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NASA NTRSDate not supplied

Parallel Hybrid Turboprop Performance Modeling and Optimization

NASA’s Electrified Powertrain Flight Demonstration (EPFD) project conducts ground and flight tests of integrated Megawatt (MW) class hybrid-electric powertrain systems on regional turboprop aircraft demonstrators. To meet the increased demand for assessment of potential capabilities and benefits from these novel vehicle configurations, NASA is developing tooling and models to estimate the performance of hybridized regional turboprops. This paper covers the development of a parametrically driven performance model for a De Havilland Canada Dash 8-400 (Q400) regional turboprop integrated with a novel parallel hybrid architecture using the Gascon framework. Gascon is a modern reimplementation of the General Aviation Synthesis Program (GASP) built using the Condor mathematical modeling framework in Python. Within Gascon, a parametric representation of the parallel hybrid architecture was synthesized, which features the electric motor coupled to the power turbine. This capability allows for in-the-loop optimization of the parametric parallel hybrid architecture to characterize the mission capabilities and fuel savings of the design and determine optimal power scheduling strategies for efficient electric power management for a given mission. The study shows that a fuel savings of up to 20% can be achieved, but that increased fuel savings comes at the expense of payload capacity.

Gascon↗

NASA NTRSDate not supplied

Parallel Hybrid Turboprop Performance Modeling and Optimization

Gascon↗

NASA NTRS2012

Validation of Atmosphere/Ionosphere Signals Associated with Major Earthquakes by Multi-Instrument Space-Borne and Ground Observations

The latest catastrophic earthquake in Japan (March 2011) has renewed interest in the important question of the existence of pre-earthquake anomalous signals related to strong earthquakes. Recent studies have shown that there were precursory atmospheric/ionospheric signals observed in space associated with major earthquakes. The critical question, still widely debated in the scientific community, is whether such ionospheric/atmospheric signals systematically precede large earthquakes. To address this problem we have started to investigate anomalous ionospheric / atmospheric signals occurring prior to large earthquakes. We are studying the Earth's atmospheric electromagnetic environment by developing a multisensor model for monitoring the signals related to active tectonic faulting and earthquake processes. The integrated satellite and terrestrial framework (ISTF) is our method for validation and is based on a joint analysis of several physical and environmental parameters (thermal infrared radiation, electron concentration in the ionosphere, lineament analysis, radon/ion activities, air temperature and seismicity) that were found to be associated with earthquakes. A physical link between these parameters and earthquake processes has been provided by the recent version of Lithosphere-Atmosphere-Ionosphere Coupling (LAIC) model. Our experimental measurements have supported the new theoretical estimates of LAIC hypothesis for an increase in the surface latent heat flux, integrated variability of outgoing long wave radiation (OLR) and anomalous variations of the total electron content (TEC) registered over the epicenters. Some of the major earthquakes are accompanied by an intensification of gas migration to the surface, thermodynamic and hydrodynamic processes of transformation of latent heat into thermal energy and with vertical transport of charged aerosols in the lower atmosphere. These processes lead to the generation of external electric currents in specific regions of the atmosphere and the modifications, by dc electric fields, in the ionosphere-atmosphere electric circuit. We retrospectively analyzed temporal and spatial variations of four different physical parameters (gas/radon counting rate, lineaments change, long-wave radiation transitions and ionospheric electron density/plasma variations) characterizing the state of the lithosphere/atmosphere coupling several days before the onset of the earthquakes. Validation processes consist in two phases: A. Case studies for seven recent major earthquakes: Japan (M9.0, 2011), China (M7.9, 2008), Italy (M6.3, 2009), Samoa (M7, 2009), Haiti (M7.0, 2010) and, Chile (M8.8, 2010) and B. A continuous retrospective analysis was preformed over two different regions with high seismicity- Taiwan and Japan for 2003-2009. Satellite, ground surface, and troposphere data were obtained from Terra/ASTER, Aqua/AIRS, POES and ionospheric variations from DEMETER and COSMIC-I data. Radon and GPS/TEC were obtaining from monitoring sites in Taiwan, Japan and Italy and from global ionosphere maps (GIM) respectively. Our analysis of ground and satellite data during the occurrence of 7 global earthquakes has shown the presence of anomalies in the atmosphere. Our results for Tohoku M9.0 earthquake show that on March 7th, 2011 (4 days before the main shock and 1 day before the M7.2 foreshock of March 8, 2011) a rapid increase of emitted infrared radiation was observed by the satellite data and an anomaly was developed near the epicenter. The GPS/TEC data indicate an increase and variation in electron density reaching a maximum value on March 8. From March 3 to 11 a large increase in electron concentration was recorded at all four Japanese ground-based ionosondes, which returned to normal after the main earthquake. Similar approach for analyzing atmospheric and ionospheric parameters has been applied for China (M7.9, 2008), Italy (M6.3, 2009), Samoa (M7, 2009), Haiti (M7.0, 2010) and Chile (M8.8, 2010) eahquakes. Results have revealed the presence of related variations of these parameters implying their connection with the earthquake process. The second phase (B) of this validation included 102 major earthquakes (M>5.9) in Taiwan and Japan. We have found anomalous behavior before all of these events with no false negatives. False alarm ratio for false positives is less then 10% and has been calculated for the same month of the earthquake occurrence for the entire period of analysis (2003-2009). The commonalities for detecting atmospheric/ionospheric anomalies are: i.) Regularly appearance over regions of maximum stress (i.e., along plate boundaries); ii.) Anomaly existence over land and sea; and iii) association with M>5.9 earthquakes not deeper than 100km. Due to their long duration over the same region these anomalies are not consistent with a meteorological origin. Our initial results from the ISTF validation of multi-instrument space-borne and ground observations show a systematic appearance of atmospheric anomalies near the epicentral area, one to seven (average) days prior to the largest earthquakes, and suggest that it could be explained by a coupling process between the observed physical parameters and the pre-earthquake preparation processes.

