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At least 163 records · Page 9

Influence of NOx chemistry on the prediction of natural gas end-gas autoignition in CFD engine simulations

Natural gas (NG) represents a promising low-cost/low-emission alternative to diesel fuel when used in high-efficiency internal combustion engines. Advanced combustion strategies utilizing high EGR rates and controlled end-gas autoignition can be implemented with NG to achieve diesel-like efficiencies; however, to support the design of these next-generation NG ICEs, computational tools, including single- and multi-dimensional simulation packages will need to account for the complex chemistry that can occur between the reactive species found in EGR (including NOx) and the fuel. Research has shown that NOx plays an important role in the promotion/inhibition of large hydrocarbon autoignition and when accounted for in CFD engine simulations, can significantly improve the prediction of end-gas autoignition for these fuels. However, reduced NOx-enabled NG mechanisms for use in CFD engine simulations are lacking, and as a result, the influence of NOx chemistry on NG engine operation remains unknown. Here, we analyze the effects of NOx chemistry on the prediction of NG/oxidizer/EGR autoignition and generate a reduced mechanism of a suitable size to be used in engine simulations. Results indicate that NG ignition is sensitive to NOx chemistry, where it was observed that the addition of EGR, which included NOx, promoted NG autoignition. The modified mechanism captured well all trends and closely matched experimentally measured ignition delay times for a wide range of EGR rates and NG compositions. Here, the importance of C2-C3 chemistry is noted, especially for wet NG compositions containing high fractions of ethane and propane. Finally, when utilized in CFD simulations of a Cooperative Fuels Research (CFR) engine, the new reduced mechanism was able to predict the knock onset crank angle (KOCA) to within one crank angle degree of experimental data, a significant improvement compared to previous simulations without NOx chemistry.

33 ADVANCED PROPULSION SYSTEMS↗

Verification of component mode techniques for flexible multibody systems

Investigations were conducted in the modeling aspects of flexible multibodies undergoing large angular displacements. Models were to be generated and analyzed through application of computer simulation packages employing the 'component mode synthesis' techniques. Multibody Modeling, Verification and Control Laboratory (MMVC) plan was implemented, which includes running experimental tests on flexible multibody test articles. From these tests, data was to be collected for later correlation and verification of the theoretical results predicted by the modeling and simulation process.

Wiens, Gloria J.↗

Pulsar Simulations for the Fermi Large Area Telescope

Pulsars are among the prime targets for the Large Area Telescope (LAT) aboard the recently launched Fermi observatory. The LAT will study the gamma-ray Universe between 20 MeV and 300 GeV with unprecedented detail. Increasing numbers of gamma-ray pulsars are being firmly identified, yet their emission mechanisms are far from being understood. To better investigate and exploit the tAT capabilities for pulsar science. a set of new detailed pulsar simulation tools have been developed within the LAT collaboration. The structure of the pulsar simulator package (PulsarSpeccrum) is presented here. Starting from photon distributions in energy and phase obtained from theoretical calculations or phenomenological considerations, gamma-rays are generated and their arrival times at the spacecraft are determined by taking Into account effects such as barycentric effects and timing noise. Pulsars in binary systems also can be simulated given orbital parameters. We present how simulations can be used for generating a realistic set of gamma rays as observed by the LAT, focusing on some case studies that show the performance of the LAT for pulsar observations.

Razzano, M.↗

Formula for the ionisation rate of an atom or ion in a strong electromagnetic field for numerical simulation

A formula is proposed for calculating the rate of field ionisation of an atom or ion, taking into account both tunnel ionisation and barrier suppression ionisation. Compared with the previous formula proposed in 2018, it more accurately describes the transition region between both ionisations and is determined mainly by two parameters: the ionisation potential of an atom or ion and the amplitude of an external electric field. This makes the presented formula suitable for use in numerical packages simulating the interaction of high-power laser radiation with matter by the particle-in-cell (PIC) method. (paper)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Modeling and Simulation of Austenitic Welds and Coarse-grained Specimens: Part II

