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Rotation of EOFs by the Independent Component Analysis: Towards A Solution of the Mixing Problem in the Decomposition of Geophysical Time Series

The Independent Component Analysis is a recently developed technique for component extraction. This new method requires the statistical independence of the extracted components, a stronger constraint that uses higher-order statistics, instead of the classical decorrelation, a weaker constraint that uses only second-order statistics. This technique has been used recently for the analysis of geophysical time series with the goal of investigating the causes of variability in observed data (i.e. exploratory approach). We demonstrate with a data simulation experiment that, if initialized with a Principal Component Analysis, the Independent Component Analysis performs a rotation of the classical PCA (or EOF) solution. This rotation uses no localization criterion like other Rotation Techniques (RT), only the global generalization of decorrelation by statistical independence is used. This rotation of the PCA solution seems to be able to solve the tendency of PCA to mix several physical phenomena, even when the signal is just their linear sum.

Aires, Filipe↗

Rotation of EOFs by the Independent Component Analysis: Towards a Solution of the Mixing Problem in the Decomposition of Geophysical Time Series

The Independent Component Analysis is a recently developed technique for component extraction. This new method requires the statistical independence of the extracted components, a stronger constraint that uses higher-order statistics, instead of the classical decorrelation, a weaker constraint that uses only second-order statistics. This technique has been used recently for the analysis of geophysical time series with the goal of investigating the causes of variability in observed data (i.e. exploratory approach). We demonstrate with a data simulation experiment that, if initialized with a Principal Component Analysis, the Independent Component Analysis performs a rotation of the classical PCA (or EOF) solution. This rotation uses no localization criterion like other Rotation Techniques (RT), only the global generalization of decorrelation by statistical independence is used. This rotation of the PCA solution seems to be able to solve the tendency of PCA to mix several physical phenomena, even when the signal is just their linear sum.

Aires, Filipe↗

Investigation of Fundamental Modeling and Thermal Performance Issues for a Metallic Thermal Protection System Design

A study was performed to develop an understanding of the key factors that govern the performance of metallic thermal protection systems for reusable launch vehicles. A current advanced metallic thermal protection system (TPS) concept was systematically analyzed to discover the most important factors governing the thermal performance of metallic TPS. A large number of relevant factors that influence the thermal analysis and thermal performance of metallic TPS were identified and quantified. Detailed finite element models were developed for predicting the thermal performance of design variations of the advanced metallic TPS concept mounted on a simple, unstiffened structure. The computational models were also used, in an automated iterative procedure, for sizing the metallic TPS to maintain the structure below a specified temperature limit. A statistical sensitivity analysis method, based on orthogonal matrix techniques used in robust design, was used to quantify and rank the relative importance of the various modeling and design factors considered in this study. Results of the study indicate that radiation, even in small gaps between panels, can reduce significantly the thermal performance of metallic TPS, so that gaps should be eliminated by design if possible. Thermal performance was also shown to be sensitive to several analytical assumptions that should be chosen carefully. One of the factors that was found to have the greatest effect on thermal performance is the heat capacity of the underlying structure. Therefore the structure and TPS should be designed concurrently.

Blosser, Max L.↗

Entry Trajectory and Atmosphere Reconstruction Methodologies for the Mars Exploration Rover Mission

The Mars Exploration Rover (MER) mission will land two landers on the surface of Mars, arriving in January 2004. Both landers will deliver the rovers to the surface by decelerating with the aid of an aeroshell, a supersonic parachute, retro-rockets, and air bags for safely landing on the surface. The reconstruction of the MER descent trajectory and atmosphere profile will be performed for all the phases from hypersonic flight through landing. A description of multiple methodologies for the flight reconstruction is presented from simple parameter identification methods through a statistical Kalman filter approach.

