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At least 937 records · Page 52
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Random field estimation approach to robot dynamics

The difference equations of Kalman filtering and smoothing recursively factor and invert the covariance of the output of a linear state-space system driven by a white-noise process. Here it is shown that similar recursive techniques factor and invert the inertia matrix of a multibody robot system. The random field models are based on the assumption that all of the inertial (D'Alembert) forces in the system are represented by a spatially distributed white-noise model. They are easier to describe than the models based on classical mechanics, which typically require extensive derivation and manipulation of equations of motion for complex mechanical systems. With the spatially random models, more primitive locally specified computations result in a global collective system behavior equivalent to that obtained with deterministic models. The primary goal of applying random field estimation is to provide a concise analytical foundation for solving robot control and motion planning problems.

Rodriguez, Guillermo↗
DOE OSTI2023

Dynamics of multilayer Rayleigh–Taylor instability at moderately high Atwood numbers

This paper investigates the multilayer Rayleigh–Taylor instability (RTI) using statistically stationary experiments conducted in a gas tunnel. Employing diagnostics such as particle image velocimetry (PIV) and planar laser induced fluorescence (PLIF), we make simultaneous velocity–density measurements to study how dynamics and mixing are linked in this variable density flow. Experiments are conducted in a newly built, blow-down three-layer gas tunnel facility. Mixing between three gas streams is studied, where the top and bottom streams are comprised of air, and the middle stream is an air–helium mixture. Shear is minimized between these streams by matching their inlet velocities. The four experimental conditions investigated here consist of two different density ratios (Atwood numbers 0.3 and 0.6), each investigated at two instability development times (or equivalently, two streamwise locations), and all experiments are with the same middle stream thickness of 3 cm. The growth of the middle layer is measured using laser-based planar Mie scattering visualization. The mixing width is found to grow linearly with time at late times. Various quantitative measures of molecular mixing indicate a very high degree of molecular mixing at late times in the multilayer RTI flow. The vertical turbulent mass flux $a_y$ is calculated. In addition to mostly negative values of $a_y$ , typical of buoyancy-dominated flows due to negative correlation between velocity and density fluctuations, positive regions are also observed in profiles of $a_y$ due to entrainment and erosion at the lower edge of the mixing region. Global energy budgets are calculated for the multilayer RTI flow at late times and it is found that the majority of potential energy released has been dissipated due to viscous effects, and a large value of mixing efficiency ( $\sim$ 60 %) is observed.

Mechanics↗
DOE OSTI2025

Si-Cr-Al-Mn Alloy for High Specific Resistivity

Laboratory material produced in budget period one met the target resistivity, mechanical and magnetic requirements for the Go/No-Go decision to move to industrial trials. The chosen chemistry settled on a high Cr strategy, with moderate Mn and Al additions, providing a good comprise on core loss and induction with minimal impact on mechanical properties, important to successful downstream processing. Industrial trials began in budget period two with the chosen chemistry, referred to as Alloy X. Difficulties occurred during initial hot rolling trials. Reheating the material using the standard NOES practice caused slab cracking from high thermal gradients in areas exposed to the roof burners, this was solved using a modified reheat practice. High Cr caused poor dynamic recrystallization during hot rolling, which was solved using a modified hot rolling practice. The high Cr content of the steel also caused poor decarburization during final annealing, which necessitated lowering the melt carbon aim for the final heat, together with a modified decarburization practice. Steel was finished to final thicknesses of 0.20 – 0.50 mm and evaluated for magnetic and mechanical properties. Although the target core loss for the 0.25 and 0.35 mm material was not achieved, significant reductions in high frequency core loss were measured, compared to equivalent commercially available material. Alloy X at 0.35 mm showed a 26 % and 23 % improvement at 400 HZ and 1000 Hz respectively, over Cliffs’ M-19 (0.35 mm) commercially available NOES. At 0.25 mm, Alloy X showed a 23 % and a 26 % improvement at 400 HZ and 1000 Hz respectively, over Cliffs’ HF-10 (0.25 mm) commercially available NOES. The 0.25 mm product was chosen for motor efficiency evaluation. ORNL collaborated with Cleveland-Cliffs (CC) to build, assemble, and test two 5HP motors: a baseline motor with M19 steel and a motor made with high efficiency steel (Alloy X) developed for the project. Overall, results were as expected with comparable performance at low speeds, and with more than 8% efficiency improvement for high speeds. Increased motor steel efficiency at high frequencies not only results in direct efficiency improvements but can yield reductions in motor size and cost by facilitating higher operation speeds, or by increasing the number of poles in the machine. This allows the production of more power-dense motors which are sometimes avoided with conventional material due to increased core losses. The material developed on this project provides more viable options for achieving improved motor efficiency or reduced motor size and cost.

