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NASA NTRS2008

Gender Differences in Bed Rest: Preliminary Analysis of Vascular Function

Orthostatic intolerance is a recognized consequence of spaceflight. Numerous studies have shown that women are more susceptible to orthostatic intolerance following spaceflight as well as bed rest, the most commonly used ground-based analog for spaceflight. One of the possible mechanisms proposed to account for this is a difference in vascular responsiveness between genders. We hypothesized that women and men would have differing vascular responses to 90 days of 6-degree head down tilt bed rest. Additionally, we hypothesized that vessels in the upper and lower body would respond differently, as has been shown in the animal literature. Thirteen subjects were placed in bedrest for 90 days (8 men, 5 women) at the Flight Analogs Unit, UTMB. Direct arterial and venous measurements were made with ultrasound to evaluate changes in vascular structure and function. Arterial function was assessed, in the arm and leg, during a reactive hyperemia protocol and during sublingual nitroglycerin administration to gauge the contributions of endothelial dependent and independent dilator function respectively. Venous function was assessed in dorsal hand and foot veins during the administration of pharmaceuticals to assess constrictor and dilator function. Both gender and day effects are seen in arterial dilator function to reactive hyperemia, but none are seen with nitroglycerin. There are also differences in the wall thickness in the arm vs the leg during bed rest, which return toward pre-bed rest levels by day 90. More subjects are required, especially females as there is not sufficient power to properly analyze venous function. Day 90 data are most underpowered.

Platts, Steven H.↗

NASA NTRS2017

Quantifying Pilot Contribution to Flight Safety During an In-Flight Airspeed Failure

Accident statistics cite the flight crew as a causal factor in over 60% of large transport fatal accidents. Yet a well-trained and well-qualified crew is acknowledged as the critical center point of aircraft systems safety and an integral component of the entire commercial aviation system. A human-in-the-loop test was conducted using a Level D certified Boeing 737-800 simulator to evaluate the pilot's contribution to safety-of-flight during routine air carrier flight operations and in response to system failures. To quantify the human's contribution, crew complement was used as an independent variable in a between-subjects design. This paper details the crew's actions and responses while dealing with an in-flight airspeed failure. Accident statistics often cite flight crew error (Baker, 2001) as the primary contributor in accidents and incidents in transport category aircraft. However, the Air Line Pilots Association (2011) suggests "a well-trained and well-qualified pilot is acknowledged as the critical center point of the aircraft systems safety and an integral safety component of the entire commercial aviation system." This is generally acknowledged but cannot be verified because little or no quantitative data exists on how or how many accidents/incidents are averted by crew actions. Anecdotal evidence suggest crews handle failures on a daily basis and Aviation Safety Action Program data generally supports this assertion, even if the data is not released to the public. However without hard evidence, the contribution and means by which pilots achieve safety of flight is difficult to define. Thus, ways to improve the human ability to contribute or overcome deficiencies are ill-defined.

Etherington, Timothy J.↗

NASA NTRS2019

Agile Approach to Assuring the Safety-Critical Embedded Software for NASA's Orion Spacecraft

Human-rated missions like NASA's Exploration Mission - 1 (EM-1) and the Orion Multi-Purpose Crew Vehicle are becoming exceedingly complex in terms of software's contribution to achieving mission objectives. The increasing complexity and inherent safety critical nature of the embedded flight software imposes a unique resource challenge to assurance providers responsible for affirming that the mission is going to fly safely. Another challenge NASA and other Government agencies are facing is that more and more software is being developed using an agile development methodology, which is divergent from the typical waterfall, iterative, and incremental development methodologies assurance providers generally observe in the development of safety-critical embedded software. Orion Independent Verification and Validation (IV&V) has addressed these challenges by providing focused assurance results of critical mission capabilities prioritized by a dynamic assessment of risk level. Prior to this approach, Orion IV&V evaluated areas of risk in much broader, and more static, terms. Due to the agile software development life cycle that Orion follows, IV&V findings were often reported months out of phase with the developer thereby imposing increased rework costs. As a result of evolving the approach to adding assurance on Orion, IV&V is able to incrementally deliver high-priority assurance conclusions and more impactful issues more in phase with the developer activities, thereby increasing the value of the findings to the project. The agile IV&V approach employed by the Orion IV&V team strives to achieve a cadence of delivery that matches the pace of development. This agile approach provides increased flexibility for the assurance provider to become more efficient in reporting assurance conclusions and issues. This paper and presentation will discuss the principles which drive the design of our approach, results to date, and stimulate thinking for groups looking to add assurance to software being developed using an agile methodology.