Desai, Prasun N.↗

Long-Range Solar Activity Predictions: A Reprieve from Cycle #24's Activity

We discuss the field of long-range solar activity predictions and provide an outlook into future solar activity. Orbital predictions for satellites in Low Earth Orbit (LEO) depend strongly on exospheric densities. Solar activity forecasting is important in this regard, as the solar ultra-violet (UV) and extreme ultraviolet (EUV) radiations inflate the upper atmospheric layers of the Earth, forming the exosphere in which satellites orbit. Rather than concentrate on statistical, or numerical methods, we utilize a class of techniques (precursor methods) which is founded in physical theory. The geomagnetic precursor method was originally developed by the Russian geophysicist, Ohl, using geomagnetic observations to predict future solar activity. It was later extended to solar observations, and placed within the context of physical theory, namely the workings of the Sun s Babcock dynamo. We later expanded the prediction methods with a SOlar Dynamo Amplitude (SODA) index. The SODA index is a measure of the buried solar magnetic flux, using toroidal and poloidal field components. It allows one to predict future solar activity during any phase of the solar cycle, whereas previously, one was restricted to making predictions only at solar minimum. We are encouraged that solar cycle #23's behavior fell closely along our predicted curve, peaking near 192, comparable to the Schatten, Myers and Sofia (1996) forecast of 182+/-30. Cycle #23 extends from 1996 through approximately 2006 or 2007, with cycle #24 starting thereafter. We discuss the current forecast of solar cycle #24, (2006-2016), with a predicted smoothed F10.7 radio flux of 142+/-28 (1-sigma errors). This, we believe, represents a reprieve, in terms of reduced fuel costs, etc., for new satellites to be launched or old satellites (requiring reboosting) which have been placed in LEO. By monitoring the Sun s most deeply rooted magnetic fields; long-range solar activity can be predicted. Although a degree of uncertainty in the long-range predictions remains, requiring future monitoring, we do not expect the next cycle's + 2-sigma value will rise significantly above solar cycle #23's activity level.

Richon, K.↗

Constraints on the Energy Content of the Universe from a Combination of Galaxy Cluster Observables

We demonstrate that constraints on cosmological parameters from the distribution of clusters as a function of redshift (dN/dz) are complementary to accurate angular diameter distance (D(sub A)) measurements to clusters, and their combination significantly tightens constraints on the energy density content of the Universe. The number counts can be obtained from X-ray and/or SZ (Sunyaev-Ze'dovich effect) surveys, and the angular diameter distances can be determined from deep observations of the intra-cluster gas using their thermal bremsstrahlung X-ray emission and the SZ effect. We combine constraints from simulated cluster number counts expected from a 12 deg(sup 2) SZ cluster survey and constraints from simulated angular diameter distance measurements based on the X-ray/SZ method assuming a statistical accuracy of 10% in the angular diameter distance determination of 100 clusters with redshifts less than 1.5. We find that Omega(sub m), can be determined within about 25%, Omega(sub lambda) within 20% and w within 16%. We show that combined dN/dz+(sub lambda) constraints can be used to constrain the different energy densities in the Universe even in the presence of a few percent redshift dependent systematic error in D(sub lambda). We also address the question of how best to select clusters of galaxies for accurate diameter distance determinations. We show that the joint dN/dz+ D(lambda) constraints on cosmological parameters for a fixed target accuracy in the energy density parameters are optimized by selecting clusters with redshift upper cut-offs in the range 0.55 approx. less than 1. Subject headings: cosmological parameters - cosmology: theory - galaxies:clusters: general

Molnar, Sandor M.↗

Preliminary Assessment of the Interior Noise Environment in the Large Civil Tiltrotor (LCTR2)

The second-generation Large Civil Tiltrotor (LCTR2) serves as a representative vehicle under the NASA Fundamental Aeronautics Program (FAP) Subsonic Rotary Wing (SRW) project with a design goal to transport 90 passengers over a distance of 1800 km at a speed of 550 km/hr. The tiltrotor combines the vertical lift capability of a helicopter with the speed, altitude, and range of a turboprop airplane. The blade-passage frequency of the four-bladed rotor is as low as 6.9 Hz during cruise conditions. The resulting low-frequency acoustic excitation and its harmonics, combined with the anticipated use of lightweight composite and sandwich materials for the fuselage sidewall, may pose a challenge to achieving acceptable interior noise levels. The objective of the present study is to perform a preliminary assessment of the expected interior noise environment in the LCTR2 cabin. The approach includes a combination of semi-empirical, analytical, and statistical energy analysis methods. Because the LCTR2 is a notional vehicle, the prediction approach was also applied to the XV-15 tiltrotor and Bombardier Q400 turobprop aircraft to compare predictions with publicly available experimental data. Guidance for the expected interior noise levels in the LCTR2 was obtained by considering both the predicted exterior noise levels and the transmission loss of a basic fuselage sidewall consisting of a skin, porous layer and a trim panel. Structural and acoustic resonances are expected to coincide with low order harmonics of the blade passage frequency. The estimated sound pressure levels in the LCTR2 may not be acceptable when evaluated against known characteristics of human response to low frequency sound.