The Pacific Northwest National Laboratory (PNNL) is conducting confirmatory research for the U.S. Nuclear Regulatory Commission (NRC) to evaluate commercially available nondestructive examination (NDE) modeling and simulation software used in the nuclear industry. Simulation results from ultrasonic testing (UT) models can inform the design and qualification of inspection techniques and help interpret inspection results. CIVA is a modeling and simulation package developed by the French Alternative Energies and Atomic Energy Commission (CEA). CIVA was selected for this study because it is readily available and has been used for NDE in the US commercial nuclear power industry. This report is focused on completing the efforts initiated in the previous PNNL report to evaluate UT modeling and simulation performance, reliability, and accuracy in relation to common inservice inspection (ISI) scenarios in nuclear power plants (NPP). This work will be used to provide guidance when establishing methods to perform and evaluate simulations for more standardized model implementation, simulation analysis, and interpretation of results.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Modeling ESA's TT/C systems

After a brief introduction on the need for simulation packages for the analysis and design of satellite communications systems, the software tool developed for the European Space Agency (ESA), its main objectives and the design choices made during the development are presented. A very concise description of the available communications and measurement block follows. The ESA standard Telemetry, Tracking and Command (TT&C) system simulator is then introduced along with a description of the ESA standard modulation and coding schemes. As an example, the simulation of the ranging system which is a non-standard communications block, is described in details. Several examples of TT&C simulations outputs are given and compared with measurement results or theoretical approximations, when available. Finally, future developments like the support of advanced modulation schemes and the dynamic satellite link simulation are presented.

Vassallo, Enrico↗

Development and refinement of test bed simulations

Lewis Research Center of NASA, with support from Rocketdyne, was engaged in non-real time computer simulation effort for the Space Station Freedom Electric Power System (EPS) EASY5, a simulation package, is used as the primary tool for this activity. Early in the design of the EPS, two test beds were set up at Lewis. The Integrated Test Bed (ITB), that combines and upgrades these test beds, is in the planning stage. The test beds are designed to functionally represent many of the components of the EPS and their interconnections. The simulation effort is primarily directed towards these test beds. Model verification is performed using test bed data.

Dravid, Narayan V.↗

Development and refinement of test bed simulations

Lewis Research Center of NASA, with support from Rocketdyne, has engaged in a nonreal-time computer simulation effort for the Space Station Freedom Electric Power System (EPS). EASYS, a simulation package, is used as the primary tool for this activity. Early in the design of the EPS, two test beds were set up at Lewis. The Integrated Test Bed (ITB) that combines and upgrades these test beds is in the planning stage. The test beds are designed to functionally represent many of the components of the EPS and their interconnections. The simulation effort is primarily directed towards these test beds. Model verification is performed using test bed data.

Dravid, N. V.↗

Turbofan Engine Simulated in a Graphical Simulation Environment

Recently, there has been an increase in the development of intelligent engine technology with advanced active component control. The computer engine models used in these control studies are component-level models (CLM), models that link individual component models of state space and nonlinear algebraic equations, written in a computer language such as Fortran. The difficulty faced in performing control studies on Fortran-based models is that Fortran is not supported with control design and analysis tools, so there is no means for implementing real-time control. It is desirable to have a simulation environment that is straightforward, has modular graphical components, and allows easy access to health, control, and engine parameters through a graphical user interface. Such a tool should also provide the ability to convert a control design into real-time code, helping to make it an extremely powerful tool in control and diagnostic system development. Simulation time management is shown: Mach number versus time, power level angle versus time, altitude versus time, ambient temperature change versus time, afterburner fuel flow versus time, controller and actuator dynamics, collect initial conditions, CAD output, and component-level model: CLM sensor, CAD input, and model output. The Controls and Dynamics Technologies Branch at the NASA Glenn Research Center has developed and demonstrated a flexible, generic turbofan engine simulation platform that can meet these objectives, known as the Modular Aero-Propulsion System Simulation (MAPSS). MAPSS is a Simulink-based implementation of a Fortran-based, modern high pressure ratio, dual-spool, low-bypass, military-type variable-cycle engine with a digital controller. Simulink (The Mathworks, Natick, MA) is a computer-aided control design and simulation package allows the graphical representation of dynamic systems in a block diagram form. MAPSS is a nonlinear, non-real-time system composed of controller and actuator dynamics (CAD) and component-level model (CLM) modules. The controller in the CAD module emulates the functionality of a digital controller, which has a typical update rate of 50 Hz. The CLM module simulates the dynamics of the engine components and uses an update rate of 2500 Hz, which is needed to iterate to balance mass and energy among system components. The actuators in the CAD module use the same sampling rate as those in the CLM. Two graphs of normalized spool speed versus time in seconds and one graph of normalized average metal temperature versus time in seconds is shown. MAPSS was validated via open-loop and closed-loop comparisons with the Fortran simulation. The preceding plots show the normalized results of a closed-loop comparison looking at three states of the model: low-pressure spool speed, high-pressure spool speed, and the average metal temperature measured from the combustor to the high-pressure turbine. In steady state, the error between the simulations is less than 1 percent. During a transient, the difference between the simulations is due to a correction in MAPSS that prevents the gas flow in the bypass duct inlet from flowing forward instead of toward the aft end, which occurs in the Fortran simulation. A comparison between MAPSS and the Fortran model of the bypass duct inlet flow for power lever angles greater than 35 degrees is shown.