Justin Smith↗

DOE OSTI2020

SNF Interim Storage Canister Corrosion and Surface Environment Investigations (FY2020 Status Report)

This progress report describes work performed during FY20 at Sandia National Laboratories (SNL) to assess the localized corrosion performance of container/cask materials used in the interim storage of spent nuclear fuel (SNF). Of particular concern is stress corrosion cracking (SCC), by which a through-wall crack could potentially form in a canister outer wall over time intervals that are shorter than possible dry storage times. Work in FY20 further defined our understanding of the potential chemical and physical environment present on canister surfaces, evaluated the relationship between the environment and the resultant corrosion that occurs, and initiated crack growth rate testing under relevant environmental conditions. In FY20, work to define dry storage canister surface environments included several tasks. First, collection of dust deposition specimens from independent spent fuel storage installation (ISFSI) site locations helped to establish a more complete understanding of the potential chemical environment formed on the canister. Second, the predicted evolution of canister surface relative humidity RH) values was estimated using ISFSI site weather data and the horizontal canister thermal model used by the SNL probabilistic SCC model. These calculations determined that for typical ISFSI weather conditions, seasalt deliquescence to produce MgCl2-rich brines could occur in less than 20 years at the coolest locations on the canister surface, and, even after nearly 300 years, conditions for NaCl deliquescence (75% RH) are not reached. This work illustrates the importance of understanding the stability of MgCl2-rich brines on the heated canister surface, and the potential impact of brine composition on corrosion processes, including pitting and stress corrosion cracking. In an additional study, the description of the canister surface environment was refined in order to define more realistic corrosion testing environments including diurnal cycles, soluble salt chemistries, and inert mineral particles. The potential impacts of these phenomena on canister corrosion are being evaluated experimentally. Finally, work over the past few years to evaluate the stability of magnesium chloride brines continued in FY20. MgCl2 degassing experiments were carried out, confirming that MgCl2 brines slowly degas HCl on heated surfaces, converting to less deliquescent magnesium hydroxychloride phases and potentially leading to brine dryout.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

Evaluating Trade-offs in Potential Exascale Interconnect Technologies

This report details work to study trade-offs in topology and network bandwidth for potential interconnects in the exascale (2021-2022) timeframe. The work was done using multiple interconnect models across two parallel discrete event simulators. Results from each independent simulator are shown and discussed and the areas of agreement and disagreement are explored.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Results of a fishery-independent longline survey targeting coastal sharks in the eastern Bahamas between 1979 and 2013

Long-term trends in shark abundance offer important insights for fisheries management. Few fisheries-independent, extended time-series data exist for coastal shark species in the northwest Atlantic Ocean or Caribbean outside of the United States. A decades old dataset comprised of standardized longline surveys provided us with the opportunity to characterize diversity and evaluate changes in the relative abundance of sharks in the eastern Bahamas between 1979–1990 and 2011–2013. Caribbean reef sharks Carcharhinus perezi and tiger sharks Galeocerdo cuvier were the two most commonly captured species throughout the survey and were the only two species analyzed in detail. For both species, sex ratios favored females. Using Bayesian generalized linear models, we found that Caribbean reef shark catch-per-unit-effort (CPUE) exhibited a positive relationship with year and temperature, while size exhibited no relationship with year and a negative relationship with temperature. There was no relationship between tiger shark CPUE and year but there was a positive relationship between size and year. These results are presented in the context of Bahamian shark conservation efforts and the results of other surveys in the region.

