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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Confronting Models with Data: The GEWEX Cloud Systems Study

The GEWEX Cloud System Study (GCSS; GEWEX is the Global Energy and Water Cycle Experiment) was organized to promote development of improved parameterizations of cloud systems for use in climate and numerical weather prediction models, with an emphasis on the climate applications. The strategy of GCSS is to use two distinct kinds of models to analyze and understand observations of the behavior of several different types of clouds systems. Cloud-system-resolving models (CSRMs) have high enough spatial and temporal resolutions to represent individual cloud elements, but cover a wide enough range of space and time scales to permit statistical analysis of simulated cloud systems. Results from CSRMs are compared with detailed observations, representing specific cases based on field experiments, and also with statistical composites obtained from satellite and meteorological analyses. Single-column models (SCMs) are the surgically extracted column physics of atmospheric general circulation models. SCMs are used to test cloud parameterizations in an un-coupled mode, by comparison with field data and statistical composites. In the original GCSS strategy, data is collected in various field programs and provided to the CSRM Community, which uses the data to "certify" the CSRMs as reliable tools for the simulation of particular cloud regimes, and then uses the CSRMs to develop parameterizations, which are provided to the GCM Community. We report here the results of a re-thinking of the scientific strategy of GCSS, which takes into account the practical issues that arise in confronting models with data. The main elements of the proposed new strategy are a more active role for the large-scale modeling community, and an explicit recognition of the importance of data integration.

Randall, David↗
DOE OSTI2021

Large-Scale Welding Process Simulation by GPU Parallelized Computing

The computational design of industrially relevant welded structures is extremely time consuming due to coupled physics and high nonlinearity. Previously, most welding distortion and residual stress simulations have been limited to small coupons and reduced order (from three-dimensional [3D] to two-dimensional [2D]), or inherent strain approximations were used for large structures. In this current study, an explicit finite element code based on a graphics processing unit was utilized to perform 3D transient thermomechanical simulation of structural components during welding. Laser brazing of aluminum alloy panels as representative of automotive manufacturing scenarios was simulated to predict out-of-plane distortion under different clamping conditions. The predicted deformation pattern and magnitude were validated by laser scanning data of physical assemblies. In addition, the code was used to investigate residual stresses developed during multipass arc welding of a nuclear industry pressurizer surge nozzle and subsequent welding repair where a 3D simulation was necessary. Taking the experimental data as reference, the 3D model predicted better residual stress distribution than a typical 2D asymmetrical model. Stress evolution in welding repair was also presented and discussed in this study. Furthermore, the efficient numerical model made it feasible to use integrated computational welding engineering to simulate welding processes for large-scale structures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Linear two-pool models are insufficient to infer soil organic matter decomposition temperature sensitivity from incubations

Abstract Terrestrial carbon (C)-climate feedbacks depend strongly on how soil organic matter (SOM) decomposition responds to temperature. This dependency is often represented in land models by the parameter Q 10 , which quantifies the relative increase of microbial soil respiration per 10 °C temperature increase. Many studies have conducted paired laboratory soil incubations and inferred “active” and “slow” pool Q 10 values by fitting linear two-pool models to measured respiration time series. Using a recently published incubation study (Qin et al. in Sci Adv 5(7):eaau1218, 2019) as an example, here we first show that the very high parametric equifinality of the linear two-pool models may render such incubation-based Q 10 estimates unreliable. In particular, we show that, accompanied by the uncertain initial active pool size, the slow pool Q 10 can span a very wide range, including values as high as 100, although all parameter combinations are producing almost equally good model fit with respect to the observations. This result is robust whether or not interactions between the active and slow pools are considered (typically these interactions are not considered when interpreting incubation data, but are part of the predictive soil carbon models). This very large parametric equifinality in the context of interpreting incubation data is consistent with the poor temporal extrapolation capability of linear multi-pool models identified in recent studies. Next, using a microbe-explicit SOM model (RESOM), we show that the inferred two pools and their associated parameters (e.g., Q 10 ) could be artificial constructs and are therefore unreliable concepts for integration into predictive models. We finally discuss uncertainties in applying linear two-pool (or more generally multiple-pool) models to estimate SOM decomposition parameters such as temperature sensitivities from laboratory incubations. We also propose new observations and model structures that could enable better process understanding and more robust predictive capabilities of soil carbon dynamics.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1985

Bounding solutions of geometrically nonlinear viscoelastic problems

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Stubstad, J. M.↗
NASA NTRS1986