Parker, Khary I.↗

Extensions to the Dynamic Aerospace Vehicle Exchange Markup Language

The Dynamic Aerospace Vehicle Exchange Markup Language (DAVE-ML) is a syntactical language for exchanging flight vehicle dynamic model data. It provides a framework for encoding entire flight vehicle dynamic model data packages for exchange and/or long-term archiving. Version 2.0.1 of DAVE-ML provides much of the functionality envisioned for exchanging aerospace vehicle data; however, it is limited in only supporting scalar time-independent data. Additional functionality is required to support vector and matrix data, abstracting sub-system models, detailing dynamics system models (both discrete and continuous), and defining a dynamic data format (such as time sequenced data) for validation of dynamics system models and vehicle simulation packages. Extensions to DAVE-ML have been proposed to manage data as vectors and n-dimensional matrices, and record dynamic data in a compatible form. These capabilities will improve the clarity of data being exchanged, simplify the naming of parameters, and permit static and dynamic data to be stored using a common syntax within a single file; thereby enhancing the framework provided by DAVE-ML for exchanging entire flight vehicle dynamic simulation models.

Brian, Geoffrey J.↗

Modeling and Simulation of Variable Mass, Flexible Structures

The advent of the new Ares I launch vehicle has highlighted the need for advanced dynamic analysis tools for variable mass, flexible structures. This system is composed of interconnected flexible stages or components undergoing rapid mass depletion through the consumption of solid or liquid propellant. In addition to large rigid body configuration changes, the system simultaneously experiences elastic deformations. In most applications, the elastic deformations are compatible with linear strain-displacement relationships and are typically modeled using the assumed modes technique. The deformation of the system is approximated through the linear combination of the products of spatial shape functions and generalized time coordinates. Spatial shape functions are traditionally composed of normal mode shapes of the system or even constraint modes and static deformations derived from finite element models of the system. Equations of motion for systems undergoing coupled large rigid body motion and elastic deformation have previously been derived through a number of techniques [1]. However, in these derivations, the mode shapes or spatial shape functions of the system components were considered constant. But with the Ares I vehicle, the structural characteristics of the system are changing with the mass of the system. Previous approaches to solving this problem involve periodic updates to the spatial shape functions or interpolation between shape functions based on system mass or elapsed mission time. These solutions often introduce misleading or even unstable numerical transients into the system. Plus, interpolation on a shape function is not intuitive. This paper presents an approach in which the shape functions are held constant and operate on the changing mass and stiffness matrices of the vehicle components. Each vehicle stage or component finite element model is broken into dry structure and propellant models. A library of propellant models is used to describe the distribution of mass in the fuel tank or Solid Rocket Booster (SRB) case for various propellant levels. Based on the mass consumed by the liquid engine or SRB, the appropriate propellant model is coupled with the dry structure model for the stage. Then using vehicle configuration data, the integrated vehicle model is assembled and operated on by the constant system shape functions. The system mode shapes and frequencies can then be computed from the resulting generalized mass and stiffness matrices for that mass configuration. The rigid body mass properties of the vehicle are derived from the integrated vehicle model. The coupling terms between the vehicle rigid body motion and elastic deformation are also updated from the constant system shape functions and the integrated vehicle model. This approach was first used to analyze variable mass spinning beams and then prototyped into a generic dynamics simulation engine. The resulting code was tested against Crew Launch Vehicle (CLV-)class problems worked in the TREETOPS simulation package and by Wilson [2]. The Ares I System Integration Laboratory (SIL) is currently being developed at the Marshall Space Flight Center (MSFC) to test vehicle avionics hardware and software in a hardware-in-the-loop (HWIL) environment and certify that the integrated system is prepared for flight. The Ares I SIL utilizes the Ares Real-Time Environment for Modeling, Integration, and Simulation (ARTEMIS) tool to simulate the launch vehicle and stimulate avionics hardware. Due to the presence of vehicle control system filters and the thrust oscillation suppression system, which are tuned to the structural characteristics of the vehicle, ARTEMIS must incorporate accurate structural models of the Ares I launch vehicle. The ARTEMIS core dynamics simulation models the highly coupled nature of the vehicle flexible body dynamics, propellant slosh, and vehicle nozzle inertia effects combined with mass and flexible body properties that vary significant with time during the flight. All forces that act on the vehicle during flight must be simulated, including deflected engine thrust force, spatially distributed aerodynamic forces, gravity, and reaction control jet thrust forces. These forces are used to excite an integrated flexible vehicle, slosh, and nozzle dynamics model for the vehicle stack that simulates large rigid body translations and rotations along with small elastic deformations. Highly effective matrix math operations on a distributed, threaded high-performance simulation node allow ARTEMIS to retain up to 30 modes of flex for real-time simulation. Stage elements that separate from the stack during flight are propagated as independent rigid six degrees of freedom (6DOF) bodies. This paper will present the formulation of the resulting equations of motion, solutions to example problems, and describe the resulting dynamics simulation engine within ARTEMIS.

