both elastic loading and unloading, so long as the maximum previous strain is not exceeded. The effect of loading from a configuration of maximum previous strain is to further stress-soften the material. Results demonstrating the effects of stress-softening are obtained for general isotropic stress-softening materials in simple uniaxial extension and in simple shear. A simplified analytical model together with a special softening function are introduced to illustrate some general results and to provide specific analytical and graphical examples. Both general and model-specific analytical results obtained for simple uniaxial extension are shown to be consistent with the overall ideal phenomenological behavior exhibited in experiments by others on stress-softening in simple tension and compression. Similar but totally new results for simple shear are derived, and their relation to effects in simple tension are discussed. It is demonstrated that the larger effect of softening occurs in the simple uniaxial extension, the effect in even a gross equivalent simple shear being small. All results are obtained from general three-dimensional constitutive equations.

The wave speed criterion is applied to discuss restrictions on the material response functions of an isotropic, Bell constrained material in order that small amplitude, plane waves may propagate in the material with real-wave speeds. The case of a body subjected to a biaxial stress is related to the elastic stability of a Bell constrained slab. We show that two cases among five reported by Beatty and Pan in study of the elastic stability of a thick plate cannot support such waves. These cases, therefore, are not possible and must be excluded as potential solutions. The question of the stability of the equibiaxial deformations of a Bell constrained material under an all-around Cauchy stress, suggested in primary work of Beatty and Hayes on homogeneous deformations of Bell materials, is investigated. It is shown that for a general Bell material model, the state of equibiaxial deformation under an all-around Cauchy stress is materially unstable, unless all stretches are equal to one, their value in the initial undistorted state.

The elastic stability of an internally constrained thick plate is investigated on the basis of the well-known Euler dead load criterion of existence of adjacent equilibrium states. Two classes of internally constrained materials are examined—the Bell constrained material characterized by tr V=3, and the incompressible material for which det V=1, V being the left-stretch tensor. Although this study focuses mainly on instability of a Bell constrained slab, some new results are presented as well for an incompressible neo-Hookean slab. Graphical illustrations of the critical stretch as a function of the slenderness measure of the slab are provided for two classes of Bell materials—the simple hyperelastic Bell material model and an empirical model first described in experiments by Bell. The oscillatory nature of the stability results for Bell’s empirical model differ from the monotone solutions found for both the simple hyperelastic Bell material and the neo-Hookean material models. Estimates for buckling loads of thin plates deduced from the thick-plate analysis are compared with classical results. The critical load found for the simple hyperelastic Bell material coincides with the result deduced from classical thin plate theory, while the solution found for Bell’s law, which is parabolic in the engineering strain, does not. The half-space stability problem is examined as an extension of results deduced for a thick plate based on Bell’s law.

It is a common practice to manually stretch a toy balloon several times prior to inflation. This preconditioning reduces the pressure required to fully inflate the balloon, and thus eases the task of inflation. The reduction in pressure required to inflate the balloon is mainly a result of the Mullins effect. The Mullins effect, also known as stress softening, refers to a change in material behavior resulting from prior deformation. The results of cyclic inflation experiments performed with latex rubber balloons are presented. Some interesting aspects of the inflation behavior are noted, and the effect of preconditioning on the inflation behavior is quantified. The balloons are modeled as incompressible, spherical membranes which undergo an equibiaxial extension during inflation. This model is used to calculate the stress-strain behavior of the balloon material in an equibiaxial extension. We generalize a constitutive equation for the Mullins effect in uniaxial extension, first proposed by Johnson and Beatty [1], to an equibiaxial extensional deformation. We are able to make certain predictions about the results of our balloon inflation experiments without specification of the two functions which comprise the constitutive equation. Our method of interpretation of experimental results from the balloon inflation tests is similar to the method in [1] for the small transverse vibration of a stretched rubber cord. Finally, we demonstrate that the equibiaxial extensional deformation of an isotropic, incompressible material is kinematically equivalent to the uniaxial compression of that material. The results of our balloon inflation experiments are used to calculate the stress softening behavior of latex rubber in uniaxial compression. The calculated behavior indicates that latex rubber does indeed stress soften in uniaxial compression. This observation confirms the early experimental findings of Mullins [2], but contradicts the analytical predictions of Lee and Williams [3].