Ouzounov, Dimitar↗

DOE OSTI2025

Chromatin structures from integrated AI and polymer physics model

The physical organization of the genome in three-dimensional space regulates many biological processes, including gene expression and cell differentiation. Three-dimensional characterization of genome structure is critical to understanding these biological processes. Direct experimental measurements of genome structure are challenging; computational models of chromatin structure are therefore necessary. We develop an approach that combines a particle-based chromatin polymer model, molecular simulation, and machine learning to efficiently and accurately estimate chromatin structure fromindirectmeasures of genome structure. More specifically, we introduce a new approach where the interaction parameters of the polymer model are extracted from experimental Hi-C data using a graph neural network (GNN). We train the GNN on simulated data from the underlying polymer model, avoiding the need for large quantities of experimental data. The resulting approach accurately estimates chromatin structures across all chromosomes and across several experimental cell lines despite being trained almost exclusively on simulated data. The proposed approach can be viewed as a general framework for combining physical modeling with machine learning, and it could be extended to integrate additional biological data modalities. Ultimately, we achieve accurate and high-throughput estimations of chromatin structure from Hi-C data, which will be necessary as experimental methodologies, such as single-cell Hi-C, improve.

Biochemistry & Molecular Biology↗

DOE OSTI2023

Bayesian optimal experimental design for constitutive model calibration

Computational simulation is increasingly relied upon for high/consequence engineering decisions, which necessitates a high confidence in the calibration of and predictions from complex material models. However, the calibration and validation of material models is often a discrete, multi-stage process that is decoupled from material characterization activities, which means the data collected does not always align with the data that is needed. To address this issue, an integrated workflow for delivering an enhanced characterization and calibration procedure—Interlaced Characterization and Calibration (ICC)—is introduced and demonstrated. Further, this framework leverages Bayesian optimal experimental design (BOED), which creates a line of communication between model calibration needs and data collection capabilities in order to optimize the information content gathered from the experiments for model calibration. Eventually, the ICC framework will be used in quasi real-time to actively control experiments of complex specimens for the calibration of a high-fidelity material model. This work presents the critical first piece of algorithm development and a demonstration in determining the optimal load path of a cruciform specimen with simulated data. Calibration results, obtained via Bayesian inference, from the integrated ICC approach are compared to calibrations performed by choosing the load path a priori based on human intuition, as is traditionally done. The calibration results are communicated through parameter uncertainties which are propagated to the model output space (i.e. stress–strain). In these exemplar problems, data generated within the ICC framework resulted in calibrated model parameters with reduced measures of uncertainty compared to the traditional approaches.