Tobbe, Patrick A.↗

Common workflows for computing material properties using different quantum engines

The prediction of material properties based on density-functional theory has become routinely common, thanks, in part, to the steady increase in the number and robustness of available simulation packages. This plurality of codes and methods is both a boon and a burden. While providing great opportunities for cross-verification, these packages adopt different methods, algorithms, and paradigms, making it challenging to choose, master, and efficiently use them. We demonstrate how developing common interfaces for workflows that automatically compute material properties greatly simplifies interoperability and cross-verification. We introduce design rules for reusable, code-agnostic, workflow interfaces to compute well-defined material properties, which we implement for eleven quantum engines and use to compute various material properties. Each implementation encodes carefully selected simulation parameters and workflow logic, making the implementer’s expertise of the quantum engine directly available to non-experts. All workflows are made available as open-source and full reproducibility of the workflows is guaranteed through the use of the AiiDA infrastructure.

36 MATERIALS SCIENCE↗

Efficient Parallel Kernel Solvers for Computational Fluid Dynamics Applications

Distributed-memory parallel computers dominate today's parallel computing arena. These machines, such as Intel Paragon, IBM SP2, and Cray Origin2OO, have successfully delivered high performance computing power for solving some of the so-called "grand-challenge" problems. Despite initial success, parallel machines have not been widely accepted in production engineering environments due to the complexity of parallel programming. On a parallel computing system, a task has to be partitioned and distributed appropriately among processors to reduce communication cost and to attain load balance. More importantly, even with careful partitioning and mapping, the performance of an algorithm may still be unsatisfactory, since conventional sequential algorithms may be serial in nature and may not be implemented efficiently on parallel machines. In many cases, new algorithms have to be introduced to increase parallel performance. In order to achieve optimal performance, in addition to partitioning and mapping, a careful performance study should be conducted for a given application to find a good algorithm-machine combination. This process, however, is usually painful and elusive. The goal of this project is to design and develop efficient parallel algorithms for highly accurate Computational Fluid Dynamics (CFD) simulations and other engineering applications. The work plan is 1) developing highly accurate parallel numerical algorithms, 2) conduct preliminary testing to verify the effectiveness and potential of these algorithms, 3) incorporate newly developed algorithms into actual simulation packages. The work plan has well achieved. Two highly accurate, efficient Poisson solvers have been developed and tested based on two different approaches: (1) Adopting a mathematical geometry which has a better capacity to describe the fluid, (2) Using compact scheme to gain high order accuracy in numerical discretization. The previously developed Parallel Diagonal Dominant (PDD) algorithm and Reduced Parallel Diagonal Dominant (RPDD) algorithm have been carefully studied on different parallel platforms for different applications, and a NASA simulation code developed by Man M. Rai and his colleagues has been parallelized and implemented based on data dependency analysis. These achievements are addressed in detail in the paper.

