Search NASA⌕ Search

SEARCH · Search NASA

Results for “Constitutive relations”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Space-time dependent thermal conductivity in nonlocal thermal transport

Nonlocal thermal transport is generally described by the Peierls-Boltzmann transport equation (PBE). However, solving the PBE for a general space-time dependent problem remains a challenging task due to the high dimensionality of the integro-differential equation. In this work, we present a direct solution to the space-time dependent PBE with a linearized collision matrix using an eigendecomposition method. We show that there exists a generalized Fourier-type relation that links heat flux to the local temperature, and this constitutive relation defines a thermal conductivity that depends on both time and space. Combining this approach with ab initio calculations of phonon properties, we demonstrate that the space-time dependent thermal conductivity gives rise to an oscillatory response in temperature in a transient grating geometry in high thermal conductivity materials. The present solution method allows us to extend the reach of our computational capability for heat conduction to space-time dependent nondiffusive transport regimes. Here, this capability will not only enable a more accurate interpretation of thermal measurements that observe nonlocal thermal transport, but also enhance our physical understanding of nonlocal thermal transport in high thermal conductivity materials that are promising candidates for nanoscale thermal management applications.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1985

A comparison of smooth specimen and analytical simulation techniques for notched members at elevated temperatures

Experimental strain measurements have been made at the highly strained regions on notched plate specimens that were made of Hastelloy X. Tests were performed at temperatures up to 1,600 F. Variable load patterns were chosen so as to produce plastic and creep strains. Were appropriate, notch root stresses were experimentally estimated by subjecting a smooth specimen to the measured notch root strains. The results of three analysis techniques are presented and compared to the experimental data. The most accurate results were obtained from an analysis procedure that used a smooth specimen and the Neuber relation to simulate the notch root stress-strain response. When a generalized constitutive relation was used with the Neuber relation, good results were also obtained, however, these results were not as accurate as those obtained when the smooth specimen was used directly. Finally, a general finite element program, ANYSIS, was used which resulted in acceptable solutions, but, these were the least accurate predictions.

Martin, J. F.↗
NASA NTRS1992

Elastoviscoplastic buckling behavior of simply supported columns

The elastoviscoplastic buckling behavior of simply supported columns is investigated. The analysis is based on an incremental formulation that can deal with nonlinear geometrical and constitutive relations. Both viscoelastic and viscoplastic models are discussed, and Bodner-Partom's constitutive equations are used in the viscoplastic case. A numerical example is given to demonstrate the buckling behavior of columns under various temperature and loading levels.

Song, Y.↗
NASA NTRS1993

Multiple degree of freedom force-state component identification

Force-state mapping is extended to allow the quasistatic characterization of realistic multiple degree of freedom systems whose constitutive relations are nonlinear, dissipative, coupled and depend on memory of past states. A general constitutive force-state model is formulated, which includes dynamic hysteresis phenomena typical of that found in deployable structures. A two step parameter identification approach is developed, which employs a linear extended Kalman filter and a nonlinear least squares fit. A six degree of freedom force-state testing device was constructed, and used to obtain data on one bay of a simple truss and on one bay of the MODE deployable truss.

Masters, Brett P.↗
NASA NTRSDate not supplied

Nonlinear Homogenization of Finitely Deformed Viscoelastic-Viscoplastic Composites Using Mechanics of Structure Genome

The objective of this paper is to develop a micromechanics approach to homogenizing finitely deformed viscoelastic-viscoplastic composites using the mechanics of structure genome. The incremental constitutive relation for glassy polymers, formulated in the spatial configuration, is implemented in the present approach.This involves (1) pulling-back the constitutive model to the material configuration and (2)choosing the deformation gradient tensor and the first Piola–Kirchhoff stress tensor as the strain and the stress measures during homogenization, respectively. An Euler–Newton predictor–corrector method is developed for homogenization. Each step involves formulating a variational statement using the mechanics of structure genome, discretizing the statement in a finite-dimensional space, and solving the problem using an Euler/multilevel Newton method. The present approach is demonstrated by homogenizing fiber- and particle-reinforced composites undergoing uniaxial, biaxial, or shear deformation, at different stain rates.