42 ENGINEERING↗

DOE OSTI2020

Repair and Resource Scheduling in Unbalanced Distribution Systems Using Neighborhood Search

—This paper proposes an optimization strategy to assist utility operators to recover power distribution systems after large outages. Specifically, a mixed-integer linear programming (MILP) model is developed for co-optimizing crews, resources, and network operations. The MILP model coordinates damage isolation, network reconfiguration, distributed generator re-dispatch, and crew/resource logistics. In addition, a framework for integrating different types of photovoltaic (PV) systems in the restoration process is developed. We consider two different types of crews, namely, line crews for damage repair and tree crews for obstacle removal. We also model the repair resource logistic constraints. Furthermore, a new algorithm is developed for solving the distribution system repair and restoration problem (DSRRP). The algorithm starts by solving DSRRP using an assignmentbased method, then a neighborhood search method is designed to iteratively improve the solution. The proposed method is validated on modified IEEE 123- and 8500-bus distribution test systems.

Outage management↗

DOE OSTI2023

CompLaB v1.0: a scalable pore-scale model for flow, biogeochemistry, microbial metabolism, and biofilm dynamics

Abstract. Microbial activity and chemical reactions in porous media depend on the local conditions at the pore scale and can involve complex feedback with fluid flow and mass transport. We present a modeling framework that quantitatively accounts for the interactions between the bio(geo)chemical and physical processes and that can integrate genome-scale microbial metabolic information into a dynamically changing, spatially explicit representation of environmental conditions. The model couples a lattice Boltzmann implementation of Navier–Stokes (flow) and advection–diffusion-reaction (mass conservation) equations. Reaction formulations can include both kinetic rate expressions and flux balance analysis, thereby integrating reactive transport modeling and systems biology. We also show that the use of surrogate models such as neural network representations of in silico cell models can speed up computations significantly, facilitating applications to complex environmental systems. Parallelization enables simulations that resolve heterogeneity at multiple scales, and a cellular automaton module provides additional capabilities to simulate biofilm dynamics. The code thus constitutes a platform suitable for a range of environmental, engineering and – potentially – medical applications, in particular ones that involve the simulation of microbial dynamics.

58 GEOSCIENCES↗

DOE OSTI2020

A large-scale, agent-based simulation of metropolitan freight movements with passenger and freight market interactions

This study summarizes the first stage in the implementation of an agent-based freight modeling system that has a global representation of agents and detailed modeling of a large-scale transportation network. The model is used to evaluate the transportation and energy impacts of goods movement across urban and national scales. The framework is implemented within POLARIS, a C++-based Planning and Operations Language for Agent-based Regional Integrated Simulation, which consists of an activity-based modeling (ABM) and dynamic traffic assignment (DTA) system that has robust features for passenger travel. This platform provides a tool to model interactions among consumers, producers, and the transportation system. The main objective of this initial implementation is to implement a freight model within POLARIS following an agent-based paradigm with behavioral and simulation methods. This paper presents the initial framework and illustrates the application of the model. Building upon earlier works, a parcel location assignment algorithm for business establishments in the population is documented, along with a method for estimating establishment production and consumption volumes. In addition to population generation, other features of the model include push-pull supply chains, multimodal path choice, choice of transportation logistics node, and dynamic traffic assignment. A module with e-commerce supply and demand was also developed to analyze the effects of e-commerce delivery on last-mile energy use and congestion.

agent-based freight↗

DOE OSTI2026

From 2D to 4D: a containerized workflow and browser to explore dynamic chromatin architecture