36 MATERIALS SCIENCE↗
NASA NTRS1981

Vibrations of three-dimensional pipe systems with acoustic coupling

A general algorithm is developed to calculate the beam-type dynamic response of three dimensional multiplane finite length pipe systems, consisting of elbow and straight ducts with continuous interfaces. Emphasis is on secondary acoustic wave effects giving rise to coupling mechanisms; and the simulation accounts for one-dimensional elastoacoustic coupling from a plane acoustic wave and secondary loads resulting from wave asymmetries. The transfer matrix approach is adopted in modeling the elastodynamics of each duct, with allowance for distribution loads. Secondary loads from plane wave distortion are considered with a solution of the Helmholtz equation in an equivalent rigid waveguide, and effects of path imperfection are introduced as a perturbation from the hypothetical perfectly straight pipe. Computations indicate that the one-dimensional acoustic assumption is valid for frequencies below one-half the first cut-off frequency, and the three-dimensional acoustic effects produce an increase in response levels near and above cut-off.

El-Raheb, M.↗
NASA NTRS1959

Investigation of the Effects of Low Reynolds Number Operation on the Performance of a Single-Stage Turbine with a Downstream Stator

High-altitude turbojet performance is adversely affected by the effects of low air density. This performance loss is evaluated as a Reynolds number effect, which represents the increased significance of high fluid viscous forces in relation to dynamic fluid forces as the Reynolds number is decreased. An analytical and experimental investigation of the effects of low Reynolds number operation on a single-stage, high-work-output turbine with a downstream stator was carried out at Reynolds numbers of 182,500, 39,600, and 23,000, based on average rotor-design flow conditions. At low Reynolds numbers and turbulent flow conditions, increased viscous losses caused decreased effective flow area, and thus decreased weight flow, torque, and over-all efficiency at a given equivalent speed and pressure ratio. Decreasing the Reynolds number from 182,500 to 23,000 at design equivalent speed resulted in a 5.00-point loss in peak over-all turbine efficiency for both theory and experiment. The choking equivalent weight flow decreased 2.30 percent for these conditions. Limiting loading work output was reached at design equivalent speed for all three Reynolds numbers. The value of limiting loading work output at design speed decreased 4.00 percent as Reynolds number was decreased from 182,500 to 23,000. A theoretical performance-prediction method using basic boundary-layer relations gave good agreement with experimental results over most of the performance range at a given Reynolds number if the experimental and analytical design operating conditions were carefully matched at the highest Reynolds number with regard to design performance parameters. High viscous losses in the inlet stator and rotor prevented the attainment of design equivalent work output at the lowest Reynolds number of 23,000.

Forrette, Robert E.↗
NASA NTRSDate not supplied

Multiobjective Multidisciplinary Optimization of Low-Boom Supersonic Transports Using Multifidelity Models

A multidisciplinary optimization (MDO) method has been developed to design a computational fluid dynamics (CFD) based low-boom configuration that can be obtained from a Pareto solution of a low-fidelity multiobjective MDO problem with mission constraints. This paper refines the developed MDO method using multifidelity models for CFD-based multiobjective MDO. The refined MDO method can generate a low-boom configuration that satisfies the mission requirements, has the lowest takeoff gross weight and the longest range for the low-boom mission, trims the low-boom cruise flight with fuel redistributions, and has a reversed equivalent area distribution closely matching a low-boom target with ground noise level below 70 PLdB. The validity of the refined MDO method is demonstrated by a design study of a low-boom supersonic transport that carries 40 passengers, flies a low-boom mission with cruise Mach of 1.7 and range of 3500 nm, and cruises overwater at Mach 1.8 with range of 3882 nm. Moreover, the refined MDO method eliminates the difference between the assumed cruise weight for CFD-based low-boom inverse design optimization and the estimated cruise weight of the optimal inverse design solution with respect to the mission requirements.

