Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Engineering Model”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 937 records · Page 52

FluxRETAP: a REaction TArget Prioritization genome-scale modeling technique for selecting genetic targets

MOTIVATION: Metabolic engineering is rapidly evolving as a result of new advances in synthetic biology tools and automation platforms that enable high throughput strain construction, as well as the development of machine learning tools (ML) for biology. However, selecting genetic engineering targets that effectively guide the metabolic engineering process is still challenging. ML can provide predictive power for synthetic biology, but current technical limitations prevent the independent use of ML approaches without previous biological knowledge. RESULTS: Here, we present FluxRETAP, a simple and computationally inexpensive method that leverages the prior mechanistic knowledge embedded in genome-scale models for suggesting targets for genetic overexpression, downregulation or deletion, with the final goal of increasing the production of a desired metabolite. This method can provide a list of desirable engineering targets that can be combined with current ML pipelines. FluxRETAP captured 100% of reaction targets experimentally verified to improve Escherichia coli isoprenol production, 50% of targets that experimentally improved taxadiene production in E. coli and ∼60% of genetic targets from a verified minimal constrained cut-set in Pseudomonas putida, while providing additional high priority targets that could be tested. Overall, FluxRETAP is an efficient algorithm for identifying a prioritized list of testable genetic and reaction targets. AVAILABILITY AND IMPLEMENTATION: FluxRETAP is implemented in python and released under the creative commons license. The implementation and code are freely available at: https://github.com/JBEI/FluxRETAP.

Czajka, Jeffrey J↗

On Transfer Learning Of Neural Networks Using Bi-Fidelity Data For Uncertainty Propagation

Due to their high degree of expressiveness, neural networks have recently been used as surrogate models for mapping inputs of an engineering system to outputs of interest. Once trained, neural networks are computationally inexpensive to evaluate and remove the need for repeated evaluations of computationally expensive models in uncertainty quantification applications. However, given the highly parameterized construction of neural networks, especially deep neural networks, accurate training often requires large amounts of simulation data that may not be available in the case of computationally expensive systems. In this paper, to alleviate this issue for uncertainty propagation, we explore the application of transfer learning techniques using training data generated from both high- and low-fidelity models. We explore two strategies for coupling these two datasets during the training procedure, namely, the standard transfer learning and the bi-fidelity-weighted learning. In the former approach, a neural network model mapping the inputs to the outputs of interest is trained based on the low-fidelity data. The high-fidelity data are then used to adapt the parameters of the upper layer(s) of the low-fidelity network, or train a simpler neural network to map the output of the low-fidelity network to that of the high-fidelity model. In the latter approach, the entire low-fidelity network parameters are updated using data generated via a Gaussian process model trained with a small high-fidelity dataset. The parameter updates are performed via a variant of stochastic gradient descent with learning rates given by the Gaussian process model. Using three numerical examples, we illustrate the utility of these bi-fidelity transfer learning methods where we focus on accuracy improvement achieved by transfer learning over standard training approaches.

97 MATHEMATICS AND COMPUTING↗

Investigation of powertrain system decarbonization using electrically assisted turbocharging and hybridization in off-road vehicles