Background Characterizing the physical organization of the genome is essential for understanding long-range gene regulation, chromatin compartmentalization, and epigenetic accessibility. Hi-C experiments generate two-dimensional (2D) genome-wide contact maps of chromatin interactions by capturing the spatial proximity between genomic loci, which reveal interaction frequencies but lack the spatial resolution needed to interpret the three-dimensional (3D) genome structure(s). Emerging evidence suggests that epigenetic regulation is closely linked to 3D genome architecture, and that structural changes over time (4D) drive key biological processes in development, disease, and environmental response. Thus, integrating 3D structure with functional data is critical for a more complete understanding of genome regulation. Previous work, most notably the 4DHiC chromosome modeling framework, has shown that physical multi-dimensional modeling approaches rooted in polymer physics and molecular dynamics can resolve these structures at biologically meaningful resolutions by integrating temporal Hi-C data with physical constraints to uncover dynamic chromosome reorganization. Thus, molecular dynamics simulations, constrained by Hi-C contact matrices, can resolve fine-scale structural changes and reveal functionally significant transitions in chromatin conformation. Results Herein, we present the 4D Genome Browser Workflow (4DGBWorkflow) and the 4D Genome Browser (4DGB). The algorithm is based on the 4DHiC method, and the containerized tool is an end-to-end workflow that can transform, filter, and view 4D epigenomics and chromatin datasets, allowing non-specialists to apply three-dimensional modeling principles to diverse datasets and experimental conditions. The software executes on a laptop running macOS, Linux or Windows. From input Hi-C files (.hic), the 4DGBWorkflow produces 3D reconstructions of chromosomes, integrates the reconstruction with track data (e.g., epigenetic marks, transcriptome profiles), and provides comparative visualization of the results in a single workflow. Conclusions The 4DGBWorkflow and 4D Genome Browser are open-source tools for comparative analysis and visualization of 4D chromosome datasets, including chromatin architecture and epigenomic signals. Automatic integration of Hi-C data with molecular dynamics democratizes the construction of time resolved 3D genome structures, simplifying complex simulations and data integration schemes.

3D Genome Browser↗

DOE OSTI2025

Probabilistic Deliverability Assessment of Distributed Energy Resources via Scenario-Based AC Optimal Power Flow

As electric grids decarbonize and distributed energy resources (DERs) become increasingly prevalent, interconnection assessments must evolve to reflect operational variability and control flexibility. This paper highlights key modeling limitations observed in practice and reviews approaches for modeling uncertainty. It then introduces a Probabilistic Deliverability Assessment (PDA) framework designed to complement and extend existing procedures. The framework integrates scenario-based AC optimal power flow (AC OPF), corrective dispatch, and optional multi-temporal constraints. Together, these form a structured methodology for quantifying DER utilization, deliverability, and reliability under uncertainty in load, generation, and topology. Outputs include interpretable metrics with confidence intervals that inform siting decisions and evaluate compliance with reliability thresholds across sampled operating conditions. A case study on Puerto Rico’s publicly available bulk power system model demonstrates the framework’s application using minimal input data, consistent with current interconnection practice. Across staged fossil generation retirements, the PDA identifies high-value DER sites and regions requiring additional reactive power support. Results are presented through mean dispatch signals, reliability metrics, and geospatial visualizations, demonstrating how the framework provides transparent, data-driven siting recommendations. The framework’s modular design supports incremental adoption within existing workflows, encouraging broader use of AC OPF in interconnection and planning contexts.

14 SOLAR ENERGY↗

DOE OSTI2026

Co-Location of Cellulosic Bioethanol and Alcohol-to-Jet (ATJ) Production Facilities for Targeted Scale-Up of Sustainable Aviation Fuel (SAF) Production

Achieving aerospace industry net-zero emissions by 2050 requires rapid scaling of sustainable aviation fuel (SAF) production. Leveraging existing infrastructure, proven technologies like Alcohol-to-Jet (ATJ), and low carbon intensity (CI) feedstocks (e.g., switchgrass and miscanthus) can support this transition and help achieve near-term emissions reduction targets. This study evaluates the implications of lignocellulosic ethanol biorefinery siting and integration with petroleum refineries to produce SAF across 1000 sites randomly sampled from areas suitable for perennial grasses in the U.S. rainfed region. To better understand the logistics of material transport and handoffs, we integrated models of biomass harvest, transport, ethanol, and ATJ production in a stochastic framework based on Monte Carlo simulations to characterize SAF minimum selling price (MSP) and carbon intensity (CI), considering site-specific parameters (e.g., feedstock production, transportation, taxes, incentives). The results indicate trade-offs between MSP and CI across locations, with median MSP ranging from 7.9 to 12.8 USD·gal −1 and CI from −9.7 to 39.4 gCO 2 e·MJ −1 . Despite high estimated decarbonization costs (580 USD·tonCO 2 e −1 ), our results indicate that site-specific deployment of ATJ with low-CI feedstocks can improve sustainability outcomes. The framework provides a systematic approach to assess cost and sustainability trade-offs across locations, considering the end-to-end supply chain and supporting an informed investment in SAF production.