Grosveld, Ferdinand W.↗

Updated System-Availability and Resource-Allocation Program

A second version of the Availability, Cost and Resource Allocation (ACARA) computer program has become available. The first version was reported in an earlier tech brief. To recapitulate: ACARA analyzes the availability, mean-time-between-failures of components, life-cycle costs, and scheduling of resources of a complex system of equipment. ACARA uses a statistical Monte Carlo method to simulate the failure and repair of components while complying with user-specified constraints on spare parts and resources. ACARA evaluates the performance of the system on the basis of a mathematical model developed from a block-diagram representation. The previous version utilized the MS-DOS operating system and could not be run by use of the most recent versions of the Windows operating system. The current version incorporates the algorithms of the previous version but is compatible with Windows and utilizes menus and a file-management approach typical of Windows-based software.

Viterna, Larry↗

Designing an Exploration Atmosphere Prebreathe Protocol

Extravehicular activities (EVAs) at remote locations must maximize limited resources such as oxygen (O2) and also minimize the risk of decompression sickness (DCS). A proposed remote denitrogenation (prebreathe) protocol requires astronauts to live in a mildly hypoxic atmosphere at 8.2 psia while periodically performing EVAs at 4.3 psia. Empirical data are required to confirm that the protocol meets the current accept requirements: less than or equal to 15% incidence of Type I DCS, less than or equal to 20% incidence of Grade IV venous gas emboli (VGE), both at 95% statistical confidence, with no Type II DCS symptom during the validation trial. METHODS: A repeated measures statistical design is proposed in which groups of 6 subjects with physical characteristics similar to active-duty astronauts would first become equilibrated to an 8.2 psia atmosphere in a hypobaric chamber containing 34% O2 and 66% N2, over 48 h, and then perform 4 simulated EVAs at 4.3 psia over the next 9 days. In the equilibration phase, subjects undergo a 3-h 100% O2 mask prebreathe prior to and during a 5-min ascent to 8.2 psia to prevent significant tissue N2 supersaturation on reaching 8.2 psia. Masks would be removed once 34% O2 is established at 8.2 psia, and subjects would then equilibrate to this atmosphere for 48 h. The hypoxia is equivalent to breathing air at 1,220 meters (4,000 ft) altitude, just as was experienced in the shuttle 10.2 psia - 26.5% O2 staged denitrogenation protocol and the current ISS campout denitrogenation protocol. For simulated EVAs, each subject dons a mask and breathes 85% O2 and 15% N2 during a 3-min depressurization to 6.0 psia, holds for 15 min, and then completes a 3-min depressurization to 4.3 psia. The simulated EVA period starts when 6.0 psia is reached and continues for a total of 240 min (222 min at 4.3 psia). During this time, subjects will follow a prescribed repetitive activity against loads in the upper and lower body with mean metabolic rate approaching 1500 BTU/hr [378 kcal/hr (O2 consumption about 1.3 l(sub STPD)/min)] in ambulatory subjects. Noninvasive Doppler ultrasound bubble monitoring for VGE in the pulmonary artery will be performed on subjects by 2 Doppler Technicians at about 15 min intervals while at 4.3 psia. At the end of this period, a 15-min repressurization returns all subjects back to 8.2 psia and the cycle is repeated 3 additional times with a day of rest between simulated EVAs. RESULTS: With an assumed 1.5% probability of DCS [P(DCS)] and accounting for within-subject correlation, running the proposed study with 20 subjects has a 95% probability of meeting the accept criterion for DCS. But if the true probability of DCS is 3.0%, then 30 subjects would be needed to achieve about the same probability to meet our accept criterion. These results assume a standard deviation of 1.4 for the between-subjects random component of P(DCS) on a logit scale, which was estimated from a previous study.