multidisciplinary optimization↗
DOE OSTI2024

Momentum-exchange interactions in a Bragg atom interferometer suppress Doppler dephasing

Large ensembles of laser-cooled atoms interacting through infinite-range photon-mediated interactions are powerful platforms for quantum simulation and sensing. Here we realize momentum-exchange interactions in which pairs of atoms exchange their momentum states by collective emission and absorption of photons from a common cavity mode, a process equivalent to a spin-exchange or XX collective Heisenberg interaction. The momentum-exchange interaction leads to an observed all-to-all Ising-like interaction in a matter-wave interferometer. A many-body energy gap also emerges, effectively binding interferometer matter-wave packets together to suppress Doppler dephasing in analogy to Mössbauer spectroscopy. The tunable momentum-exchange interaction expands the capabilities of quantum interaction–enhanced matter-wave interferometry and may enable the realization of exotic behaviors, including simulations of superconductors and dynamical gauge fields.

Science & Technology - Other Topics↗
DOE OSTI2025

The Water Table Model (WTM) (v2.0.1): coupled groundwater and dynamic lake modelling

Abstract. Ice-free land comprises 26 % of the Earth's surface and holds liquid water that delineates ecosystems, affects global geochemical cycling, and modulates sea levels. However, we currently lack the capacity to simulate and predict these terrestrial water changes across the full range of relevant spatial (watershed to global) and temporal (monthly to millennial) scales. To address this knowledge gap, we present the Water Table Model (WTM), which integrates coupled components to compute dynamic lake and groundwater levels. The groundwater component solves the 2D horizontal groundwater flow equation using non-linear equation solvers from the C++ PETSc (Portable, Extensible Toolkit for Scientific Computation) library. The dynamic lake component makes use of the Fill–Spill–Merge (FSM) algorithm to move surface water into lakes, where it may evaporate or affect groundwater flow. In a proof-of-concept application, we demonstrate the continental-scale capabilities of the WTM by simulating the steady-state climate-driven water table for the present day and the Last Glacial Maximum (LGM; 21 000 calendar years before present) across the North American continent. During the LGM, North America stored an additional 14.98 cm of sea-level equivalent (SLE) in lakes and groundwater compared to the climate-driven present-day scenario. We compare the present-day result to other simulations and real-world data. Open-source code for the WTM is available on GitHub and Zenodo.

Callaghan, Kerry L. (ORCID:0000000226740838)↗
NASA NTRS1999

Asymptotic Stability of Interconnected Passive Non-Linear Systems

This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.

Isidori, A.↗
NASA NTRS2005

Thrust Augmentation Measurements for a Pulse Detonation Engine Driven Ejector

Thrust augmentation results of an ongoing study of pulse detonation engine driven ejectors are presented and discussed. The experiments were conducted using a pulse detonation engine (PDE) setup with various ejector configurations. The PDE used in these experiments utilizes ethylene (C2H4) as the fuel, and an equi-molar mixture of oxygen and nitrogen as the oxidizer at an equivalence ratio of one. High fidelity thrust measurements were made using an integrated spring damper system. The baseline thrust of the PDE engine was first measured and agrees with experimental and modeling results found in the literature. Thrust augmentation measurements were then made for constant diameter ejectors. The parameter space for the study included ejector length, PDE tube exit to ejector tube inlet overlap distance, and straight versus rounded ejector inlets. The relationship between the thrust augmentation results and various physical phenomena is described. To further understand the flow dynamics, shadow graph images of the exiting shock wave front from the PDE were also made. For the studied parameter space, the results showed a maximum augmentation of 40%. Further increase in augmentation is possible if the geometry of the ejector is tailored, a topic currently studied by numerous groups in the field.