In recent years, the causes, effects, and existential threat of a global anthropogenic climate shift have drawn significant attention and stimulated mitigation efforts from all genres of scientific, political, and industrial bodies. The greenhouse effect and the detrimental environmental impact of excess greenhouse gas (GHG) emissions, like carbon dioxide, is well studied and targeted as the primary culprit for aversive action. However, some fields exist where reducing GHG emissions is met by considerable challenges. One such field is the production and operations of off-road vehicles. Applications of these vehicles are highly diverse and are often characterized by rugged, especially transient, and power intensive duty cycles that make one-fits-all vehicle configuration solutions impractical. This research surveys existing literature to identify the modern technologies packages and challenges that face development and configuration of powertrain systems which currently navigate the regulated emissions and unique duty cycle requirements of this market space. A novel powertrain concept is proposed and evaluated with respect to the pinnacle objectives of load performance improvement, criteria pollutant reduction, and reducing the life cycle GHG intensity of its operation. A sure-fire path to vehicular GHG reduction is through improving the fuel efficiency of internal combustion engines (ICEs), an entrenched component of the off-road vehicle sector. Unfortunately, this is more easily said than done. An approach that has proven successful in this endeavor is engine downsizing and turbocharging, where a larger engine is replaced with a smaller one with added air system boosting via turbocharger to reduce frictional and pumping losses while also enabling access to additional fuel energy. However, practical realization of these potential benefits is often impeded by the transient response capability of the smaller engine across the operating space. For this reason, downsized ICE powertrains have turned to electrified forced induction systems (EFISs) for a decoupling of exhaust energy and engine speed from boost capability. Platformed on 48V hybrid technology, these systems introduce the need for more sophisticated controls around the engine gas-exchange process for the management of boost performance and exhaust gas emissions. On this account, simulation studies utilizing a GT-POWER model of a turbocharged 4.5 L engine outfit with an EFIS using an electrically driven compressor (eBooster®) are conducted to provide insight into the performance of this air handling architecture on an off-road engine. The results show that improvement in transient torque response time in sync with reduction in engine-out soot and NOx emissions are possible with an engine recalibration that leverages the transient air-fuel ratio authority of the eBooster®. Benefits are further demonstrated when duty cycle simulations of the 48V mild-hybrid engine concept are exercised, showing an acute decrease in cumulative fuel usage and soot production. Powertrain hybridization is another technological pathway achieving pronounced GHG reduction successes in modern on-road vehicle applications through integration of Li-ion battery technology. In the off-road vehicle segment, a review of available literature concludes that hybridized architectures are present but generally lack the depth of technologies that have both high specific energy and power capabilities, and thus are limited in their inclusion of Li-ion batteries for ICE assistance and enhanced energy storage capability. Therefore, building on the mild-hybrid engine results, the downsized and eBoosted engine concept was integrated into a larger high-voltage battery-hybrid series-electric powertrain system. Hybrid powertrain parameter sensitivity studies were carried out in a numerical charge-sustaining framework, providing novel insights into power flows between the battery and the engine and how their respective capabilities and operation contribute to GHG and criteria pollutant emissions of diverse duty cycles. Application of supervisory power management introduced robustness into the power sourcing and battery SOC control process and showed that optimum specification of battery properties can yield synergies between GHG emissions and battery energy capacity. Furthermore, examination of recent literature on Li-ion batteries has shown that pack manufacturing is a highly energy intensive process, thereby producing considerable quantities of GHGs that scale with energy storage capacity. Also scaling with a battery’s energy storage capacity is its investment cost. In consideration of these factors, an inclusive technoeconomic and GHG life cycle analysis is conducted. This analysis systematically compares the carbon footprint and total cost of ownership associated with the proposed hybrid powertrain concept to reference and alternative powertrain configurations, facilitating a thorough evaluation of the decarbonization effectiveness and economic viability.

99 GENERAL AND MISCELLANEOUS↗

Multiscale Modeling of the Mechanical Response of Silicon Carbide Composite Within the Accelerated Fuel Qualification Framework

The accelerated fuel qualification (AFQ) framework has been used for the initial development of multiscale modeling of silicon carbide (SiC) fiber reinforced composite (SiC-SiC). The AFQ framework provides a methodology to leverage physics-informed multiscale modeling along with a reduced set of empirical test data to reduce the time and cost of licensing and qualification of new nuclear fuel systems while maintaining the overall nuclear power plant safety case. SiC-SiC is being proposed for in-core applications, most notably fuel cladding, for current and next-generation nuclear reactors because of its high temperature stability, irradiation tolerance, and ability to withstand many accident conditions. As these composites exhibit multiscale architectures and complex microstructure-based fracture mechanics, it is an appealing use case for the AFQ methodology. While the end goal of this work is a single multiscale model that can be used for predictive in-core performance, current focus is on the individual various length scale models. Four individual models have been initially developed from microscale to engineering system level to capture key physics-based effects across different length scales. These models include a microscale homogenized tow model, a mesoscale fast Fourier transform–based weave model that integrates the homogenized tow model, a mesoscale finite element–based weave model, and a system-level BISON fuel performance model. Results of these models have undergone an initial comparison with separate-effects test data showing a good match to experimental results. By using the AFQ framework during model development, several near-term benefits have been secured including a reduction in development time for the SiC-SiC cladding, more targeted irradiation testing, and a better understanding of uncertainty.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Important powertrain dynamics for developing models for control of connected and automated electrified vehicles