Viscoelastic constitutive equations of the differential type and of the rate type are applied in the study of the mechanical response of rubberlike materials in a simple shearing deformation superimposed on a specified static longitudinal stretch. Creep, recovery and stress relaxation processes are formulated for a class of incompressible, isotropic viscoelastic quadratic materials. Equations characterizing the creep and recovery processes for materials of differential type are derived, and their exact solutions are obtained. For materials of the rate type, the stress relaxation process is independent of the elastic material response functions. A coupled system of equations for the creep and recovery processees in a material of rate type are presented ; these must be solved numerically. The finite amplitude, damped, free vibration of a rigid body supported by incompressible, viscoelastic quadratic simple shear mountings of the differential type is investigated. The motion of the body is governed by a damped Duffing equation whose solution is discussed by the averaging method.

A constitutive equation for an incompressible, isotropic, nonlinear viscoelastic solid of differential type, a class which includes the Voigt-Kelvin solid of classical linear viscoelasticity, is applied to study the quasi-static response of the material in a simple shearing deformation superimposed on a given static homogeneous strain. The Cauchy stress is determined and general relations that characterize creep and recovery phenomena are obtained. Specific equations are derived for a viscoelastic Mooney-Rivlin model. Then the finite amplitude, damped, free vibration of a rigid body supported symmetrically by viscoelastic Mooney-Rivlin shear mountings is examined, and solutions are given for heavily damped and lightly damped motions. The effects of the primary static deformation on creep and recovery phenomena of the shear blocks, and its effects on the frequency, damping, and logarithmic decrement characteristic of the motion are described analytically and illustrated graphically. Effects of the ultimate equilibrium shear induced by the load also are described. Universal frequency and damping relations for viscoelastic Mooney-Rivlin and neo-Hookean models are noted. It is shown that the primary homogeneous deformation plays an important role in determination of all aspects of the mechanical response. General equations for the exact solution of the problem for free vibrations of a load on nonlinear, perfectly elastic shear mountings also are provided.

Deep crustal reflections, appearing at two-way times of 6–20 s, are characterised by a low signal-to-noise ratio and a low-frequency content (~ 5–30 Hz). Optimising the visibility of these reflections requires that: 1. (1) the source energy be concentrated in this band; 2. (2) the receiver be as long as practically possible; 3. (3) the shot spacing be as snail as possible. An airgun array simulation program was used to investigate the effect of operating a 10-gun array at different depths. It predicted that the source energy could be enhanced at low frequencies by running the gun array at depths of up to 25 m, which would improve the signal-to-noise ratio for deep reflectors by a factor of 2 relative to the same array at 7.5 m depth at the expense of some loss of temporal resolution. The receiver length was limited to 4.4 km by the number of cable sections available and the maximum tension allowable in the cable. It was configured as 88 channels of 50 m length. To reduce the shot spacing, minimise the tow noise and reduce tension in the cable, the ship speed was reduced to 4 knots. A cable depth of 20 m was chosen to reduce sea state noise and keep the receiver ghost notch frequency outside the frequency band of interest. A variety of operational problems was encountered. Fish bites holed 50% of the total cable inventory and cable sections were damaged when they sank below their maximum rated depth after being holed. Shot-generated noise was the limiting factor in deep water. Despite these problems, useful data were obtained over the Lord Howe Rise, Dampier Ridge, Gippsland Basin margin and the deep abyssal plain and the survey demonstrated the use of an airgun array tuned for maximum energy.

Equations for small deformations superimposed on a finite deformation of an arbitrary isotropic and compressible, non-linearly elastic solid constrained by inextensible fibers are reviewed. The instability of a thick slab of infinite extent reinforced by strong fibers oriented through its thickness normal to the loading axis is then examined by application of Euler's criterion for dead loading. Solutions are obtained which suggest that special results in the literature on the tension instability of an ideal reinforced Blatz-Ko foamed rubber slab are questionable. It is proved that if the non-linearly elastic matrix material of the ideal reinforced slab satisfies the empirical inequalities and the tension-extension principle, the only mode of instability consistent with plane strain conditions occurs for compression loading, never for tension loading. The class of generalized Blatz-Ko materials that respect these rules is described; the foamed rubber model is not in this class.