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A cavitation and dynamic void growth model for a general class of strain-softening amorphous materials

In this work, we derive a homogenized framework for cavitation and dynamic void growth in a general class of strain-softening materials with particular emphasis on amorphous materials. Analytic solutions are derived by considering an assemblage of spherical shells subject to dynamic hydrostatic tensile pressure. The isochoric response of the matrix material is captured by a free volume theory based amorphous viscoplasticity model. The framework accounts for the coupled rate-dependent, strain-softening behavior typically exhibited in amorphous materials. Validation of the homogenized theory is carried out against numerous direct numerical simulations with excellent agreement. Furthermore, we find that a reduction in cavitation strength and significant acceleration of dynamic void growth rates is induced as a consequence of strain-softening in the amorphous matrix material. Lastly, the model is utilized to interpret some non-intuitive experimental observations of amorphous materials subject to shock compression and subsequent spall failure.

36 MATERIALS SCIENCE↗

Scale Invariance of Hot Spot Formation in TATB High Explosives

Shock-induced detonation of insensitive high explosives based on 1,3,5-triamino-2,4,6-trinitrobenzene starts with formation of hot spots at microstructural defects but has eluded atomistic modeling treatment at micron length scales. To this end, we performed multimicron scale all-atom molecular dynamics (MD) simulations of hot spots that form during the collapse of cylindrical pores with diameters between 10 and 300 nm. Our MD simulations show that hot spots formed at pores larger than 20 nm exhibit temperature fields with scale-invariant features for sizes up to at least 300 nm. Through a continuum-based grain-scale modeling framework, we span and extend beyond the size scales currently accessible to MD and find that hot spot scale invariance is a general feature that arises when the mechanical strength is insensitive to strain rate. Finally, our results demonstrate the applicability of all-atom MD to simulate the complicated dynamical evolution of micron-sized systems and bolster confidence in insights from MD simulations of materials that exhibit strength with negligible rate dependence over the relevant intervals.