Connected and Automated Vehicles (CAV) technology presents significant opportunities for energy saving in the transportation sector. CAV technology forecasts vehicle and powertrain power needs under various terrain, ambient, and traffic conditions. Integration of the CAV technology in Hybrid Electric Vehicles (HEVs) provides the opportunity for optimal vehicle operation. Indeed, Hybrid Electric Vehicle powertrains present high degrees of flexibility and possibility for choosing optimum powertrain modes based on the predicted traction power needs. In modeling complex CAV powertrain dynamics, the modeler needs to consider short-time scale powertrain dynamics, such as engine transients, and hysteresis of mode-switching for a multi-mode HEV. Therefore, the powertrain dynamics essential for developing powertrain controllers for a class of connected HEVs is presented. To this end, control-oriented powertrain dynamic models for a test vehicle consisting of full electric, hybrid, and conventional engine operating modes are developed. The resulting powertrain model can forecast vehicle traction torque and energy consumption for the specified prediction horizon of the test vehicle. The model considers different operating modes and associated energy penalty terms for mode switching. Thus, the vehicle controller can determine the optimum powertrain mode, torque, and speed for forecasted vehicle operation via utilizing connectivity data. The powertrain model is validated against the experimental data and shows prediction error of less than 5% for predicting vehicle energy consumption. The model is used to create energy penalty maps that can be used for CAV control, for example fuel penalty map for engine torque changes (10–40 Nm) at each engine speed. The results of model-based optimization show optimum switching delays ranging from 0.4 to 1.4 s to avoid hysteresis in mode switching.

Engineering↗

Novel Temperature Sensors and Wireless Telemetry for Active Condition Monitoring of Advanced Gas Turbines

The objective of the program is to develop and engine test hardware and software technologies that will enable active condition monitoring to be implemented on hot gas path turbine blades in large industrial gas turbines. The specific objectives are (1) to fabricate and install Smart Turbine Blades with thermally sprayed sensors and high temperature wireless telemetry systems in a gas turbine engine, (2) to integrate the component engine test data with remaining useful life (RUL) models and develop an approach for networking the component RUL data with Siemens' Power Diagnostics® engine monitoring system. These significant advances carried out in Phase 1 in temperature wide bandgap telemetry, along with new induced power driver and receiver geometry combined with an innovative approach to transmit digital data wirelessly will enable the opportunity to proceed with more technical innovation. The Phase 2 program focused on validation testing of sensor-wireless telemetry package in spin rig and advanced operation-based assessment (OBA) model utilizing artificial intelligence. Significant efforts were dedicated on the download of the technology onto components to be tested an actual gas turbine engine for full realization of active condition monitoring for Smart Turbine Blades.

03 NATURAL GAS↗

IMAGINE BioSecurity: Mesocosm-Based Methods to Evaluate Biocontainment Strategies and Impact of Industrial Microbes Upon Native Ecosystems

Project Goals: The Integrative Modeling and Genome-scale Engineering for Biosystems Security (IMAGINE BioSecurity) SFA project seeks to establish an understanding of the behavior of engineered microbes in controlled versus environmental conditions to predictively devise new strategies for responding to biological escape. To this end, the IMAGINE Team has established a plant-soil mesocosm platform to track and quantify the fate of industrial microbes in environmental systems and assess the efficacy of biocontainment constraints upon genetically engineered microbe escape frequency and the impact of industrial microbes upon native ecological microbiomes. Abstract Text: Genetically modified industrial production microbes and their associated bioproducts have emerged as an integral component of a sustainable bioeconomy. However, the rapid development of these innovative technologies raises biosecurity concerns, namely, the risk of environmental escape. Thus, the realization of a bioeconomy hinges not only on the development and deployment of microbial production hosts, but also on the development of secure biosystems and biocontainment designs. Current laboratory-based biocontainment testing systems do not accurately reflect complexities found in natural environments, necessitating an environmentally relevant analysis pipeline that allows for the detection of rare escapees, the effect of associated bio-products, and the impact on native ecologies. To this end, we have developed an approach that utilizes soil mesocosms and integrated systems analyses to evaluate the efficacy of novel biocontainment strategies and to assess the impact of production systems upon terrestrial microbiome dynamics. We demonstrate the utility of this approach by modeling a contamination with industrial microbial chasses versus their biocontained counterparts. Here we demonstrate the broad utility of this system by highlighting findings from both strains of Saccharomyces cerevisiae that are contained with an inducible toxin anti-toxin system, and stains of Escherichia coli that are contained via genomic recoding. The resultant data demonstrate that this system has broad utility across diverse microbial chassis and biocontainment strategies, enables us to track the fate of our contaminating microbe with high sensitivity in the soil, as well as monitor broader impacts of the perturbation on the underlying soil system. The findings presented here support the use of this mesocosm-based approach to assess the environmental impact of industrial microbes and to validate biocontainment strategies.