Pal, S.↗
NASA NTRS2008

Deflection Analysis of the Space Shuttle External Tank Door Drive Mechanism

Upon observing an abnormal closure of the Space Shuttle s External Tank Doors (ETD), a dynamic model was created in MSC/ADAMS to conduct deflection analyses for assessing whether the Door Drive Mechanism (DDM) was subjected to excessive additional stress, and more importantly, to evaluate the magnitude of the induced step or gap with respect to shuttle s body tiles. To model the flexibility of the DDM, a lumped parameter approximation was used to capture the compliance of individual parts within the drive linkage. These stiffness approximations were then validated using FEA and iteratively updated in the model to converge on the actual distributed parameter equivalent stiffnesses. The goal of the analyses is to determine the deflections in the mechanism and whether or not the deflections are in the region of elastic or plastic deformation. Plastic deformation may affect proper closure of the ETD and would impact aero-heating during re-entry.

Tosto, Michael A.↗
NASA NTRS2020

Combustion Dynamics Characteristics and Fuel Pressure Modulation Responses of a Three-Cup Third-Generation Swirl-Venturi Lean Direct Injection Combustion Concept

This paper presents the combustion dynamic data and fuel modulation response of a three-cup Lean Direct Injection combustor developed by Woodward, FST. The test was conducted at the NASA Glenn Research Center CE-5 flame tube test facility. The facility provided inlet air up to 922 K and pressure up to 19.0 bar. At the low-power configuration, the combustion noise was quiet. Large combustion pressure oscillations were observed with the High-power configuration at an off design condition, with low inlet air temperature and pressure conditions and a high equivalence ratio (about T3=600 K, P3 = 800 kPa, and ER =0.46). The noise amplitude was as high as 1.5 psi at around 220 Hz. As inlet air pressure and temperature increased, this combustion instability decreased. Fuel modulated signals were produced with the WASK fuel modulator located in the fuel line upstream of the center cup pilot fuel-air mixer. The amplitudes of the modulated signals detected in the combustor were low. Only less than 0.13% (0.06 psi) of the input energy was detected, and the signal amplitudes decreased as the modulated frequencies increased. Interaction between the modulated signals and the combustion noise varied with operating conditions. At a condition with low combustion noise around 150 hz, modulating a signal at around the same frequency would increase the combustion noise from 0.2 psi to as high as 0.6 psi, whereas at a condition with a high combustion instability around 250 hz, the modulated signal did not seem to have much effect on the combustion noise.

Fuel flexible combustor↗
NASA NTRSDate not supplied

Estimation of Permanent Magnet Synchronous Motor Parameters using a Linear Unknown Input Interval Observer

This paper develops and evaluate a technique to estimate the speed and unknown load torque of a permanent magnet synchronous motor (PMSM). An interval unknown input observer (UIO) for linear time-invariant (LTI) systems is designed and utilized to estimate the PMSM parameters. Interval UIOs are advantageous as they allow for the estimation of both states and unknown inputs, while accounting for varying uncertainty sources, such as model and measurement uncertainties inherent in dynamic systems and processes. First, the nonlinear PMSM model is linearized to transform it to a suitable form for application of the linear interval UIO. Then, the interval UIO is applied to jointly estimate the motor speed and the unknown load torque disturbance. Assuming that the measurement noise and disturbances are bounded, lower and upper bounds are first computed for the unmeasured state (motor speed) and then for the unknown input (load torque). The proposed approach and its limitations are demonstrated for the nonlinear PMSM model derived from its equivalent electrical circuit.

Elinirina I Robinson↗
NASA NTRS2024

Aera-Mip: Emission Pathways, Remaining Budgets, and Carbon Cycle Dynamics Compatible With 1.5 and 2 °C Global Warming Stabilization