36 MATERIALS SCIENCE↗

Evaluation of Zero-Net-Rate Pumping Tests

Accurately estimating the distribution of aquifer properties is key to understanding contaminant movement in the subsurface. The distribution of aquifer properties is typically addressed using slug or constant-rate well tests, and the pros and cons of these tests are well known. Slug tests are appealing because they avoid removing contaminated water, but their results are affected by well skin and the small volume of displaced water limits the volume of aquifer that can be evaluated. Constant-rate well tests have the disadvantage of requiring disposal of potentially contaminated water, but they can generate properties that are more representative than slug tests, and they can be used to estimate well efficiency and storativity, which are difficult to characterize using slug tests. Periodic pumping tests are appealing because they have many of the advantages and few of the disadvantages of slug and constant-rate well tests. Periodic pumping tests involve cycling the pumping rate with a regular period and measuring the resulting response in monitoring wells. Some of these tests involve imposing a periodic rate on a constant mean rate. However, other tests involve moving water out and back into the well at rates that are balanced so the net rate after each period is zero. Some zero-net-rate (ZNR) well tests use rates that follow a sinusoidal pattern, whereas others use a square wave pattern that switches between a constant rate of pumping and a constant rate of injection to achieve a zero-net rate. ZNR well tests appear to be a useful compromise between slug and constant rate tests, but methods for conducting and analyzing the results from these tests have received limited evaluation. Periodic pumping tests are typically evaluated through recorded pressure responses to a disturbance source. Recent work has demonstrated that the strain field in the vadose zone shows a response to disturbances in the underlying aquifer. Various instrument designs are available that can record vertical and horizontal strain to very precise resolutions (10-9 ε). Measuring the strain in the vadose zone can present lower costs than measuring pressure in a monitoring well, so using strain could improve the resolution of ZNR tests, as well as make these tests potentially cheaper. A ZNR periodic pumping system was constructed and used to perform tests in the Clemson, South Carolina area. The system was designed to pump and inject with a periodic square-wave, so pumping occurs at a constant rate for half the period and is followed by injection at the same rate for half the period resulting in no net gain or loss of water from the aquifer. The system is designed to generate flow rates from 1 to 3.5 gallons per minute (gpm) with a capacity of 875-gallon per half period. Pressure and strain monitoring points are located in the vicinity of the pumping well. A series of 10 ZNR periodic pumping tests were conducted at the field site, with periods ranging from 2 to 540 minutes. Pressure data were collected and recorded in four monitoring wells in various locations around the pumping well. In addition, vertical and horizontal strain and tilt data were recorded in various locations around the pumping well. Traditional aquifer tests, including slug tests and constant-rate pumping tests were conducted at the field site to provide a baseline of aquifer parameter estimates that are compared the results of ZNR tests. Pressure data measured at monitoring wells during ZNR tests were analyzed utilizing an analytical solution (Streltsova, 1988) that assumes a confined aquifer and estimates hydraulic diffusivity and transmissivity using the time lag and amplitude of the pressure signal. The storativity can be separated out from the hydraulic diffusivity using the transmissivity estimate. The time-lag and amplitude of the pressure signals were estimated using a Fourier transform. The time-lag of the primary period of the pressure increases as a linear function of distance from the pumping well, and it increases as the square root of the period of the ZNR test over a range of periods spanning two orders of magnitudes. The first few harmonics follow similar trends, but the higher frequency harmonics diverge from this trend. Strain and tilt data from various instruments in the vadose and saturated zones are periodic during ZNR tests. The time lags of the strain components increase roughly linearly with distance from the well. Many of the time lags of the strain data from the vadose zone are similar to the time lags observed in the pressure data from a similar distance and pumping period. Theoretical experiments were performed to understand how pressure and strain responds to ZNR periodic pumping. The time-lags of the simulated pressure responses match the field data trends. The results were used to validate the Streltsova (1988) solution for periodic pumping to estimate hydraulic diffusivity. Hydraulic diffusivity was estimated to be 1.8 x 10-2 m2s-1 < Dh < 9.0 x 10-2 m2s-1 using pressure data from all the wells during ZNR tests. Transmissivity was estimated to be 0.8 x 10-4 m2s-1 < T < 4.3 x 10-4 m2s-1. Assuming Storativity = T/Dh gives 1.1 x 10-3 < S < 19 x10-3. Transmissivity is used to estimate the hydraulic conductivity, K, by dividing by the assumed aquifer thickness. Two constant-rate pumping tests were conducted and analyzed using two conceptual models: The Hantush (1961) solution was used to analyze data assuming confined conditions and the Neuman (1974) solution was used to analyze data assuming unconfined conditions. The Hantush (1961) solution estimated transmissivity to be 1.6 x 10-4 m2s-1 < T < 1.8 x 10-4 m2s-1 when using data from all the wells. Storativity was estimated to be 4.4 x 10-3 < S < 8.2 x 10-3. Assuming Dh = T/S gives 0.22 x 10-2 m2s-1 < Dh < 3.6 x 10-2 m2s-1. The Neuman (1974) solution estimated transmissivity to be 0.80 x 10-4 m2s-1 < T < 0.84 x 10-4 m2s-1. Total storativity (S + Sy) was estimated to be 22 x 10-3 < S < 110 x 10-3. Storativity excluding the Sy term was estimated to be 2.2 x 10-3 < S < 2.5 x 10-3. Assuming Dh = T/S gives 0.073 x 10-2 m2s-1 < S < 0.36 x 10-2 m2s-1. Two slug tests were performed on the pumping well, PW-2. The Bouwer and Rice (1976) solution for slug tests was used to analyze the data. This solution works for both confined and unconfined conditions, so both conceptual models were covered through the analysis. Hydraulic conductivity was estimated to be 1.95 x 10-6 ms-1 < K < 2.49 x 10-6 ms-1. Statistical comparison show generally no significant difference in the estimates of Dh, K, or S made using ZNR and conventional pumping tests.. However, the total storage estimated by the Neuman (1974) solution for unconfined settings is larger than that estimate using the Streltsove analysis applied to the ZNR tests. This is likely because the Neuman solution considers delayed yield from storage that the water table, whereas the Streltsova (1988) solution assumes confined conditions. The analysis also indicates that there is a statistically significant difference between parameters estimated with conventional slug tests and those measured with either constant-rate pumping tests or ZNR tests. Hydraulic diffusivity is estimated from the time-lag and the distance from the well. The time-lags of the strain data from the vadose zone are similar to the lags of the pressure data from a similar distance. This indicates that hydraulic diffusivities estimated from the strain data measured in the vadose zone would be similar to the estimates from the pressure data measured in the aquifer. There appear to be sign reversals in some of the strain data that were corrected to estimate the time lag. The dissolved oxygen (CO) concentration was measured during several ZNR tests to evaluate the feasibility of using the procedure to increase contaminant degradation kinetics that are related to DO. The results indicate that DO can be increased during the cycling of ZNR tests in some cases.