BASIC BIOLOGICAL SCIENCES,INORGANIC, ORGANIC, PHYS↗

Unified cohesive zone model (UCZM) for fracturing and fragmenting solids

Here, a Unified Cohesive Zone Model (UCZM), which inherits most of the advantages while overcoming the shortcomings of existing Cohesive Zone Models (CZMs), is proposed. Similar to the traditional extrinsic CZM approach, UCZM dynamically inserts the cohesive elements into the system based on local material states (e.g., stress, strain). However, the transition from continua to discontinua is smoothly achieved, thereby eliminating the “time-discontinuous” issue seen in the extrinsic CZM. Moreover, within the novel UCZM framework, the point of transition from continua to discontinua is controllable through the introduction of crack initialization criteria. As a result, the UCZM allows any material models (e.g., elastic, plastic, damage models) for continuum solids and for discrete fracture behavior to work together. In essence, both an enhanced extrinsic cohesive zone model and an intrinsic cohesive zone model can be represented by the proposed unified model. The proposed UCZM has been verified through different numerical examples. The work demonstrates that the UCZM is a highly effective approach for modeling fracture and fragmentation processes in solids.

42 ENGINEERING↗

AUTOIGNITION DELAY TIMES FOR REFORMATE GAS MIXTURES FROM METHANE GAS ENGINES

Methane slip is a prominent issue in natural gas reciprocating engines that are used in transportation and marine applications. The incomplete combustion that results in methane slip can be resolved with the introduction of hydrogen within the combustion mixture to improve methane oxidation and further enable combustion within the engine crevices where methane has previously remained unreacted. Steam methane reforming (SMR) is a common method used to produce hydrogen and can be used to design an onboard device to reduce methane slip from reciprocating engines. The development of this reformer device requires the validation of high-fidelity chemical kinetic models at the low temperatures of the crevice volumes of these engines. In this work, auto-ignition data is obtained using a shock tube at lean (φ—0.714 or λ—1.4) and stoichiometric (φ, λ = 1) equivalence ratios spanning a temperature range of 1042–1234 K at the 80-bar operating pressure of the test engine. Blends of methane, hydrogen, and reformate products from the SMR reaction are shock-heated in synthetic air, with the ignition delay time measured using an OH* chemiluminescence detector at 310 nm and a CH* detector at 430 nm. The experimental results are compared to several state-of-the-art chemical kinetic mechanisms from the literature. In general, most of the mechanisms show very good agreement with experiments at higher temperatures, with simulation results showing little deviation from experiments at lower temperatures. A sensitivity analysis was conducted, and the results reveal that the reaction H2 + CH3O2 = H + CH3O2H has a very significant role in determining low-temperature ignition delay times (IDTs) of SMR mixtures. These findings provide valuable insights into the chemical kinetics governing methane reformate combustion and contribute to the optimization of onboard reformer designs aimed at mitigating methane slip in natural gas-fueled engines.

Fraze, Matthew↗

Learning Nonlinear Reduced Models from Data with Operator Inference

This review discusses Operator Inference, a nonintrusive reduced modeling approach that incorporates physical governing equations by defining a structured polynomial form for the reduced model, and then learns the corresponding reduced operators from simulated training data. The polynomial model form of Operator Inference is sufficiently expressive to cover a wide range of nonlinear dynamics found in fluid mechanics and other fields of science and engineering, while still providing efficient reduced model computations. The learning steps of Operator Inference are rooted in classical projection-based model reduction; thus, some of the rich theory of model reduction can be applied to models learned with Operator Inference. This connection to projection-based model reduction theory offers a pathway toward deriving error estimates and gaining insights to improve predictions. Furthermore, through formulations of Operator Inference that preserve Hamiltonian and other structures, important physical properties such as energy conservation can be guaranteed in the predictions of the reduced model beyond the training horizon. This review illustrates key computational steps of Operator Inference through a large-scale combustion example.