Fisheries-independent survey, Caribbean reef shark↗

DOE OSTI2020

K-space algorithmic reconstruction (KAREN): a robust statistical methodology to separate Bragg and diffuse scattering

Diffuse scattering occurring in the Bragg diffraction pattern of a long-range-ordered structure represents local deviation from the governing regular lattice. However, interpreting the real-space structure from the diffraction pattern presents a significant challenge because of the dramatic difference in intensity between the Bragg and diffuse components of the total scattering function. In contrast to the sharp Bragg diffraction, the diffuse signal has generally been considered to be a weak expansive or continuous background signal. In this paper, using 1D and 2D models, it is demonstrated that diffuse scattering in fact consists of a complex array of high-frequency features that must not be averaged into a low-frequency background signal. To evaluate the actual diffuse scattering effectively, an algorithm has been developed that uses robust statistics and traditional signal processing techniques to identify Bragg peaks as signal outliers which can be removed from the overall scattering data and then replaced by statistically valid fill values. This method, described as a 'K-space algorithmic reconstruction' (KAREN), can identify Bragg reflections independent of prior knowledge of a system's unit cell. KAREN does not alter any data other than that in the immediate vicinity of the Bragg reflections, and reconstructs the diffuse component surrounding the Bragg peaks without introducing discontinuities which induce Fourier ripples or artifacts from underfilling `punched' voids. The KAREN algorithm for reconstructing diffuse scattering provides demonstrably better resolution than can be obtained from previously described punch-and-fill methods. The superior structural resolution obtained using the KAREN method is demonstrated by evaluating the complex ordered diffuse scattering observed from the neutron diffraction of a single plastic crystal of CBr 4 using pair distribution function analysis.

36 MATERIALS SCIENCE↗

NASA NTRSDate not supplied

Ten Year Ozone Profile Record From Suomi NPP OMPS Limb Profiler

In this study, we evaluate a decadal ozone profile record derived from Suomi NPP Ozone Mapping and Profiler Suite (OMPS) Limb Profiler (LP). The data from OMPS LP were re-processed with the new retrieval algorithm from 2012 to present. The new reprocessing includes adjustments in both Level 1 and Level 2 algorithms. The sensor’s altitude registration, updates in radiometric calibrations, under-sampling and stray light corrections were addressed in Level 1 processing. The new retrieval algorithm (version 2.7) combines measurements from UV and VIS parts of the spectra to retrieve a single vertical ozone profile between 12.5 km (or cloud tops) and 57.5 km, unlike to previous version 2.5 where ozone profiles were retrieved independently from UV and VIS. To improve ozone retrievals in the Upper Troposphere Lower Stratosphere (UTLS) region, we implemented a new aerosol correction that assumes a gamma-function particle size distribution. In addition, ozone and nitrogen dioxide cross sections and climatologies were updated. We discuss sensitivity of the ozone retrievals to implemented changes in Level 1 and Level 2 algorithms. We focus our analysis on evaluation of the stability of the 10-year record from OMPS LP. We show results from the internal methods for characterizing the stability of the LP altitude registration and compare the LP reflectivity and ozone with the similar quantities measured by OMPS nadir sensors. Finally, we will show results from comparisons with independent satellite (MLS and SAGE III) and ozone sonde measurements.

Ozone↗

DOE OSTI2022

Determination of the 161 Tb half-life

There is significant interest in the use of terbium radioisotopes for applications in cancer therapy and diagnosis. Of these, 161 Tb, a medium energy beta- and prolific auger emitter, is being investigated as a potential alternative to 177 Lu. The higher proportion of conversion electron and Auger electron emissions, and variety of low-energy gammas make 161 Tb an attractive targeted theranostic. As a product of nuclear fission, 161 Tb is also of importance to nuclear forensics. The current evaluated half-life of 6.89(2) d has a standard uncertainty that contributes significantly to the standard uncertainty of decay calculated activity determination. Furthermore, the accuracy of this evaluated half-life has been called into question by measurements reported recently at the Institute of Radiation Physics (IRP), Switzerland. In this work, the half-life of 161 Tb was measured at three independent laboratories located in the United Kingdom and United States of America for a total of five determinations using three independent measurement techniques. In conclusion, the half-life determined for 161 Tb of 6.9637(29) d confirms the observed 1 % relative increase observed by IRP, though the reported half-lives in this work and at IRP are significantly different (ζ-score = 3.1).

half-life↗

DOE OSTI2025

Challenges in integrating dissolved organic matter chemodiversity into kinetic models of soil respiration