Smith-Jones, Austin↗

Active- and transfer-learning applied to microscale-macroscale coupling to simulate viscoelastic flows

Active- and transfer-learning are applied to microscale dynamics of polymer flows for the multiscale discovery of effective constitutive approximations required in viscoelastic flow simulation. The result is macroscopic rheology directly connected to a microstructural model. Micro and macroscale simulations are adaptively coupled by means of Gaussian process regression (GPR) to run the expensive microscale computations only as necessary. This multiscale method is demonstrated with flows of a polymer solution as a model system. At the microscale level dissipative particle dynamics (DPD) is employed to model the fluid as a suspension of bead-spring micro-structures subjected to steady shear flow. The results yield the non-Newtonian viscosity and the first normal stress difference at strain rates as training data used in a GPR model. DPD parameters are calibrated with respect to experimental data for a real polymer solution. Compliance with these data requires adjustment of the DPD model's cutoff radius, which then becomes a function of the second invariant of the strain rate tensor. The FENE-P model is chosen for the macroscale description using the spectral element method (SEM) to simulate channel flow and flow past a circular cylinder. The DPD results at the lowest possible shear strain rate yield an estimate of the zero-shear rate viscosity, which allows the initiation of the macroscale flow by SEM as a Newtonian fluid. The resulting strain-rate field is surveyed to determine additional shear strain rate sampling points for the DPD system. This new information allows an initial fitting of parameters of the constitutive equation followed by new SEM simulations at the macroscale. Additionally, guided by active-learning GPR to select new sampling points, this process continues until convergence is achieved. The effectiveness of this new simulation paradigm for viscoelastic flows is tested with different macroscale operating conditions. The effective closure learned in the channel simulation is then transferred directly to the flow past a circular cylinder at low Reynolds number, where the results show that only two additional DPD simulations are required to achieve a satisfactory constitutive model. With an increase of the Reynolds number, the active-learning scheme automatically detects the inaccuracy of the learned constitutive model, and initiates additional DPD simulations for the extra data needed to once again close the microscale-macroscale coupled system. This new paradigm of active- and transfer-learning for multiscale modeling is readily applicable to other microscale-macroscale coupled simulations of complex fluids and other materials. Furthermore, the coupling between microscale and macroscale solvers can be seamlessly implemented with our open source multiscale universal interface (MUI) library.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Experimental investigation of Mach 3 cruise heating simulations on a representative wing structure for flight loads measurement

Radiant heating experiments were performed in the laboratory on an instrumented multispar wing structure to investigate: (1) how accurately the structural temperatures of a Mach 3 cruise-flight profile could be simulated, (2) what the effects of the heating and heating inaccuracies would be on the responses of strain-gage bridges installed on the structure, and (3) how these responses would affect flight loads measurements. Test temperatures throughout the structure agreed well with temperatures calculated for a Mach 3 profile. In addition, temperatures produced by two identical tests were repeatable to less than + or -6 K deg. Thermally induced strain-gage-bridge responses were large enough to be detrimental to a high-speed flight loads program with a goal of establishing aerodynamic loads (exclusive of thermal loads). It was shown that heating simulation can be used effectively for thermal calibration (that is, to provide corrections for a high-temperature environment), and that thermal calibration may not be needed if the simulation data are used to carefully select bridges and load equations.

Fields, R. A.↗

Studies on Stress-Strain Relationships of Polymeric Materials Used in Space Applications

A two-year research plan was undertaken in association with Polymers Branch, NASA Glenn Research Center, to carry out experimental and modeling work relating stress and strain behavior of polymeric materials, especially elastomers and vulcanized rubber. An experimental system based on MTS (Mechanical Testing and Simulation) A/T-4 test facility environment has been developed for a broader range of polymeric materials in addition to a design of laser compatible temperature control chamber for online measurements of various strains. Necessary material processing has been accomplished including rubber compounding and thermoplastic elastomer processing via injection molding. A broad suite of testing methodologies has been identified to reveal the complex non-linear mechanical behaviors of rubbery materials when subjected to complex modes of deformation. This suite of tests required the conceptualization, design and development of new specimen geometries, test fixtures, and test systems including development of a new laser based technique to measure large multi-axial deformations. Test data has been generated for some of these new fixtures and has revealed some complex coupling effects generated during multi-axial deformations. In addition, fundamental research has been conducted concerning the foundation principles of rubber thermodynamics and resulting theories of rubber elasticity. Studies have been completed on morphological properties of several thermoplastic elastomers. Finally, a series of steps have been identified to further advance the goals of NASA's ongoing effort.