Mechanics↗

Floquet engineering of Kitaev quantum magnets

Abstract In recent years, there has been an intense search for materials realizing the Kitaev quantum spin liquid model. A number of edge-shared compounds with strong spin-orbit coupling, such as RuCl 3 and iridates, have been proposed to realize this model. Nevertheless, an effective spin Hamiltonian derived from the microscopic model relevant to these compounds generally contains terms that are antagonistic toward the quantum spin liquid. This is consistent with the fact that the zero magnetic field ground state of these materials is generally magnetically ordered. It is a pressing issue to identify protocols to drive the system to the limit of the Kitaev quantum spin model. In this work, we propose Floquet engineering of these Kitaev quantum magnets by coupling materials to a circularly polarized laser. We demonstrate that all the magnetic interactions can be tuned in situ by the amplitude and frequency of the laser, hence providing a route to stabilize the Kitaev quantum spin liquid phase.

36 MATERIALS SCIENCE↗

Improving Subsurface Stress Characterization for Carbon Dioxide Storage Projects

Researchers at New Mexico Tech, Los Alamos National Laboratory (LANL), Sandia National Laboratory (SNL), and other collaborators are developing a methodology to improve characterization of stress in the subsurface by means of a model-based inversion of reservoir engineering data, time lapse seismic measurements, and microseismicity. Historically, various geophysical techniques have been used in efforts to understand the state of stress in the subsurface through direct and indirect imaging of stress sensitive features (faults and fractures) and observations of transient stress related observations (time variant elastic moduli and microseismicity). Standard direct and indirect techniques for seismic fault and fracture imaging suffer from detectability limits due to reliance on high data quality and multiplicity. Variations in effective elastic properties from inversion of high quality seismic (Vertical Seismic Profile (VSP)) data may be used to infer stress near the wellbore through integration with independent experimental characterization of the stress-velocity relationship. Given a sufficiently robust observation network, microseismic emissions may be inverted to characterize focal mechanisms which, together with supporting assumptions and constraints, inform estimates of in-situ stress. While each of these techniques contributes in part to the characterization of stress within limited spatial and temporal domains, no one method provides an unambiguous stress measurement or a predictive capability over a site scale spatial extent. Challenges associated with solution non-uniqueness, measurement ambiguity, and irregular sampling may be greatly minimized through combination of one or more of independent measurements within a common framework in which realistic geological, hydrodynamic, geomechanical, and seismological constituent process models may act as constraints.

02 PETROLEUM↗

Modeling Flexible Generator Operating Regions via Chance- constrained Stochastic Unit Commitment

Here, we introduce a novel chance-constrained stochastic unit commitment model to address uncertainty in renewables' production uncertainty in power systems operation. For most thermal generators,underlying technical constraints that are universally treated as "hard" by deterministic unit commitment models are in fact based on engineering judgments, such that system operators can periodically request operation outside these limits in non-nominal situations, e.g., to ensure reliability. We incorporate this practical consideration into a chance-constrained stochastic unit commitment model, specifically by in-frequently allowing minor deviations from the minimum and maximum thermal generator power output levels. We demonstrate that an extensive form of our model is computationally tractable for medium-sized power systems given modest numbers of scenarios for renewables' production. We show that the model is able to potentially save significant annual production costs by allowing infrequent and controlled violation of the traditionally hard bounds imposed on thermal generator production limits. Finally, we conduct a sensitivity analysis of optimal solutions to our model under two restricted regimes and observe similar qualitative results.