While international climate policies now focus on limiting global warming to well below 2 °C or pursuing a 1.5 °C level of global warming, the climate modelling community has not provided an experimental design in which all Earth system models (ESMs) converge and stabilize at the same prescribed global warming levels. This gap hampers accurate estimations based on comprehensive ESMs of the carbon emission pathways and budgets needed to meet such agreed warming levels and of the associated climate impacts under temperature stabilization. Here, we apply the Adaptive Emission Reduction Approach (AERA) with ESMs to provide such simulations in which all models converge at 1.5 and 2.0 °C warming levels by adjusting their emissions over time. These emission-driven simulations provide a wide range of emission pathways and resulting atmospheric CO 2 projections for a given warming level, uncovering uncertainty ranges that were previously missing in the traditional Coupled Model Intercomparison Project (CMIP) scenarios with prescribed greenhouse gas concentration pathways. Meeting the 1.5 °C warming level requires a 40 % (full model range: 7 % to 76 %) reduction in multi-model mean CO 2 -forcing-equivalent (CO 2 -fe) emissions from 2025 to 2030, a 98 % (57 % to 127 %) reduction from 2025 to 2050, and a stabilization at 1.0 (−1.7 to 2.9) PgC yr−1 from 2100 onward after the 1.5 °C global warming level is reached. Meeting the 2.0 °C warming level requires a 47 % (8 % to 92 %) reduction in multi-model mean CO 2 -fe emissions until 2050 and a stabilization at 1.7 (−1.5 to 2.7) PgC yr−1 from 2100 onward. The on-average positive emissions under stabilized global temperatures are the result of a decreasing transient climate response to cumulative CO 2 -fe emissions over time under stabilized global warming. This evolution is consistent with a slightly negative zero emissions commitment – initially assumed to be zero – and leads to an increase in the post-2025 CO 2 -fe emission budget by a factor of 2.2 (−0.8 to 6.9) by 2150 for the 1.5 °C warming level and a factor of 1.4 (0.9 to 2.4) for the 2.0 °C warming level compared to its first estimate in 2025. The median CO 2 -only carbon budget by 2150, relative to 2020, is 800 GtCO 2 for the 1.5 °C warming level and 2250 GtCO 2 for the 2.0 °C warming level. These median values exceed the median IPCC AR6 estimates by 60 % for the 1.5 °C warming level and 67 % for 2.0 °C. Some of the differences may be explained by the choice of the mitigation scenario for non-CO 2 radiative agents. Our simulations highlight shifts in carbon uptake dynamics under stabilized temperature, such as a cessation of the carbon sinks in the North Atlantic and in tropical forests. On the other hand, the Southern Ocean remains a carbon sink centuries after temperatures stabilize. Overall, this new type of warming-level-based emission-driven simulation offers a more coherent assessment across climate models and opens up a wide range of possibilities for studying both the carbon cycle and climate impacts, such as extreme events, under climate stabilization.

Adaptive Emission Reduction Approach↗
DOE OSTI2024

Nanocrystal Assemblies: Current Advances and Open Problems

Here we explore the potential of nanocrystals (a term used equivalently to nanoparticles) as building blocks for nanomaterials, and the current advances and open challenges for fundamental science developments and applications. Nanocrystal assemblies are inherently multiscale, and the generation of revolutionary material properties requires a precise understanding of the relationship between structure and function, the former being determined by classical effects and the latter often by quantum effects. With an emphasis on theory and computation, we discuss challenges that hamper current assembly strategies and to what extent nanocrystal assemblies represent thermodynamic equilibrium or kinetically trapped metastable states. We also examine dynamic effects and optimization of assembly protocols. Finally, we discuss promising material functions and examples of their realization with nanocrystal assemblies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2016

Multi-Sensor Cloud and Aerosol Retrieval Simulator and Remote Sensing from Model Parameters : Aerosols - Part 2