09 BIOMASS FUELS↗

DOE OSTI2025

Quantum annealing-assisted lattice optimization

High Entropy Alloys (HEAs) have drawn great interest due to their exceptional properties compared to conventional materials. The configuration of HEA system is considered a key to their superior properties, but exhausting all possible configurations of atom coordinates and species to find the ground energy state is extremely challenging. In this work, we proposed a quantum annealing-assisted lattice optimization (QALO) algorithm, which is an active learning framework that integrates the Field-aware Factorization Machine (FFM) as the surrogate model for lattice energy prediction, Quantum Annealing (QA) as an optimizer and Machine Learning Potential (MLP) for ground truth energy calculation. By applying our algorithm to the NbMoTaW alloy, we reproduced the Nb depletion and W enrichment observed in bulk HEA. We found our optimized HEAs to have superior mechanical properties compared to the randomly generated alloy configurations. Our algorithm highlights the potential of quantum computing in materials design and discovery, laying a foundation for further exploring and optimizing structure-property relationships.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Integration of RNTuple in ATLAS Athena

After using ROOT’s TTree I/O subsystem for over two decades and storing more than an exabyte of compressed High Energy Physics (HEP) data, advances in technology have motivated a complete redesign, RNTuple, which breaks backward-compatibility to take better advantage of these storage options. The RNTuple I/O subsystem has been designed to address performance bottlenecks and other shortcomings of TTree. Specifically, RNTuple comes with an updated, more compact binary data format that can be stored both in ROOT files and natively in object stores. It is designed for modern storage hardware (e.g. high-throughput low-latency NVMe SSDs), and provides robust and easy to use interfaces. The binary format of RNTuple is scheduled to become production grade in 2024, and recently has become mature enough to start exploring the integration into software used by HEP experiments. In this contribution, we discuss the developments to support the features as required by the ATLAS analysis Event Data Model (EDM) in RNTuple, which will enable its integration into the Athena software framework. With these developments in place, we evaluate the performance of the current most recent versions of RNTuple-based ATLAS data sets and compare this to that of TTree.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

The Schwarz Alternating Method for the Seamless Coupling of Nonlinear Reduced Order Models and Full Order Models

Projection-based model order reduction allows for the parsimonious representation of full order models (FOMs), typically obtained through the discretization of a set of partial differential equations (PDEs) using conventional techniques (e.g., finite element, finite volume, finite difference methods) where the discretization may contain a very large number of degrees of freedom. As a result of this more compact representation, the resulting projection-based reduced order models (ROMs) can achieve considerable computational speedups, which are especially useful in real-time or multi-query analyses. One known deficiency of projection-based ROMs is that they can suffer from a lack of robustness, stability and accuracy, especially in the predictive regime, which ultimately limits their useful application. Another research gap that has prevented the widespread adoption of ROMs within the modeling and simulation community is the lack of theoretical and algorithmic foundations necessary for the “plug-and-play” integration of these models into existing multi-scale and multi-physics frameworks. This paper describes a new methodology that has the potential to address both of the aforementioned deficiencies by coupling projection-based ROMs with each other as well as with conventional FOMs by means of the Schwarz alternating method [41]. Leveraging recent work that adapted the Schwarz alternating method to enable consistent and concurrent multiscale coupling of finite element FOMs in solid mechanics [35, 36], we present a new extension of the Schwarz framework that enables FOM-ROM and ROM-ROM coupling, following a domain decomposition of the physical geometry on which a PDE is posed. In order to maintain efficiency and achieve computation speed-ups, we employ hyper-reduction via the Energy-Conserving Sampling and Weighting (ECSW) approach [13]. We evaluate the proposed coupling approach in the reproductive as well as in the predictive regime on a canonical test case that involves the dynamic propagation of a traveling wave in a nonlinear hyper-elastic material.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Effective Field Theory of Random Quantum Circuits