Sun, Xian-He↗

Modelling Beam Loss Within the LANSCE Proton Storage Ring

Several upgrades are being considered for the proton storage ring (PSR) at the Los Alamos Neutron Science Center (LANSCE) to reduce beam loss and thereby reduce the cooldown period of the PSR following a beam run. First, we have considered an increased beam pipe diameter would reduce beam loss due to beam scraping caused by misalignments and tuning errors. However, this would require increased pole-to-pole gap height within the dipoles and quadrupoles, which would change their effective length and alter their fringe fields. The effect of different magnet gaps on the beam optical parameters and on beam loss was studied using the simulation codes MAD-X and PyORBIT. Second, we are developing a detailed particle tracking model within the framework of the simulation package General Particle Tracer (GPT) for the PSR H - stripping system. This model will be used to study the effect of the stripper foil parameters (position, composition, areal density, depth, etc.) on first-turn losses, where most of the observed beam loss and emittance growth occurs due to foil scattering, foil stripping, and Lorentz stripping. The model implements C++ custom elements created to model foil scattering, foil stripping, and Lorentz stripping, as these are not built-in features of GPT. The preliminary results of the MAD-X and PyORBIT simulations, as well as the GPT simulation model, is described in this tech note.

43 PARTICLE ACCELERATORS↗

NASA Tech Briefs, January 2013

Topics include: Single-Photon-Sensitive HgCdTe Avalanche Photodiode Detector; Surface-Enhanced Raman Scattering Using Silica Whispering-Gallery Mode Resonators; 3D Hail Size Distribution Interpolation/Extrapolation Algorithm; Color-Changing Sensors for Detecting the Presence of Hypergolic Fuels; Artificial Intelligence Software for Assessing Postural Stability; Transformers: Shape-Changing Space Systems Built with Robotic Textiles; Fibrillar Adhesive for Climbing Robots; Using Pre-Melted Phase Change Material to Keep Payloads in Space Warm for Hours without Power; Development of a Centrifugal Technique for the Microbial Bioburden Analysis of Freon (CFC-11); Microwave Sinterator Freeform Additive Construction System (MS-FACS); DSP/FPGA Design for a High-Speed Programmable S-Band Space Transceiver; On-Chip Power-Combining for High-Power Schottky Diode-Based Frequency Multipliers; FPGA Vision Data Architecture; Memory Circuit Fault Simulator; Ultra-Compact Transputer-Based Controller for High-Level, Multi-Axis Coordination; Regolith Advanced Surface Systems Operations Robot Excavator; Magnetically Actuated Seal; Hybrid Electrostatic/Flextensional Mirror for Lightweight, Large-Aperture, and Cryogenic Space Telescopes; System for Contributing and Discovering Derived Mission and Science Data; Remote Viewer for Maritime Robotics Software; Stackfile Database; Reachability Maps for In Situ Operations; JPL Space Telecommunications Radio System Operating Environment; RFI-SIM: RFI Simulation Package; ION Configuration Editor; Dtest Testing Software; IMPaCT - Integration of Missions, Programs, and Core Technologies; Integrated Systems Health Management (ISHM) Toolkit; Wind-Driven Wireless Networked System of Mobile Sensors for Mars Exploration; In Situ Solid Particle Generator; Analysis of the Effects of Streamwise Lift Distribution on Sonic Boom Signature; Rad-Tolerant, Thermally Stable, High-Speed Fiber-Optic Network for Harsh Environments; Towed Subsurface Optical Communications Buoy; High-Collection-Efficiency Fluorescence Detection Cell; Ultra-Compact, Superconducting Spectrometer-on-a-Chip at Submillimeter Wavelengths; UV Resonant Raman Spectrometer with Multi-Line Laser Excitation; Medicine Delivery Device with Integrated Sterilization and Detection; Ionospheric Simulation System for Satellite Observations and Global Assimilative Model Experiments - ISOGAME; Airborne Tomographic Swath Ice Sounding Processing System; flexplan: Mission Planning System for the Lunar Reconnaissance Orbiter; Estimating Torque Imparted on Spacecraft Using Telemetry; PowderSim: Lagrangian Discrete and Mesh-Free Continuum Simulation Code for Cohesive Soils; Multiple-Frame Detection of Subpixel Targets in Thermal Image Sequences; Metric Learning to Enhance Hyperspectral Image Segmentation; Basic Operational Robotics Instructional System; Sheet Membrane Spacesuit Water Membrane Evaporator; Advanced Materials and Manufacturing for Low-Cost, High-Performance Liquid Rocket Combustion Chambers; Motor Qualification for Long-Duration Mars Missions.