Jana, Sadhan C.↗

Link statistics of dislocation network during strain hardening

Dislocations are line defects in crystals that multiply and self-organize into a complex network during strain hardening. The length of dislocation links, connecting neighboring nodes within this network, contains crucial information about the evolving dislocation microstructure. By analyzing data from Discrete Dislocation Dynamics (DDD) simulations in face-centered cubic (fcc) Cu, we characterize the statistical distribution of link lengths of dislocation networks during strain hardening on individual slip systems. Here, our analysis reveals that link lengths on active slip systems follow a double-exponential distribution, while those on inactive slip systems conform to a single-exponential distribution. The distinctive long tail observed in the double-exponential distribution is attributed to the stress-induced bowing out of long links on active slip systems, a feature that disappears upon removal of the applied stress. We further demonstrate that both observed link length distributions can be explained by extending a one-dimensional Poisson process to include different growth functions. Specifically, the double-exponential distribution emerges when the growth rate for links exceeding a critical length becomes super-linear, which aligns with the physical phenomenon of long links bowing out under stress. This work advances our understanding of dislocation microstructure evolution during strain hardening and elucidates the underlying physical mechanisms governing its formation.

Crystal plasticity↗

Predicted and observed effects of stacking sequence and delamination size on instability-related delamination growth

A three-dimensional, geometrically nonlinear finite element analysis was used to calculate strain-energy release rate distributions for several laminates which exhibited instability-related delamination growth. Two stacking sequences, (0/90/90/0)6 and (90/0/0/90)6 were considered. The specimens were fabricated with a double layer of 0.013 mm Kapton film located between the fourth and fifth plies, thereby simulating a delamination. Initial delamination sizes were 30, 40, or 60 mm in diameter. The static strain corresponding to delamination growth was determined experimentally. Comparison of the analytical and experimental results indicated that delamination growth was governed by the magnitude of GI.

Whitcomb, John D.↗

Delamination growth analysis in quasi-isotropic laminates under loads simulating low-velocity impact

A geometrically nonlinear finite-element analysis was developed to calculate the strain energy released by delamination plates during impact loading. Only the first mode of deformation, which is equivalent to static deflection, was treated. Both the impact loading and delamination in the plate were assumed to be axisymmetric. The strain energy release rate in peeling, G sub I, and shear sliding, G sub II, modes were calculated using the fracture mechanics crack closure technique. Energy release rates for various delamination sizes and locations and for various plate configurations and materials were compared. The analysis indicated that shear sliding (G sub II) was the primary mode of delamination growth. The analysis also indicated that the midplane (maximum transverse shear stress plane) delamination was more critical and would grow before any other delamination of the same size near the midplane region. The delamination growth rate was higher (neutrally stable) for a low toughness (brittle) matrix and slower (stable) for high toughness matrix. The energy release rate in the peeling mode, G sub I, for a near-surface delamination can be as high as 0.5G sub II and can contribute significantly to the delamination growth.

Shivakumar, K. N.↗

Community Modeling and Flux Balance Analysis of Synthetic Bacterial Community in MOPS Medium

This narrative was used for the 4-member community modeling using MOPS medium for the bacteria isolated from Populus deltoides (PD). 10 bacterial strains isolated from PD were co-cultured as a synthetic microbial community in MOPS minimal medium. After 15 passages there were 4 members survived in MOPS medium. The genome of each community member was sequenced and uploaded into KBase for genome annotation and metabolic modeling. To simulate the metabolic interactions among the finally surviving community members, the individual metabolic models of each strain were merged into a compartmentalized community model, and then the community model was gapfilled using MOPS medium. The FBA modeling was performed and the metabolites exchange among community members was proposed. The publication by Jia Wang, Dana L. Carper, Leah H. Burdick, Him Shrestha, Manasa Appidi, Paul E. Abraham, Collin M. Timm, Robert L. Hettich, Dale A. Pelletier, Mitchel J. Doktycz can be found here: https://doi.org/10.​1016/​j.​csbj.​2021.​03.​034

59 BASIC BIOLOGICAL SCIENCES↗

Community Modeling and Flux Balance Analysis of Synthetic Bacterial Community in R2A Medium