The Multi-sensor Cloud Retrieval Simulator (MCRS) produces a simulated radiance product from any high-resolution general circulation model with interactive aerosol as if a specific sensor such as the Moderate Resolution Imaging Spectroradiometer (MODIS) were viewing a combination of the atmospheric column and land ocean surface at a specific location. Previously the MCRS code only included contributions from atmosphere and clouds in its radiance calculations and did not incorporate properties of aerosols. In this paper we added a new aerosol properties module to the MCRS code that allows users to insert a mixture of up to 15 different aerosol species in any of 36 vertical layers. This new MCRS code is now known as MCARS (Multi-sensor Cloud and Aerosol Retrieval Simulator). Inclusion of an aerosol module into MCARS not only allows for extensive, tightly controlled testing of various aspects of satellite operational cloud and aerosol properties retrieval algorithms, but also provides a platform for comparing cloud and aerosol models against satellite measurements. This kind of two-way platform can improve the efficacy of model parameterizations of measured satellite radiances, allowing the assessment of model skill consistently with the retrieval algorithm. The MCARS code provides dynamic controls for appearance of cloud and aerosol layers. Thereby detailed quantitative studies of the impacts of various atmospheric components can be controlled. In this paper we illustrate the operation of MCARS by deriving simulated radiances from various data field output by the Goddard Earth Observing System version 5 (GEOS-5) model. The model aerosol fields are prepared for translation to simulated radiance using the same model sub grid variability parameterizations as are used for cloud and atmospheric properties profiles, namely the ICA technique. After MCARS computes modeled sensor radiances equivalent to their observed counterparts, these radiances are presented as input to operational remote-sensing algorithms. Specifically, the MCARS-computed radiances are input into the processing chain used to produce the MODIS Data Collection 6 aerosol product (MOYD04). TheMOYD04 product is of course normally produced from MOYD021KM MODIS Level-1B radiance product directly acquired by the MODIS instrument. MCARS matches the format and metadata of a MOYD021KM product. The resulting MCARS output can be directly provided to MODAPS (MODIS Adaptive Processing System) as input to various operational atmospheric retrieval algorithms. Thus the operational algorithms can be tested directly without needing to make any software changes to accommodate an alternative input source. We show direct application of this synthetic product in analysis of the performance of the MOD04 operational algorithm. We use biomass-burning case studies over Amazonia employed in a recent Working Group on Numerical Experimentation (WGNE)-sponsored study of aerosol impacts on numerical weather prediction (Freitas et al., 2015). We demonstrate that a known low bias in retrieved MODIS aerosol optical depth appears to be due to a disconnect between actual column relative humidity and the value assumed by the MODIS aerosol product.

aerosol retrieval↗
NASA NTRS2016

Analysis and Characterization of Damage and Failure Utilizing a Generalized Composite Material Model Suitable for Use in Impact Problems

A material model which incorporates several key capabilities which have been identified by the aerospace community as lacking in state-of-the art composite impact models is under development. In particular, a next generation composite impact material model, jointly developed by the FAA and NASA, is being implemented into the commercial transient dynamic finite element code LS-DYNA. The material model, which incorporates plasticity, damage, and failure, utilizes experimentally based tabulated input to define the evolution of plasticity and damage and the initiation of failure as opposed to specifying discrete input parameters (such as modulus and strength). The plasticity portion of the orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. For the damage model, a strain equivalent formulation is utilized to allow for the uncoupling of the deformation and damage analyses. In the damage model, a semi-coupled approach is employed where the overall damage in a particular coordinate direction is assumed to be a multiplicative combination of the damage in that direction resulting from the applied loads in the various coordinate directions. Due to the fact that the plasticity and damage models are uncoupled, test procedures and methods to both characterize the damage model and to covert the material stress-strain curves from the true (damaged) stress space to the effective (undamaged) stress space have been developed. A methodology has been developed to input the experimentally determined composite failure surface in a tabulated manner. An analytical approach is then utilized to track how close the current stress state is to the failure surface.

Finite Element Method↗
NASA NTRS2017

Incorporation of Failure Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased use in the aerospace and automotive communities. The aerospace community has identified several key capabilities which are currently lacking in the available material models in commercial transient dynamic finite element codes. To attempt to improve the predictive capability of composite impact simulations, a next generation material model is being developed for incorporation within the commercial transient dynamic finite element code LS-DYNA. The material model, which incorporates plasticity, damage and failure, utilizes experimentally based tabulated input to define the evolution of plasticity and damage and the initiation of failure as opposed to specifying discrete input parameters such as modulus and strength. The plasticity portion of the orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. For the damage model, a strain equivalent formulation is used to allow for the uncoupling of the deformation and damage analyses. In the damage model, a semi-coupled approach is employed where the overall damage in a particular coordinate direction is assumed to be a multiplicative combination of the damage in that direction resulting from the applied loads in various coordinate directions. For the failure model, a tabulated approach is utilized in which a stress or strain based invariant is defined as a function of the location of the current stress state in stress space to define the initiation of failure. Failure surfaces can be defined with any arbitrary shape, unlike traditional failure models where the mathematical functions used to define the failure surface impose a specific shape on the failure surface. In the current paper, the complete development of the failure model is described and the generation of a tabulated failure surface for a representative composite material is discussed.

Impact↗