The chemodiversity of dissolved organic matter (DOM) in soil has been proposed to influence the microbial metabolism and fate of belowground organic carbon (C). However, integrating DOM chemistry into soil C cycle models to improve predictions of C stocks and fluxes—beyond simply considering DOM pool size—remains a challenge. While recent research suggests that incorporating DOM chemodiversity into models can improve predictions of microbial respiration, there is still a lack of mechanistic understanding describing how DOM chemodiversity affects microbial metabolism and soil respiration. Here, we evaluated whether DOM chemodiversity was a determinant of soil respiration using paired measurements of high-resolution DOM chemistry, obtained from Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS), and potential soil respiration rates from across the United States (U.S.), all data provided by the Molecular Observation Network. Our objectives were to (1) assess statistical relationships between DOM chemodiversity and microbial respiration, and (2) evaluate the ability of kinetic models to leverage DOM chemistry to explain empirical relationships found in statistical models. Statistical regressions revealed that DOM chemodiversity (alpha diversity) was nonlinearly related to potential soil respiration rates, both independently and through its interactions with DOM and total C concentrations. In soils with relatively high DOM but low total C concentrations, potential soil respiration rates were negatively correlated with DOM alpha diversity, whereas in soils with relatively low DOM and high total C concentrations showed the opposite trend. However, when metabolic transition theory kinetic models were modified to include chemodiversity, their performance was comparable to traditional Monod kinetics approaches, which simulate respiration rates as a function of DOM concentration. The inability to account for nonlinearities in DOM chemodiversity–respiration relationships highlight an opportunity to advance substrate uptake kinetics by establishing causal links between DOM chemodiversity, microbial metabolism trade-offs, and potential interactions under varied environmental conditions.

Bioenergetic model↗

DOE OSTI2025

Evaluating the Origins of Aerobic Oxidation Catalysis with TAM-3, a MOF with Accessible Co(II) Sites and Large Pores

Metal-organic frameworks (MOFs) are attractive platforms that merge concepts of homogeneous and heterogeneous catalysis. Catalyst design and optimization are enabled by an array of synthetic methods that offer independent control over the local chemical structure of lattice-embedded metal ions (i.e., ligand identity and geometry) and the long-range materials properties (i.e., porosity). Establishing the origin of catalytic activity in MOF-promoted reactions remains a significant challenge: The relative rates of catalyst turnover and substrate diffusion dictate the extent to which interstitial sites are accessible and operational in catalysis. To minimize the contributions of surface sites in catalysis, materials with large pore dimensions are often sought, however, the impact of pore expansion on the origins of catalytic activity is similarly challenging to establish. Here, we describe TAM-3, a Co(II) based MOF with accessible metal sites supported by a facially coordinating tris-tetrazole ligand set. TAM-3 features large channel-like pores (17 × 23 Å) and promotes aerobic C−H oxidation and olefin epoxidation. Using a set of simple kinetics experiments, based on the analysis of kinetic isotope effects and olefin oxidation diastereoselectivities, we demonstrate that despite the large pores, interstitial metal ions do not significantly contribute to the observed substrate oxidation. This study highlights the importance of conducting kinetic experiments to assess the origin of apparent catalytic activity with MOFs and the challenge of harnessing reactive oxidants with microporous catalyst materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Computing equilibrium free energies through a nonequilibrium quench

Many methods to accelerate sampling of molecular configurations are based on the idea that temperature can be used to accelerate rare transitions. These methods typically compute equilibrium properties at a target temperature using reweighting or through Monte Carlo exchanges between replicas at higher temperatures. A recent paper [G. M. Rotskoff and E. Vanden-Eijnden, Phys. Rev. Lett. 122, 150602 (2019)] demonstrated that accurate equilibrium densities of states can also be computed through a nonequilibrium “quench” process, where sampling is performed at a higher temperature to encourage rapid mixing and then quenched to lower energy states with dissipative dynamics. Here, we provide an implementation of the quench dynamics in LAMMPS and evaluate a new formulation of nonequilibrium estimators for the computation of partition functions or free energy surfaces (FESs) of molecular systems. We show that the method is exact for a minimal model of N-independent harmonic springs and use these analytical results to develop heuristics for the amount of quenching required to obtain accurate sampling. We then test the quench approach on alanine dipeptide, where we show that it gives an FES that is accurate near the most stable configurations using the quench approach but disagrees with a reference umbrella sampling calculation in high FE regions. We then show that combining quenching with umbrella sampling allows the efficient calculation of the free energy in all regions. Moreover, by using this combined scheme, we obtain the FES across a range of temperatures at no additional cost, making it much more efficient than standard umbrella sampling if this information is required. Finally, we discuss how this approach can be extended to solute tempering and demonstrate that it is highly accurate for the case of solvated alanine dipeptide without any additional modifications.