Source record↗

Upper Troposphere Smoke Injection From Large Areal Fires

Abstract Large areal fires, such as those ignited following a nuclear detonation, can inject smoke into the upper troposphere and lower stratosphere. Detailed fire simulations allow for assessment of how local weather interacts with these fires and affects smoke lofting. In this study, we employ the fire simulation package in the Weather Research and Forecasting (WRF‐Fire) model, Version 4.0.1, to explore how smoke lofting from a fire burning a homogeneous fuel bed changes with varying local winds, relative humidity, and atmospheric boundary‐layer stability for two different‐sized areal fires. The presence of moisture has the greatest influence on the results by raising the altitude of lofting, while faster wind speeds dampen lofting and lower the injection height. Stably stratified conditions inhibit plume propagation compared with neutrally stratified conditions, although the impact of stability is not as strong as that of moisture and winds. These findings highlight the importance of using an appropriate atmospheric profile when simulating large fires, as the local weather can have a meaningful influence on smoke lofting.

54 ENVIRONMENTAL SCIENCES↗

Granular Simulation of NEO Anchoring

NASA is interested in designing a spacecraft capable of visiting a Near Earth Object (NEO), performing experiments, and then returning safely. Certain periods of this mission will require the spacecraft to remain stationary relative to the NEO. Such situations require an anchoring mechanism that is compact, easy to deploy and upon mission completion, easily removed. The design philosophy used in the project relies on the simulation capability of a multibody dynamics physics engine. On Earth it is difficult to create low gravity conditions and testing in low gravity environments, whether artificial or in space is costly and therefore not feasible. Through simulation, gravity can be controlled with great accuracy, making it ideally suited to analyze the problem at hand. Using Chrono::Engine [1], a simulation package capable of utilizing massively parallel GPU hardware, several validation experiments will be performed. Once there is sufficient confidence, modeling of the NEO regolith interaction will begin after which the anchor tests will be performed and analyzed. The outcome of this task is a study with an analysis of several different anchor designs, along with a recommendation on which anchor is better suited to the task of anchoring. With the anchors tested against a range of parameters relating to soil, environment and anchor penetration angles/velocities on a NEO.

multibody dynamics↗

Calibration and validation of the foundation for a multiphase strength model for tin

In this work, the Common Model of Multi-phase Strength and Equation of State (CMMP) model was applied to tin. Specifically, calibrations of the strength-specific elements of the CMMP foundation were developed with a combination of experiments and theory, and then the model was validated experimentally. The first element of the foundation is a multi-phase analytic treatment of the melt temperature and the shear modulus for the solid phases. These models were parameterized for each phase based on ab initio calculations using the software VASP (Vienna Ab initio Simulations Package) based on density functional theory. The shear modulus model for the ambient phase was validated with ultrasonic sound speed measurements as a function of pressure and temperature. The second element of the foundation is a viscoplastic strength model for the phase, upon which strength for inaccessible higher-pressure phases can be scaled as necessary. The stress–strain response of tin was measured at strain rates of 10 -3 to 3 x 10 3 s -1 and temperatures ranging from 87 to 373 K. The Preston–Tonks–Wallace (PTW) strength model was fit to that data using Bayesian model calibration. For validation, six forward and two reverse Taylor impact experiments were performed at different velocities to measure large plastic deformation of tin at strain rates up to ⁠10 5 s -1 . The PTW model accurately predicted the deformed shapes of the cylinders, with modest discrepancies attributed to the inability of PTW to capture the effects of twinning and dynamic recrystallization. Some material in the simulations of higher velocity Taylor cylinders reached the melting temperature, thus testing the multiphase model because of the presence of a second phase, the liquid. In simulations using a traditional modeling approach, the abrupt reduction of strength upon melt resulted in poor predictions of the deformed shape and non-physical temperatures. With CMMP, the most deformed material points evolved gradually to a mixed solid–liquid but never a fully liquid state, never fully lost strength, stayed at the melt temperature as the latent heat of fusion was absorbed, and predicted the deformed shape well.

36 MATERIALS SCIENCE↗