Bounding solutions of geometrically nonlinear viscoelastic problems

Integral transform techniques, such as the Laplace transform, provide simple and direct methods for solving viscoelastic problems formulated within a context of linear material response and using linear measures for deformation. Application of the transform operator reduces the governing linear integro-differential equations to a set of algebraic relations between the transforms of the unknown functions, the viscoelastic operators, and the initial and boundary conditions. Inversion either directly or through the use of the appropriate convolution theorem, provides the time domain response once the unknown functions have been expressed in terms of sums, products or ratios of known transforms. When exact inversion is not possible approximate techniques may provide accurate results. The overall problem becomes substantially more complex when nonlinear effects must be included. Situations where a linear material constitutive law can still be productively employed but where the magnitude of the resulting time dependent deformations warrants the use of a nonlinear kinematic analysis are considered. The governing equations will be nonlinear integro-differential equations for this class of problems. Thus traditional as well as approximate techniques, such as cited above, cannot be employed since the transform of a nonlinear function is not explicitly expressible.

Stubstad, J. M.↗
DOE OSTI2020

Open quantum systems and Schwinger-Keldysh holograms

We initiate the study of open quantum field theories using holographic methods. Specifically, we consider a quantum field theory (the system) coupled to a holographic field theory at finite temperature (the environment). We investigate the effects of integrating out the holographic environment with an aim of obtaining an effective dynamics for the resulting open quantum field theory. The influence functionals which enter this open effective action are determined by the real-time (Schwinger-Keldysh) correlation functions of the holographic thermal environment. To evaluate the latter, we exploit recent developments, wherein the semiclassical gravitational Schwinger-Keldysh saddle geometries were identified as complexified black hole spacetimes. We compute real-time correlation functions using holographic methods in these geometries, and argue that they lead to a sensible open effective quantum dynamics for the system in question, a question that hitherto had been left unanswered. In addition to shedding light on open quantum systems coupled to strongly correlated thermal environments, our results also provide a principled computation of Schwinger-Keldysh observables in gravity and holography. In particular, these influence functionals we compute capture both the dissipative physics of black hole quasi- normal modes, as well as that of the fluctuations encoded in outgoing Hawking quanta, and interactions between them. We obtain results for these observables at leading order in a low frequency and momentum expansion in general dimensions, in addition to determining explicit results for two dimensional holographic CFT environments.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1998

The Space-Time Conservation Element and Solution Element Method: A New High-Resolution and Genuinely Multidimensional Paradigm for Solving Conservation Laws: The Two Dimensional Time Marching Schemes - 1

A new high resolution and genuinely multidimensional numerical method for solving conservation laws is being, developed. It was designed to avoid the limitations of the traditional methods. and was built from round zero with extensive physics considerations. Nevertheless, its foundation is mathmatically simple enough that one can build from it a coherent, robust. efficient and accurate numerical framework. Two basic beliefs that set the new method apart from the established methods are at the core of its development. The first belief is that, in order to capture physics more efficiently and realistically, the modeling, focus should be placed on the original integral form of the physical conservation laws, rather than the differential form. The latter form follows from the integral form under the additional assumption that the physical solution is smooth, an assumption that is difficult to realize numerically in a region of rapid chance. such as a boundary layer or a shock. The second belief is that, with proper modeling of the integral and differential forms themselves, the resulting, numerical solution should automatically be consistent with the properties derived front the integral and differential forms, e.g., the jump conditions across a shock and the properties of characteristics. Therefore a much simpler and more robust method can be developed by not using the above derived properties explicitly.

Chang, Sin-Chung↗
DOE OSTI2025

A physics-constrained neural ordinary differential equations approach for robust learning of stiff chemical kinetics

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. While deep learning techniques have been explored to develop faster surrogate models, they often fail to integrate reliably with CFD solvers. This instability arises because traditional deep learning approaches optimize for training error without ensuring compatibility with ordinary differential equation (ODE) solvers, resulting in accumulation of errors over time. Recently, neuralODE (NODE) based approaches have been shown to be a promising technique to emulate and accelerate detailed chemistry computations. Here, in the present work, we extend this NODE framework for stiff chemical kinetics by incorporating mass conservation constraints directly into the loss function during training. This ensures that the total mass as well as the individual elemental species masses are conserved in an a-posteriori manner. Proof-of-concept studies are performed with the novel physics-constrained NODE (PC-NODE) approach for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions. It is demonstrated that the PC-NODE framework not only improves the physical consistency of the resulting data-driven model with respect to mass conservation criteria, but also improves training efficiency. PC-NODE is shown to achieve 2–100× speedup relative to the hydrogen-air detailed chemical mechanism depending on the type of the ODE solver (implicit or explicit) used during autoregressive inference tests. Lastly, a-posteriori studies are performed wherein the trained PC-NODE model is coupled with a CFD solver. It is shown that higher accuracy is achieved with PC-NODE relative to the purely data-driven NODE approach. Moreover, PC-NODE also exhibits robustness and generalizability to unseen initial conditions from within (interpolative capability) as well as outside (extrapolative capability) the training regime.