Conkin, Johnny↗

Sea Ice Outlook for September 2015 June Report - NASA Global Modeling and Assimilation Office

The recent decline in perennial sea ice cover in Arctic Ocean is a topic of enormous scientific interest and has relevance to a broad variety of scientific disciplines and human endeavors including biological and physical oceanography, atmospheric circulation, high latitude ecology, the sustainability of indigenous communities, commerce, and resource exploration. A credible seasonal prediction of sea ice extent would be of substantial use to many of the stakeholders in these fields and may also reveal details on the physical processes that result in the current trends in the ice cover. Forecasts are challenging due in part to limitations in the polar observing network, the large variability in the climate system, and an incomplete knowledge of the significant processes. Nevertheless it is a useful to understand the current capabilities of high latitude seasonal forecasting and identify areas where such forecasts may be improved. Since 2008 the Arctic Research Consortium of the United States (ARCUS) has conducted a seasonal forecasting contest in which the average Arctic sea ice extent for the month of September (the month of the annual extent minimum) is predicted from available forecasts in early June, July, and August. The competition is known as the Sea Ice Outlook (SIO) but recently came under the auspices of the Sea Ice Prediction Network (SIPN), and multi-agency funded project to evaluate the SIO. The forecasts are submitted based on modeling, statistical, and heuristic methods. Forecasts of Arctic sea ice extent from the GMAO are derived from seasonal prediction system of the NASA Goddard Earth Observing System model, version 5 (GEOS 5) coupled atmosphere and ocean general circulation model (AOGCM). The projections are made in order to understand the relative skill of the forecasting system and to determine the effects of future improvements to the system. This years prediction is for a September average Arctic ice extent of 5.030.41 million km2.

SIPN↗

Comparing Theoretically Scaled Biomechanical Models

BACKGROUND An investigation into incorporating space suit aspects required a 50th-percentile male model which was not part of the existing dataset of models. Previously, theoretical models for 5th-percentile female and 95th-percentile male were created utilizing a scaled test subject as close as possible to the target height and weight. Scaling factors were created by taking the height ratio and applying it uniformly to the model body segments, then fine tuning to ensure the theoretical model’s height is as expected. This study was initiated to examine the existing method of isometrically scaling in OpenSim [1,2] and to create alternative methods which do not rely on an existing subject being close in height and weight to the theoretical model of interest. Generating a theoretical biomechanical model provides additional abilities without the reliance on available OpenSim models or real subjects. Gained abilities include creating different percentile models and attaining representative anthropometry for any target height/weight, such as targeting specific crew populations or gaps within the current dataset. METHODS AND RESULTS This study includes 3 methods for generating the theoretical model; utilizing the modified unscaled OpenSim Full Body Rajagopal Model (FBRM) [3,4], a dataset of scaled OpenSim models, and existing scaling factors from Dumas et al. [5]. All methods use the Anthropometric Survey of US Army Personnel (ANSUR II) [6] as an input of necessary anthropometric measurements. The following measurements are retrieved from the ANSUR II collection: mass, stature, cervicale height, acromial height, axilla height, waist height, trochanterion height, lateral femoral epicondyle height, lateral malleolus height, acromion-radiale length, radiale-stylion length, palm length, ball of foot length, bicristal breadth, bimalleolar breadth. Some of the measurements are direct segment lengths and others are utilized to derive segment lengths. Height, weight, and age ranges are the required inputs to parse the collection for a mean value of the measurements. A simple iterative process may be necessary for the output of mean mass and stature consistent with the theoretical model of interest. In some cases, one may specify exact values instead of a range but that is dependent upon whether those exact values pertain to a single subject from the ANSUR II collection. Equations from Dumas et al. were used to calculate scaling factors for the two methods that utilize OpenSim scaled and unscaled models. In the third method, Dumas’ scaling factors were used directly instead of generating our own. After scaling factors are achieved, they are applied along with the mass and segment lengths retrieved from ANSUR II in order to calculate the segment mass, Center of Mass (CoM), mass Moment of Inertia (MoI), and the joint location in the parent frame. The theoretical models from the different methods were compared to the previous existing method of isometrically scaling in OpenSim, as well as the standards found in NASA STD-3000 [7] and the NASA Human Integration Design Handbook [8]. The whole-body center of mass is the main comparison performed between the models and the standards. The body segment mass properties were also compared when possible. In some cases, the standards do not provide complete data, or the center of mass location is not provided with respect to the appropriate joint coordinate system. For a 50th-percentile male subject, results from isometric scaling in OpenSim and the method utilizing the unscaled FBRM were compared to the standards in NASA STD-3000. According to the standard, the whole-body vertical CoM location was taken from the head vertex to the CoM. The standards provide 80.2 cm for the CoM vertical component whereas isometric scaling in OpenSim and utilizing the unscaled FBRM provide 82.2 and 82.3 cm, respectively. Through definition, the whole-body CoM in the medial/lateral direction agreed across the models. Investigation is on-going to clearly identify the reference point pertaining to dorsal/ventral whole-body CoM position in standards and relate that to the theoretical models. REFERENCES [1] Delp, S.L., et al., “OpenSim: Open-source Software to Create and Analyze Dynamic Simulations of Movement”, IEEE Transactions on Biomedical Engineering, (2007). [2] Seth, A., Hicks J.L., Uchida, T.K., Habib, A., Dembia, C.L., Dunne, J.J., Ong, C.F., DeMers, M.S., Rajagopal, A., Millard, M., Hamner, S.R., Arnold, E.M., Yong, J.R., Lakshmikanth, S.K., Sherman,n M.A., Delp, S.L. OpenSim: Simulating musculoskeletal dynamics and neuromuscular control to study human and animal movement. Plos Computational Biology, 14(7). (2018) [3] R. K. Huffman, W. K. Thompson, C. A. Gallo, L. J. Quiocho, “Improvement of Scaling and Inverse Kinematic Results with Additional Upper Body Joints Added to Opensim Rajagopal Model”, NASA Human Research Program Investigator’s Workshop, (2019). [4] Huffman R.K., Thompson W., Gallo C., “Modified OpenSim Rajagopal Full Body Model”, New Technology Report, MSC-26872-1. (August 2020). [5] Dumas R., Cheze L. and Verriest J., 2007. “Adjustments to McConville et al. and Young et al. body segment inertial parameters”. Journal of Biomechanics 40, pp. 543-553 [6] Gordon C.C., 2012 “Anthropometric Survey of U.S. Army Personnel: Methods and Summary Statistics”, US Army Natick Soldier RD&E Center. [7] NASA STD-3000/REV-B, 1995. “The Man-System Integration Standards” [8] NASA/SP-2010-3407/REV-1, 2014. “The Human Integration Design Handbook (HIDH)”