Chemistry↗

DOE OSTI2023

The contribution of magnetized galactic outflows to extragalactic Faraday rotation

ABSTRACT Galactic outflows driven by star formation and active galactic nuclei blow bubbles into their local environments, causing galactic magnetic fields to be carried into intergalactic space. We explore the redshift-dependent effect of these magnetized bubbles on the Faraday rotation measure (RM) of extragalactic radio sources. Using the IllustrisTNG cosmological simulations, we separate the contribution from magnetic bubbles from that of the volume-filling magnetic component expected to be due to the seed field originating in the early universe. We use this separation to extract the redshift dependence of each component and to compare IllustrisTNG model predictions with observation measurements of the NRAO VLA sky survey (NVSS). We find that magnetized bubbles provide a sizeable contribution to the extragalactic RM, with redshift-independent 〈|RM|〉 ≃ 13 rad/m2 for sources at redshifts z ≥ 2. This is close to the mean residual RM of 16 rad/m2 found from NVSS data in this redshift range. Using the IllustrisTNG simulations, we also evaluate a simple model for the contribution to residual RM from individual host galaxies and show that this contribution is negligible at high-redshift. While the contribution from magnetic bubbles in the IllustrisTNG model is currently compatible with observational measurements of residual RM, the next-generation RM sky surveys, which will be free from the wrapping uncertainty, have larger statistics and better sensitivity should be able to observe predicted flat contribution from magnetic bubbles at large redshifts. This should allow to experimentally probe magnetic bubbles and check models of galaxy feedback in cosmological simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Baselining the Indirect Effect by Improving Quantification of Sea Spray and Marine Sources at Ascension Island (Final Report)

Oceans cover two-thirds of the Earth and understanding the interactions of aerosols with clouds in these large marine regions requires quantifying the man-made contributions to the budget of cloud-drop forming particles (known as cloud condensation nuclei, or CCN) relative to the non-manmade “baseline” conditions and understanding the meteorology of boundary layer clouds. Modeling studies have shown substantial uncertainties and sensitivities to natural marine CCN sources, meaning that to reduce uncertainties in indirect effects we must be able to better quantify the CCN budget in ocean regions. While models provide important constraints on these uncertainties, actually reducing uncertainties requires substantial observations in open-ocean and coastal regions in order to establish the baseline on which manmade emissions are added. The tropical South Atlantic Ocean is one of the least-sampled regions of the planet, making the comprehensive measurements of the Department of Energy Atmospheric Radiation Measurement Layered Atlantic Smoke Interactions with Clouds (LASIC) campaign provides the longest record of aerosol size distribution measurements from a differential mobility analyzer in a cloud-influenced marine location in the ARM database, with 17 months of ground-based aerosol size distribution measurements. This project addressed the research topic of Aerosol-Cloud Interactions (ACI) by supporting three publications from the LASIC measurements: 1. The ARM measurements were combined with a new value-added technique that was pioneered by the Russell group for quantifying sea salt. This quantification of sea salt uses supermicron scattering measurements for retrieving reasonable sea spray mass concentrations, providing the best-available, observationally-constrained estimate of the sea spray mode properties when supermicron size distribution measurements are not available. 2. The fitted modes of the distribution were used to investigate the signatures of cloud processing for very clean to very smoky aerosol conditions, revealing not only differences in the particles that activate in clouds but also in the mechanisms that control that droplet formation process. In clean air, the size required to form a cloud droplet is influenced by the number of particles, as well as how quickly particles take up water during growth in cloud. 3. Building on this aerosol characterization, cloud and meteorological conditions were used to evaluate aerosol-related changes in cloud albedo and optical depth. We introduced a new method of decomposing the impact of aerosols on clouds known as the Twomey effect by incorporating retrieved supersaturation from two independent sets of observations to constrain the feedback of aerosol particles on cloud properties. The method quantifies the reduction of the Twomey effect at high aerosol concentrations, which has never been explained quantitatively by observations. In addition, the results provide the first direct validation for the conditions observed in the tropical South Atlantic of a parcel-based approach that is embedded in many climate models. Together these findings illustrate how ARM extended field campaigns in stratocumulus-covered regions can be used to constrain ACI processes with direct observations, providing specific radiative effects without models. By making such process-specific constraints available to improve ACI in global climate models, ARM observations play a key role in supporting model development.