42 ENGINEERING↗

Evaporation Submodel Development for Volume of Fluid (eVOF) Method Applicable to Spray-Wall Interaction Including Film Characteristics with Validation at High Pressure and Temperature Conditions

Internal combustion engines have seen a great evolution over the last several decades through application of high pressure direct injection, multiple injections, and other technologies to reduced fuel consumption, NOx, and PM. Although combustion systems with advanced injection strategies have been studied extensively, there exists a significant fundamental knowledge gap on the fuel-spray interactions with the piston surface and chamber walls. Advanced computational codes validated with experimental techniques have to be developed for accurate representation of the drop impingement, fuel film formation, and vaporization. Current engine CFD (Computational Fluid Dynamics) spray models utilize a Lagrangian framework for modeling which lacks critical considerations of the physics pertaining to these interactions and thus requiring extensive parameterization, tuning and validation. The team from Michigan Technological University, University of Massachusetts Dartmouth, and Argonne National Laboratory is composed of experts in sprays, combustion, engines and CFD with a wide spectrum of knowledge including specific expertise in the area under consideration. In the proposed work, a VOF (Volume of Fluid) modeling approach has been adopted for the spray-wall interaction, film formation and spreading, and vaporization. With the inclusion of a vaporization submodel, a more predictive and accurate simulation of the spray-film was performed without extensive need of parameterization and tuning. Extensive experimentation of the spray-wall interaction under the range of conditions matching the thermodynamic and surface temperatures that occur in diesel and gasoline engines were conducted to validate the SWI submodels and for development of the evaporation submodel, which has been implemented in the flow solver.

42 ENGINEERING↗

An accelerated approach to inline non-LTE modeling

A goal across many physics and engineering disciplines is to use radiation-hydrodynamics codes to accurately simulate systems that are expected to deviate from local thermodynamic equilibrium (LTE), such as laser-driven hohlraums, stellar coronae, and supernova ejecta. The computational expense of traditional non-LTE (NLTE) opacity calculations can dominate the cost of simulating these systems and render NLTE physics untenable in most cases. In this paper, we present a new parallel implementation for NLTE opacity calculations that employs advanced load balancing, vectorization, and memory management to significantly reduce the computational costs of these calculations. Using the radiation-hydrodynamics code xRAGE , we demonstrate this new implementation on three test problems and present order-of-magnitude speed improvements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Library of Advanced Materials for Engineering (LAM) 4.56

Accurate and efficient constitutive modeling remains a cornerstone issue for solid mechanics analysis. Over the years, the LAME advanced material model library has grown to address this challenge by implementing models capable of describing material systems spanning soft polymers to stiff ceramics including both isotropic and anisotropic responses. Inelastic behaviors including (visco)plasticity, damage, and fracture have all incorporated for use in various analyses. This multitude of options and flexibility, however, comes at the cost of many capabilities, features, and responses and the ensuing complexity in the resulting implementation. Therefore, to enhance confidence and enable the utilization of the LAME library in application, this effort seeks to document and verify the various models in the LAME library. Specifically, the broader strategy, organization, and interface of the library itself is first presented. The physical theory, numerical implementation, and user guide for a large set of models is then discussed. Importantly, a number of verification tests are performed with each model to not only have confidence in the model itself but also highlight some important response characteristics and features that may be of interest to end-users. Finally, in looking ahead to the future, approaches to add material models to this library and further expand the capabilities are presented.

36 MATERIALS SCIENCE↗

Library of Advanced Materials for Engineering (LAMÉ) 4.58

Accurate and efficient constitutive modeling remains a cornerstone issue for solid mechanics analysis. Over the years, the LAMÉ advanced material model library has grown to address this challenge by implementing models capable of describing material systems spanning soft polymers to stiff ceramics including both isotropic and anisotropic responses. Inelastic behaviors including (visco)plasticity, damage, and fracture have all incorporated for use in various analyses. This multitude of options and flexibility, however, comes at the cost of many capabilities, features, and responses and the ensuing complexity in the resulting implementation. Therefore, to enhance confidence and enable the utilization of the LAMÉ library in application, this effort seeks to document and verify the various models in the LAMÉ library. Specifically, the broader strategy, organization, and interface of the library itself is first presented. The physical theory, numerical implementation, and user guide for a large set of models is then discussed. Importantly, a number of verification tests are performed with each model to not only have confidence in the model itself but also highlight some important response characteristics and features that may be of interest to end-users. Finally, in looking ahead to the future, approaches to add material models to this library and further expand the capabilities are presented.

36 MATERIALS SCIENCE↗