F N Matari↗

Direct Observation of Ultralow Vertical Emittance using a Vertical Undulator

In recent work, the first quantitative measurements of electron beam vertical emittance using a vertical undulator were presented, with particular emphasis given to ultralow vertical emittances [K. P. Wootton, et al., Phys. Rev. ST Accel. Beams, 17, 112802 (2014)]. Using this apparatus, a geometric vertical emittance of 0.9 ± 0.3 pm rad has been observed. A critical analysis is given of measurement approaches that were attempted, with particular emphasis on systematic and statistical uncertainties. The method used is explained, compared to other techniques and the applicability of these results to other scenarios discussed.

43 PARTICLE ACCELERATORS↗

WEC Design Response Toolbox v. 1.0

The WEC Design Response Toolbox (WDRT) is a numerical toolbox for design-response analysis of wave energy converters (WECs). The WDRT was developed during a series of efforts to better understand WEC survival design. The WDRT has been designed as a tool for researchers and developers, enabling the straightforward application of statistical and engineering methods. The toolbox includes methods for short-term extreme response, environmental characterization, long-term extreme response and risk analysis, fatigue, and design wave composition.

Coe, Ryan↗

Multi-scale theory-assisted nano-engineering of plasmonic-organic hybrid electro-optic device performance

Multi-scale (correlated quantum and statistical mechanics) modeling methods have been advanced and employed to guide the improvement of organic electro-optic (OEO) materials, including by analyzing electric field poling induced electro-optic activity in nanoscopic plasmonic-organic hybrid (POH) waveguide devices. The analysis of in-device electro-optic activity emphasizes the importance of considering both the details of intermolecular interactions within organic electro-optic materials and interactions at interfaces between OEO materials and device architectures. Dramatic improvement in electro-optic device performance--including voltage-length performance, bandwidth, energy efficiency, and lower optical losses have been realized. These improvements are critical to applications in telecommunications, computing, sensor technology, and metrology. Multi-scale modeling methods illustrate the complexity of improving the electro-optic activity of organic materials, including the necessity of considering the trade-off between improving poling-induced acentric order through chromophore modification and the reduction of chromophore number density associated with such modification. Computational simulations also emphasize the importance of developing chromophore modifications that serve multiple purposes including matrix hardening for enhanced thermal and photochemical stability, control of matrix dimensionality, influence on material viscoelasticity, improvement of chromophore molecular hyperpolarizability, control of material dielectric permittivity and index of refraction properties, and control of material conductance. Consideration of new device architectures is critical to the implementation of chipscale integration of electronics and photonics and achieving the high bandwidths for applications such as next generation (e.g., 5G) telecommunications.