58 GEOSCIENCES↗

DOE OSTI2023

Validating a Tethered Balloon System and Optical Technologies for Marine Wildlife Detection and Tracking

The interactions between marine wildlife and marine energy devices are not well understood, leading to regulatory delays for device deployments and testing. Technologies that enable marine wildlife observations can help to fill data gaps and reduce uncertainties about animal–device interactions. A validation test conducted in Galveston Bay near La Porte, Texas, in December 2022 used a technology package consisting of a tethered balloon system and three independent sensor systems, including three-band visible, eight-band multispectral, and single-band thermal to detect three marine-mammal-shaped surrogates. The field campaign aimed to provide an initial step to evaluating the use of the TBS and the effectiveness of the sensor suite for marine wildlife observations and detection. From 2 December to 7 December 2022, 6 flights were conducted under varying altitudes and environmental conditions resulting in the collection of 5454 images. A subset of the images was classified and analyzed with two collection criteria including Beaufort wind force scale and TBS altitude to assess a range of observations of a surrogate from near-shore to offshore based on pixel count. The results of this validation test demonstrate the potential for using TBSs and imaging sensors for marine wildlife observations and offer valuable information for further development and application of this technology for marine energy and other blue economy sectors.

47 OTHER INSTRUMENTATION↗

NASA NTRS1979

Application of the relative energy release criteria to enclosure fire testing

The five relative energy release criteria (RERC) which are a first step towards formulating a unified concept that can be applied to the development of fires in enclosures, place upper bounds on the rate and amount of energy released during a fire. They are independent, calculated readily, and may be applied generally to any enclosure regardless of size. They are useful in pretest planning and for interpreting experimental data. Data from several specific fire test programs were examined to evaluate the potential use of RERC to provide test planning guidelines. The RERC were compared with experimental data obtained in full-scale enclosures. These results confirm that in general the RERC do identify the proper limiting constraints on enclosure fire development and determine the bounds of the fire development envelope. Plotting actual fire data against the RERC reveals new valid insights into fire behavior and reveals the controlling constraints in fire development. The RERC were calculated and plotted for several descrpitions of full-scale fires in various aircraft compartments.

Roschke, E. J.↗

NASA NTRS1980

On the detection of a stochastic background of gravitational radiation by the Doppler tracking of spacecraft

Consideration is given to the possibility of detection of an isotropic background gravitational radiation of a stochastic nature by the method of Doppler tracking of spacecraft. Attention is given in the geometrical optics limit, to the general formula for the frequency shift of an electromagnetic signal in the gravitational radiation field, and it is shown to be gauge independent. The propagation of a free electromagnetic wave in a gravitational radiation field is examined with the conclusion that no resonance phenomena can be expected. Finally, the 'Doppler noise' due to a stochastic background is evaluated, and it is shown to depend on the total energy density of the background and a parameter that is a characteristic of the radiation spectrum and the detection system used.

Mashhoon, B.↗

NASA NTRS1983

A proposed approach to the application of nonlinear irreversible thermodynamics to fracture in composite materials

The fracture criteria upon which most fracture mechanics is based involves an energy balance that is not appropriate for the fracture mechanics of viscoelastic materials such as polymer matrix composites. A more appropriate criterion based upon nonequilibrium thermodynamics and involving a power balance rather than an energy balance is proposed. This crierion is based upon a reformulation of the second law of thermodynamics which focuses attention on the total Legendre transform of energy expressed as a functional over time and space. This excess energy functional can be shown to be equivalent to the Rice J integral if the only irreversible process is the propogation of a single crack completely through the thickness of the specimen and if the crack propogation is assured to be independent of time. For the more general case of more than one crack in a viscoelastic medium integration over both time and space is required. Two experimentally measurable parameters are proposed which should permit the evaluation of this more general fracture criterion.

Lindenmeyer, P. H.↗