computational combustion↗
DOE OSTI2026

Joint scheduling of energy, fast and primary frequency response reserves in integrated transmission–distribution networks

Inverter-based distributed energy resources (DERs) connected to distribution networks (DNs) can provide fast frequency support, but their reserve deliverability depends on feeder constraints and differs from synchronous primary frequency response (PFR). Existing transmission–distribution coordination studies usually treat reserve generically or neglect feeder-level feasibility, while frequency-security scheduling studies rarely represent distribution feeders explicitly. This paper develops a bi-level day-ahead scheduling framework for integrated transmission–distribution networks that jointly clears energy, transmission-side PFR, and distribution-side fast frequency response (FFR) under exogenous hourly inertia and largest-loss inputs from an external unit commitment (UC) schedule. The transmission problem is modeled with DC-optimal power flow (OPF) and closed-form second-order cone (SOC) frequency-security constraints, whereas each DN is represented by a reserve-aware branch-flow AC-OPF so that scheduled fast reserves remain deliverable during activation. The bi-level problem is reformulated through Karush–Kuhn–Tucker (KKT) conditions into a mixed-integer SOC program, and a penalty term is used to tighten the distribution-network relaxation. In the reduced test system, lower exogenous inertia increased the required primary response from 179.64 MW to 191.08 MW, distribution-side fast response reduced total frequency-response procurement by up to 4.9%, and neglecting distribution constraints overstated the combined distribution-side energy and reserve award by up to 18%. In the expanded study, the largest case was solved in 2.02 s with a 0.00% optimality gap. Time-domain simulations kept the frequency nadir above 59.0 Hz in all tested hours. These results demonstrate the value of fast-response modeling and distribution-feasible reserve delivery in coordinated market clearing.

Noh, Seung-Gil↗
DOE OSTI2024

Projecting Large Fires in the Western US With an Interpretable and Accurate Hybrid Machine Learning Method

More frequent and widespread large fires are occurring in the western United States (US), yet reliable methods for predicting these fires, particularly with extended lead times and a high spatial resolution, remain challenging. In this study, we proposed an interpretable and accurate hybrid machine learning (ML) model, that explicitly represented the controls of fuel flammability, fuel availability, and human suppression effects on fires. The model demonstrated notable accuracy with a F 1 -score of 0.846 ± 0.012, surpassing process-driven fire danger indices and four commonly used ML models by up to 40% and 9%, respectively. More importantly, the ML model showed remarkably higher interpretability relative to other ML models. Specifically, by demystifying the “black box” of each ML model using the explainable AI techniques, we identified substantial structural differences across ML fire models, even among those with similar accuracy. The relationships between fires and their drivers, identified by our model, were aligned closer with established fire physical principles. The ML structural discrepancy led to diverse fire predictions and our model predictions exhibited greater consistency with actual fire occurrence. With the highly interpretable and accurate model, we revealed the strong compound effects from multiple climate variables related to evaporative demand, energy release component, temperature, and wind speed, on the dynamics of large fires and megafires in the western US. Our findings highlight the importance of assessing the structural integrity of models in addition to their accuracy. They also underscore the critical need to address the rise in compound climate extremes linked to large wildfires.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

Explicit structure-preserving geometric particle-in-cell (PIC) algorithm in curvilinear orthogonal coordinate systems is developed. The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research. The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms, discrete exterior calculus, and explicit non-canonical symplectic integration. In addition to the truncated infinitely dimensional symplectic structure, the algorithm preserves exactly many important physical symmetries and conservation laws, such as local energy conservation, gauge symmetry and the corresponding local charge conservation. As a result, the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics. The algorithm has been implemented in the SymPIC code, which is designed for high-efficiency massively-parallel PIC simulations in modern clusters. The code has been applied to carry out whole-device 6D kinetic simulation studies of tokamak physics. A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor. The state also admits a steady-state sub-sonic ion flow in the range of 10 km s -1 , agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated. It is shown that high-n ballooning modes have larger growth rates than low-n global modes, and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2% level by the E × B flow generated by the instability. These results are consistent with early and recent electromagnetic gyrokinetic simulations.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Should We Conserve Entropy or Energy when Computing CAPE with Mixed-Phase Precipitation Physics?