Quantum circuits have been widely used as a platform to simulate generic quantum many-body systems. In particular, random quantum circuits provide a means to probe universal features of many-body quantum chaos and ergodicity. Some such features have already been experimentally demonstrated in noisy intermediate-scale quantum (NISQ) devices. On the theory side, properties of random quantum circuits have been studied on a case-by-case basis and for certain specific systems, and a hallmark of quantum chaos—universal Wigner–Dyson level statistics—has been derived. This work develops an effective field theory for a large class of random quantum circuits. The theory has the form of a replica sigma model and is similar to the low-energy approach to diffusion in disordered systems. The method is used to explicitly derive the universal random matrix behavior of a large family of random circuits. In particular, we rederive the Wigner–Dyson spectral statistics of the brickwork circuit model by Chan, De Luca, and Chalker [Phys. Rev. X 8, 041019 (2018)] and show within the same calculation that its various permutations and higher-dimensional generalizations preserve the universal level statistics. Finally, we use the replica sigma model framework to rederive the Weingarten calculus, which is a method of evaluating integrals of polynomials of matrix elements with respect to the Haar measure over compact groups and has many applications in the study of quantum circuits. The effective field theory derived here provides both a method to quantitatively characterize the quantum dynamics of random Floquet systems (e.g., calculating operator and entanglement spreading) and a path to understanding the general fundamental mechanism behind quantum chaos and thermalization in these systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Integrating CVMix into GOTM (v6.0): a consistent framework for testing, comparing, and applying ocean mixing schemes

Abstract. The General Ocean Turbulence Model (GOTM) is a one-dimensional water column model, including a set of state-of-the-art turbulence closure models, and has widely been used in various applications in the ocean modeling community. Here, we extend GOTM to include a set of newly developed ocean surface vertical mixing parameterizations of Langmuir turbulence via coupling with the Community Vertical Mixing Project (CVMix). A Stokes drift module is also implemented in GOTM to provide the necessary ocean surface waves information to the Langmuir turbulence parameterizations, as well as to facilitate future development and evaluation of new Langmuir turbulence parameterizations. In addition, a streamlined workflow with Python and Jupyter notebooks is also described, enabled by the newly developed and more flexible configuration capability of GOTM. The newly implemented Langmuir turbulence parameterizations are evaluated against theoretical scalings and available observations in four test cases, including an idealized wind-driven entrainment case and three realistic cases at Ocean Station Papa, the northern North Sea, and the central Baltic Sea, and compared with the existing general length scale scheme in GOTM. The results are consistent with previous studies. This development extends the capability of GOTM towards including the effects of ocean surface waves and provides useful toolsets for the ocean modeling community to further study the effects of Langmuir turbulence in a broader scope.

58 GEOSCIENCES↗

NASA NTRS1987

An evidential approach to model-based satellite diagnosis

The paper presents an approach to the implementation of an automated satellite diagnosis capability which emphasizes techniques offering flexibility in the application of diagnostic strategies. The system utilizes a structural and behavioral model of the satellite; it uses a form of spreading activation to perform the diagnostic procedures on the model. A Dempster-Shafer evidential framework was implemented, making it possible to integrate evidence from the multiple sources necessary for building useful systems.

Bickmore, Timothy W.↗

NASA NTRS2005

Fully Associative, Nonisothermal, Potential-Based Unified Viscoplastic Model for Titanium-Based Matrices

A number of titanium matrix composite (TMC) systems are currently being investigated for high-temperature air frame and propulsion system applications. As a result, numerous computational methodologies for predicting both deformation and life for this class of materials are under development. An integral part of these methodologies is an accurate and computationally efficient constitutive model for the metallic matrix constituent. Furthermore, because these systems are designed to operate at elevated temperatures, the required constitutive models must account for both time-dependent and time-independent deformations. To accomplish this, the NASA Lewis Research Center is employing a recently developed, complete, potential-based framework. This framework, which utilizes internal state variables, was put forth for the derivation of reversible and irreversible constitutive equations. The framework, and consequently the resulting constitutive model, is termed complete because the existence of the total (integrated) form of the Gibbs complementary free energy and complementary dissipation potentials are assumed a priori. The specific forms selected here for both the Gibbs and complementary dissipation potentials result in a fully associative, multiaxial, nonisothermal, unified viscoplastic model with nonlinear kinematic hardening. This model constitutes one of many models in the Generalized Viscoplasticity with Potential Structure (GVIPS) class of inelastic constitutive equations.

Source record↗