Elder, Delwin L.↗

Quantification of the systematic uncertainties associated with measuring a chance coincidence background at Chi-Nu

Modern advances in waveform digitizers allow coincidence experiments to be performed by recording singles data, and identifying coincidences in a later software analysis. It has been previously shown that for such data, the coincidence background can be obtained with unprecedented statistical precision. This method is especially attractive for experiments with complicated, time-varying backgrounds (i.e. not amenable to analytic or even a detailed Monte Carlo analysis). Many neutron detection experiments fall into this category, such as the Chi-Nu experiment to measure the prompt fission neutron spectra of the major actinides. While it is believed that use of this method will yield an improved systematic precision of the measured background, this has not previously been demonstrated. Presented here is the first analysis of the systematic uncertainties associated with this method

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Effective Long-term Monitoring Strategies by Integrating Reactive Transport Models with In situ Geochemical Measurements - 16212

Long-term monitoring of contaminant transport in groundwater is expected to account for a large fraction of future life-cycle cleanup costs at the DOE sites. The Attenuation-Based Remedies in the Subsurface Applied Field Research Initiative (ABRS AFRI) is developing an innovative approach for cost-effective in situ long-term monitoring. The approach is based on strategically adding the measurements of controlling variables (such as pH, redox potential, electrical conductivity, and groundwater level), which control the plume mobility and its spatial and temporal distribution. In situ measurements of these variables - supplemented with a reduced number of standard periodic groundwater samples - are expected to lead to more cost-effective monitoring, and can also serve as an early warning system for detecting unexpected plume migration. The objective of this study is to support the development of such a long-term monitoring approach through the application of advanced computational methods, including (1) statistical data mining and analysis, and (2) three-dimensional flow and reactive chemical transport modeling. We have performed the statistical data analysis of historical and current monitoring data at the Savannah River Site (SRS) F-Area to quantify the correlations between the controlling variables and radioactive contaminant concentrations. In parallel, we have used 3D modeling of flow and contaminant transport to provide the prediction of the contaminant plume evolution. The results of both data analysis and modeling confirmed that the correlations between controlling variables and contaminant concentrations are significant. Modeling results also suggest that the correlation parameters will change in the future, which is important to assess the long-term efficacy of the proposed monitoring approach. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Range reference atmosphere models

A description is given of the methods used to establish the statistical parameters and models for wind and various thermodynamic quantities at an altitude of 0-70 km for nine geographical locations. It is noted that wind is modeled as a vector quantity using the bivariate normal probability function. With the five parameters of the bivariate normal distribution, the distribution for wind speed is derived as a generalized Rayleigh distribution. In addition, the frequency of wind direction is derived, and the conditional distribution of wind speed given the wind direction is derived. It is pointed out that these and other wind models are consistent with the rigorous mathematical properties of the bivariate normal probability theory. The thermodynamic quantities are consistent with the hydrostatic equation and the equation of state for the mean values. With these methods, many statistical relationships can be derived.

Smith, O. E.↗

Statistically informed upscaling of damage evolution in brittle materials

The presence and growth of micro-cracks degrade the strength of brittle solids, greatly impacting the overall material response. Hence, the evolution of these micro-cracks must be accounted for in models describing the relationship between stress and strain so that accurate predictions of material failure can be made. The evolution of individual cracks and crack networks can be simulated with high-fidelity microscale models utilizing highly resolved meshes that can be computationally expensive to a point in which it limits the simulation scale. Hence, for many engineering applications that require simulations of large components, continuum-scale models, which cannot explicitly resolve individual cracks and thus lose important physical information, are required. In this work, we bridge these two scales by developing and implementing a continuum-scale effective moduli constitutive model that is informed by crack statistics generated from a high-fidelity model resolved using a finite-discrete element method (FDEM) implementation. Using statistical information describing the evolution of crack lengths and orientations, this model can capture the effects of brittle damage evolution without the need to resolve individual cracks. We have successfully captured the stress-strain behavior of the high-fidelity simulations using the statistics-based constitutive model shown through direct comparison of stress-strain curves. The curves match within error bars present in the strain-softening portions of the stress-strain curve of the high-fidelity results due to the statistical variation of the initial pre-existing crack network. In conclusion, the stress-strain curves are also compared to experimental results for similar loading conditions and show good qualitative agreement.

36 MATERIALS SCIENCE↗