Abstract The rapidly increasing resolution of global atmospheric reanalysis and climate model datasets necessitates finding methods for computing convective available potential energy (CAPE) both efficiently and accurately. To this end, this article compares two common methods for computing CAPE which conserve either energy or entropy. Inaccuracies in these computations arise from both physical and numerical errors. For instance, computing CAPE with entropy conserved results in physical errors from nonequilibrium phase transitions but minimizes numerical errors because solutions are analytic at each height. In contrast, computing CAPE with energy conserved avoids these physical errors, but accumulates numerical errors that are grid-resolution-dependent because the numerical integration of a differential equation is required. Analysis of CAPE computed with large databases of soundings from the tropical Amazon and midlatitude storm environments shows that physical errors from the entropy method are typically 1%–3% as large as CAPE, which is comparable to the numerical errors from conserving energy with grid spacing of 25 and 250 m using explicit first-order and second-order integration schemes, respectively. Errors in entropy-based CAPE calculations are also insensitive to vertical grid spacing, in contrast to energy-based calculations whose error strongly scales with the grid spacing. It is shown that entropy-based methods are advantageous when intercomparing datasets with differing vertical resolution because they produce accurate and reasonably fast results that are insensitive to grid resolution, whereas a second-order energy-based method is advantageous when analyzing data with a consistent vertical resolution because of its superior computational efficiency. Significance Statement Convective available potential energy (CAPE) is a measure of instability in the atmosphere that helps forecasters and researchers understand when and where thunderstorms will form. The purpose of this article is to identify the most efficient and accurate methods for computing CAPE. Two methods are considered here, one that relates to the entropy (a measure of thermodynamic disorder) of an air parcel and one that relates to the energy of an air parcel. Results indicate that the entropy method is most accurate and insensitive to the resolution of the data used for the calculation (which can vary considerably), whereas the energy method uses the least computation time.

Peters, John M.↗
DOE OSTI2020

Traffic Prediction for Merging Coordination Control in Mixed Traffic Scenarios

Connected and autonomous vehicles (CAVs) have the potential to bring in safety, mobility, and energy benefits to transportation. The control decisions of CAVs are usually determined for a look-ahead horizon based on previewed traffic information. This requires an effective prediction of future traffic conditions and its integration with the CAV control framework. However, the short-term traffic prediction using information from connectivity is a challenging research topic, especially for mixed traffic scenarios. This work focuses on the development of a traffic prediction framework for a merging coordination controller. The previously developed merging controller coordinates the merging sequence and travel speed of CAVs to maximize the energy efficiency and overall mobility. In mixed traffic scenarios, the controller receives information regarding the position of all the vehicles traveling inside a control zone and controls the desired speed of all CAVs. The controller has no control on the human-driven vehicles. The merging controller does not have direct information or an explicit prediction on the behaviors of human-driven vehicles. Aiming to improve the performance of the merging controller in various mixed traffic conditions, a traffic prediction algorithm is developed and evaluated in this work. The performance of this traffic prediction algorithm is investigated for various penetration rates of connectivity for a single-lane secondary road merging to a single-lane primary road. The results show that compared to a constant speed assumption of human-driven vehicles, the proposed traffic prediction algorithm is able to reduce the prediction error of the arrival time of human-driven vehicles at the merging zone by more than 50%.

Shao, Yunli↗
NASA NTRS2003

Precision Agriculture: Changing the Face of Farming

To a large extent our work has grown out of the remote sensing technology and conceptual framework developed by geologists. For example the drive to look at the physics of reflectance and atmospheric corrections is rooted in work done in the early 1980s by the United States Geological Survey and NASA. Our work on emissivity and thermal behavior of plants pulls on research done using the Thermal Infrared Multispectral Scanner, an instrument originally conceived for geologic applications. Even our ability to geometrically map the airborne imagery onto the globe was explicitly developed because of need to map sediment flow patterns in along the coast of Louisiana. Growing from this base we have learned much in the last few years and believe our integration of geologic remote sensing with the other fields of expertise was a wise investment. Clearly none of the specialties alone could develop, let alone test, the basic approach we are now finding so powerful. This is the path that will ultimately give the information needed by the farmer. We also recognize how small a portion of the total problem has been solved. Having developed the basic logic, built proto-type tools and performed initial tests everything else remains to be done. And problems, scientific and practical, are everywhere. We have not established sensitivities. We have not robustly segregated the contributions of crop residue, soil moisture, shadows, plant and soil to the energy leaving the surface. What we do is extremely expensive and difficult. It is experimental in methodology and uses research oriented tools. We are constantly alive to the practicality of moving our results into commercial applications. We know another airborne instrument will have to be available. Atmospheric parameters will have to be measured automatically. The software will have to be re-written for speed. At times the list of problems seems endless. But the potential is also enormous. Agriculture is a huge portion of our economy. Just a one percent increase in efficiency is a $2,000,000 change. We all depend on farmers, literally for the bread we eat. No other activity of man even has an impact on the land that farming has. If application of precision agriculture can nelp farmers manage their land better, we all may benefit.