Multi-scale modeling, High Strain Composites, Visc↗
DOE OSTI2021

Closures and Simulation for Thermal Radiation Transport in Stochastic Media with Nonlinear Temperature Dependence

Because of the practical challenge of rendering very complex realistic spatial structures for numerical work, it is common practice to resort to characterizing such media as stochastic mixtures of materials, ideally parametrized with low order statistics such as the mean, variance, and correlation functions of the now random material properties. This enables realizations of the medium to be repeatedly generated and radiation transport computations to, in principle, be performed for a large ensemble of these realizations to obtain a statistically well-characterized radiation field. Statistical post-processing yields desired quantities such as conditional and unconditional mean radiation flux and probability distributions of transmitted radiation. However, such computations prove expensive for all but the simplest stochastic geometries and are most suited for benchmarking approximate models. The most common approximations lead to homogenized media so that transport computations are required only on a single medium realization but by construct provide only limited statistical information on the radiation field. Almost all approximate approaches to this problem attempt to develop equations for low order moments of the radiation intensity (mean, second moment, correlation function) but inevitably encounter a closure problem: the equation for any statistical moment will contain terms depending on unknown higher-order moments. Thus, the challenge shifts to one of developing closure relations that relate the unknown moments to the lower order moments. Under very special conditions, an exact closure can be derived but in general closures are heuristically stated constitutive relations. Also, closure approaches depend on whether the mixing statistics are spatially and/or temporally continuous as in fluctuating turbulent fields, or discontinuous as in randomly mixed solid chunks of material. Thus, unconditional averaging is generally applied in the former case but conditional averaging is more appropriate when the mixing is discontinuous. In this work, the emphasis is on binary statistical mixtures of immiscible fluids as as such the quantities of interest are averages (flux, temperature) conditioned on the material type.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1992

Grain size reduction in granular flows of spheres - The effects of critical impact energy

Methods employed to derive recent kinetic theories for rapid noncomminuting granular flows are extended to homogeneous flows in which a fraction of the repeated collisions produce tiny fractures on the particles' peripheries and gradually reduce their effective diameters. The theory consists of balance equations for mass, momentum, and energy, as well as constitutive relations for the presence tensor and collisional rates of mass and energy lost. The work of Richman and Chou (1989) is improved by incorporating into the constitutive theory the critical impact energy below which no mass loss occurs in a binary collision. The theory is applied to granular shear flows and, for fixed shear rates, predicts the time variations of the solid fraction granular temperature, and induced stresses, as well as their extreme sensitivities to small changes in the critical impact energy.

Richman, M. W.↗
DOE OSTI2023

Uncertainty Quantification for Multiphase Computational Fluid Dynamics Closure Relations with a Physics-Informed Bayesian Approach

Multiphase Computational Fluid Dynamics (MCFD) based on the two-fluid model is considered a promising tool to model complex two-phase flow systems. MCFD simulation can predict local flow features without resolving interfacial information. As a result, the MCFD solver relies on closure relations to describe the interaction between the two phases. Those empirical or semi-mechanistic closure relations constitute a major source of uncertainty for MCFD predictions. In this paper, we leverage a physics-informed uncertainty quantification (UQ) approach to inversely quantify the closure relations’ model form uncertainty in a physically consistent manner. This proposed approach considers the model form uncertainty terms as stochastic fields that are additive to the closure relation outputs. Combining dimensionality reduction and Gaussian processes, the posterior distribution of the stochastic fields can be effectively quantified within the Bayesian framework with the support of experimental measurements. As this UQ approach is fully integrated into the MCFD solving process, the physical constraints of the system can be naturally preserved in the UQ results. Here, in a case study of adiabatic bubbly flow, we demonstrate that this UQ approach can quantify the model form uncertainty of the MCFD interfacial force closure relations, thus effectively improving the simulation results with relatively sparse data support.

42 ENGINEERING↗
DOE OSTI2020

SO(3)-invariance of informed-graph-based deep neural network for anisotropic elastoplastic materials