This narrative was used for the 3-member community modeling using R2A medium for the bacteria isolated from Populus deltoides (PD). 10 bacteiral strains isolated from PD were co-cultured as a synthetic microbial community in R2A complex medium. After 15 passages, there were 3 members survived in R2A medium. The genome of each community member was sequenced and uploaded into KBase for genome annotation and metabolic modeling. To simulate the metabolic interactions among the finally surviving community members, the individual metabolic models of each strain were merged into a compartmentalized community model, and then the community model was gapfilled using R2A medium. The FBA modeling was performed and the metabolites exchange among community members was proposed. The publication by Jia Wang, Dana L. Carper, Leah H. Burdick, Him Shrestha, Manasa Appidi, Paul E. Abraham, Collin M. Timm, Robert L. Hettich, Dale A. Pelletier, Mitchel J. Doktycz can be found here: https://doi.org/10.​1016/​j.​csbj.​2021.​03.​034

59 BASIC BIOLOGICAL SCIENCES↗

Uncertainty Reduction With Multi-Model Monte Carlo for Crystal Plasticity Simulations of Additively Manufactured Metals

In this work, multi-model Monte Carlo estimators are developed to reduce uncertainty in quantities of interest (QoIs) extracted from crystal plasticity simulations of additively manufactured (AM) metals. A significant concern in AM parts is uncertainty in mechanical properties caused in part by complex microstructures that arise from the AM process. Quantifying uncertainty in microstructure-sensitive behavior using experiments alone is costly, especially when mechanical allowables must be established. Quantitative relationships among microstructure, micromechanical metrics like slip accumulation, crack initiation, and failure are also difficult to capture with limited experiments. Crystal plasticity material models instead enable computational prediction of micromechanical stress and strain fields given a discretized microstructure. However, high-fidelity finely discretized crystal plasticity simulations are computationally expensive, while lower-fidelity models are less accurate and generally biased, making uncertainty quantification and reduction computationally difficult as well. Multi-model Monte Carlo methods leverage correlations between high- and low-fidelity models to produce unbiased estimators for QoIs with reduced uncertainty relative to standard Monte Carlo. Crystal plasticity QoIs considered in this work include yield strength and the mean and extreme values of micromechanical fields that are relevant to crack initiation. Multi-model Monte Carlo estimators are developed for each individual QoI and several groups of QoIs. The results of this work establish relationships among model correlations, sample allocation, and uncertainty reduction for different combinations of QoIs and demonstrate a trend of less uncertainty reduction as QoIs become more sensitive to local microstructure. Limitations from using pilot samples to estimate model covariances and train low-fidelity models are also addressed. The uncertainty reduction achieved by multi-model Monte Carlo is an important step toward using computational mechanics models to predict microstructure-sensitive crack initiation and failure in AM parts.

uncertainty quantification↗

Engineering the electronic and strained interface for high activity of PdM core @Pt monolayer electrocatalysts for oxygen reduction reaction

Alloyed nanoparticles with core-shell structures provide a favorable model to modulate interfacial interaction and surface structures at the atomic level, which is important for designing electrocatalysts with high activity and durability. Herein, core-shell structured Pd 3 M@Pt/C nanoparticles with binary PdM alloy cores (M = Fe, Ni, and Co) and a monolayer Pt shell were successfully synthesized with diverse interfaces. Among these, Pd 3 Fe@Pt/C exhibited the best oxygen reduction reaction catalytic performance, roughly 5.4 times more than that of the commercial Pt/C catalyst used as reference. The significantly enhanced activity is attributed to the combined effects of strain engineering, interfacial electron transfer, and improved Pt utilization. Density functional theory simulations and extended X-ray absorption fine structure analysis revealed that engineering the alloy core with moderate lattice mismatch and alloy composition (Pd 3 Fe) optimizes the surface oxygen adsorption energy, thereby rendering excellent electrocatalytic activity. Finally, future researches may use this study as a guide on the construction of highly effective core-shell electrocatalysts for various energy conversions and other applications.

25 ENERGY STORAGE↗

3D strain field reconstruction by inversion of dynamical scattering

Strain governs not only the mechanical response of materials but also their electronic, optical, and catalytic properties. For this reason, the measurement of the 3D strain field is crucial for a detailed understanding and for further development of material properties through strain engineering. However, measuring strain variations along the electron beam direction has remained a major challenge for (scanning-) transmission electron microscopy (S/TEM). In this article, we present a method for 3D strain field determination using 4D-STEM. The method is based on the inversion of dynamical diffraction effects, which occur at strain field variations along the beam direction. We test the method against simulated data with a known ground truth and demonstrate its application to an experimental 4D-STEM dataset from an inclined pseudomorphically grown Al0.47Ga0.53N layer.