Rickman, D.↗
DOE OSTI2023

Integrated Process Optimization for Biochemical Conversion

This research is motivated by the challenges faced during biomass processing in bioenergy plants. It has been observed that variations in biomass characteristics, such as moisture, ash, and carbohydrate contents cause variations in feeding of the system which led to underutilization of equipment and the reactor. The objective of this research is to ensure a continuous flow of biomass to the reactor in plants that use the biochemical conversion process to generate liquid fuels. The overall goal is to lower the cost of producing biofuels, which could lead to improving US’s energy independency and growing US’s rural economy. The research team developed analytical models, such as discrete element method (DEM) models and mathematical models. The DEM models are unit-level models that explicitly capture biomass characteristics and quantify the impacts of biomass characteristics on bulk material properties and the performance of specific equipment. The mathematical models are system-level models that capture the impacts of system infeed rate, equipment processing rate, storage location and capacity, and biomass characteristics on system throughput. The functional relations predicting the bulk material properties from DEM models are incorporated to the mathematical models. The models developed were validated and evaluated using data collected at Idaho National Laboratory’s biomass processing facility. Via these models, we identified process control strategies that ensure a continuous flow of biomass to the reactor, while meeting the requirements of biochemical conversion process. Our analysis indicates that sequencing of biomass bales based on moisture level, and carbohydrate contents could have a positive impact on reducing processing time and inventory level and increasing throughput rate. Short bale sequences that repeat frequently, seem to have the greatest impact on improving system’s performance. Based on our experiments, the total annual system operating costs reduced by 20-30%, and the maximum inventory level reduced by 3 to 4 times. The operating costs include the annual equipment amortization cost and processing cost. The implementation of the models developed requires the use of standardized bale format, Radio Frequency Identification technology, sensing and real time monitoring of material attributes, automated material handling equipment, and automated process control. The scope of the model proposed can be extended to include the whole supply chain. The supply chain models help identify how many bales of different biomass feedstock to purchase given biomass availability in the region, biomass price and quality, and the biomass processing capabilities of the biorefinery. Thus, the outcomes of supply chain models can be used to inform the design of long-term contracts among farmers and the biorefinery.

09 BIOMASS FUELS↗
DOE OSTI2021

Scalar field in Reissner–Nordström spacetime: Bound state and scattering state (with appendix on eliminating oscillation in partial sum approximation of periodic function)

Highlights: • Bound-state and scattering-state solutions of massive scalar fields in R-N spacetime. • Bound-state wave functions and eigenvalues of massive scalar fields in R-N spacetime. • Solving explicit expressions of scattering phase shifts by integral equation methods. • Introducing tortoise coordinates for R-N spacetime. • Eliminating oscillations in the partial sum approximation of periodic functions. In this paper, we solve the massive scalar field in the Reissner–Nordström spacetime. The scalar field in the Reissner–Nordström spacetime has both bound states and scattering states. For bound states, we solve the bound-state wave function and the eigenvalue spectrum. For scattering states, we solve the scattering wave function and give an explicit expression for scattering phase shift by the integral equation method. Especially, we introduce the tortoise coordinate for the Reissner–Nordström spacetime. Moreover, in the calculation of scattering cross sections, we encounter a difficulty in partial sum approximation. If the sum of partial waves cannot be performed exactly, one has to turn to the partial sum approximation which approximates a function by the first several terms of the series. However, in the partial sum approximation there exists an incorrect oscillation which cannot be eliminated by keeping more terms. In the appendix we suggest an approach for eliminating such oscillations in the partial sum.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1995

Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 1: Theoretical developments and applications

This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present first part of the report, we focus on the theoretical developments, and discussions of the results of numerical-performance studies using the integration schemes for GVIPS and NAV models.

Saleeb, Atef F.↗
NASA NTRS1995

Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 2: Algorithmic developments and implementation

This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present second part of the report, we focus on the specific details of the numerical schemes, and associated computer algorithms, for the finite-element implementation of GVIPS and NAV models.

Li, Wei↗