Niermann, Laura↗

A Computational Procedure for Assessing I$_{c}(\varepsilon$) in Nb$_{3}$Sn/Bi-2212 Hybrid Magnets

The critical current of superconductors is commonly measured by testing unloaded wires under an external magnetic field. While stressed by intense Lorentz forces, the existing HTS/LTS superconductors are prone to a reduction in critical current before reaching their structural mechanical limit. Here, in this work, the magnetic and mechanical analysis of the FNAL 4-layer Bi-2212/Nb$_{3}$Sn hybrid dipole magnet is reported, aimed at predicting the critical current degradation for both the superconductors during powering at 16T. All the Rutherford cables in the coils of the hybrid magnet were modeled at the strand level in Ansys APDL with the heterogeneous cable model. Utilizing this detailed geometry, it was possible to evaluate the effects of strain on the critical current degradation for both the Nb$_{3}$Sn and Bi-2212 superconductors under the intense Lorentz forces. The analysis presented in this paper integrates strain-dependent critical current laws, with parameters derived from experimental data, to simulate the hybrid magnet's performance for all possible current-powering configurations. The proposed methodology enables a detailed assessment of conductor integrity and I$_{C}(\varepsilon$) reduction in existing hybrid magnet designs, providing a versatile and rigorous framework for optimizing future high-field hybrid magnets.

D'Agliano, A. [Lawrence Berkeley National Laborato↗

Mechanism-Based Energy Regularization in Computational Modeling of Quasibrittle Fracture

Abstract Quasibrittle materials are featured by a strain-softening constitutive behavior under many loading scenarios, which could eventually lead to localization instability. It has long been known that strain localization would result in spurious mesh sensitivity in finite element (FE) simulations. Previous studies have shown that, for the case of fully localized damage, the mesh sensitivity can be mitigated through energy regularization of the material constitutive law. However, depending on the loading configuration and structural geometry, quasibrittle structures could exhibit a complex damage process, which involves both localized and diffused damage patterns at different stages of loading. This study presents a generalized energy regularization method that considers the spatial and temporal evolution of damage pattern. The method introduces a localization parameter, which describes the local damage pattern. The localization parameter governs the energy regularization of the constitutive model, which captures the transition from diffused to localized damage during the failure process. The method is cast into an isotropic damage model, and is further extended to rate-dependent behavior. The energy regularization scheme is directly incorporated into the kinetics of damage growth. The model is applied to simulate static and dynamic failures of ceramic specimens. It is shown that the present model is able to effectively mitigate the spurious mesh sensitivity in FE simulations of both types of failure. The present analysis demonstrates the essential role of mechanism-based energy regularization of constitutive relation in FE simulations of quasibrittle fracture.

Mechanics↗

An ILLIAC program for the numerical simulation of homogeneous incompressible turbulence

An algorithm and ILLIAC computer program, developed for the simulation of homogeneous incompressible turbulence in the presence of an applied mean strain, are described. The turbulence field is represented spatially by a truncated triple Fourier series (spectral method) and followed in time using a fourth-order Runge-Kutta algorithm. These include: (1) transformation of variables suggested by Taylor's sudden-distortion theory; (2) implicit viscous diffusion by use of an integrating factor; (3) implicit pressure calculation suggested by Taylor's sudden-distortion theory, and (4) inexpensive control of aliasing by random and phased coordinate shifts.

Rogallo, R. S.↗

Estimation of blade airloads from rotor blade bending moments

A method is developed to estimate the blade normal airloads by using measured flap bending moments; that is, the rotor blade is used as a force balance. The blade's rotation is calculated in vacuum modes and the airloads are then expressed as an algebraic sum of the mode shapes, modal amplitudes, mass distribution, and frequency properties. The modal amplitudes are identified from the blade bending moments using the Strain Pattern Analysis Method. The application of the method is examined using simulated flap bending moment data that have been calculated for measured airloads for a full-scale rotor in a wind tunnel. The estimated airloads are compared with the wind tunnel measurements. The effects of the number of measurements, the number of modes, and errors in the measurements and the blade properties are examined, and the method is shown to be robust.

Bousman, William G.↗