This work examines the frame-invariance (and the lack thereof) exhibited in simulated anisotropic elasto-plastic responses generated from supervised machine learning of classical multi-layer and informed-graph-based neural networks, and proposes different remedies to fix this drawback. The inherent hierarchical relations among physical quantities and state variables in an elasto-plasticity model are first represented as informed, directed graphs, where three variations of the graph are tested. While feed-forward neural networks are used to train path-independent constitutive relations (e.g., elasticity), recurrent neural networks are used to replicate responses that depends on the deformation history, i.e. or path dependent. In dealing with the objectivity deficiency, we use the spectral form to represent tensors and, subsequently, three metrics, the Euclidean distance between the Euler Angles, the distance from the identity matrix, and geodesic on the unit sphere in Lie algebra, can be employed to constitute objective functions for the supervised machine learning. In this, the aim is to minimize the measured distance between the true and the predicted 3D rotation entities. Following this, we conduct numerical experiments on how these metrics, which are theoretically equivalent, may lead to differences in the efficiency of the supervised machine learning as well as the accuracy and robustness of the resultant models. Neural network models trained with tensors represented in component form for a given Cartesian coordinate system are used as a benchmark. Our numerical tests show that, even given the same amount of information and data, the quality of the anisotropic elasto-plasticity model is highly sensitive to the way tensors are represented and measured. The results reveal that using a loss function based on geodesic on the unit sphere in Lie algebra together with an informed, directed graph yield significantly more accurate rotation prediction than the other tested approaches.

42 ENGINEERING↗
DOE OSTI2019

Validation of RELAP-7 for Forced Convective and Natural Circulation Reactor Flows

New reactor designs such as small modular reactors and newly proposed passive safety systems rely on natural circulation two-phase flow cooling of the reactor core under accident conditions. Without a pump to drive the flow, the circulation rate is a strong function of void fraction. Under these conditions where the flow rate, pressure drop, and heat transfer are all closely coupled through the mixture density, the accurate prediction of void fraction is pivotal. Furthermore, while these passive systems boast a more reliable cooling option, the sensitivity of the system to two-phase flow instabilities is more likely than in forced convective cooling and can result in dangerous density wave or flow excursion conditions. Improvement of one-dimensional system codes and further development of three-dimensional code capability are all important efforts in addressing these issues. The proposed work is a critical step towards providing confidence through validation of the capability of thermal-hydraulic tools to meet the emerging challenges in reactor simulation. Historically, system analysis codes develop a stiffness over time due to fine-tuning of adjustable code parameters that result in a reluctance or inability to adopt improved models. Therefore, a rigorous effort should be invested in preparation for RELAP-7 to identify required modeling improvements of constitutive relations and validation of the code applicability to the wide range of possible reactor flow conditions. Part of this validation involves the uncertainty quantification which is a critical step in the Code Scaling, Applicability, and Uncertainty (CSAU) methodology and Best-Estimate Plus Uncertainty (BEPU) licensing method. BEPU allows recovery of safety margins and potentially optimizing plant performance, resulting in economic benefit for the reactor operators. Beginning with the collection of past experimental data covering prototypic LWR conditions, this document reviews three critical datasets available for the validation of system codes. The experimental methods, procedures, facilities, instrumentation, and supplementary information are consolidated to aid the validation efforts of this work and future projects. These three datasets (824 conditions) are chosen due to their wide acceptance and demonstrated application for code validation. Two experimental datasets from the Nuclear Power Engineering Corporation (NUPEC) span prototypic conditions of Boiling Water Reactors (BWR) and Pressurized Water Reactors (PWR). These datasets are labeled as the BFBT (BWR Full-size Fine-mesh Bundle Test) and the PSBT (PWR Subchannel and Bundle Test) datasets respectively. The third dataset is taken in an internally heated annulus that is scaled based on a BWR subassembly and includes two-phase flows important to post-blowdown analysis. Together, the datasets consider the full range of pressure and mass flux expected in LWR forced convective flows from steady-state to long term cooling conditions. Recognizing the deficiency of available data under low-pressure, low-flow, a new natural circulation dataset consisting of 107 conditions is obtained. With system pressures ranging between 145 and 950 kPa, natural circulation is driven by a heat flux up to 275 kW/m2 in a 3 m long heated region of the annulus test section which is followed by a 2 m long unheated region before entering a condenser. Stable natural circulation flow rates in this facility were measured to be between 182 and 590 kg/m2-s. Pressure and temperature are measured at ten locations in the facility. In addition, measurements of void fraction, interfacial area concentration, and gas velocity are obtained at five axial locations in the annulus test section. The RELAP5-3D code demonstrates good accuracy for void fraction predictions in BFBT and PSBT benchmarks, but shows relatively large discrepancy in the annulus experiments at lower pressures. In two-phase natural circulation, large oscillations are observed in many system parameters during the simulation of 19 experiment cases which were conducted at low pressures, and the model shows good predictive performance with the remaining 88 experiment cases. However, some discrepancies in void fraction and temperature predictions are found which may require improved constitutive modeling under these low-pressure, low-flow condition. The quantified uncertainty in void fraction predictions in three forced convection benchmarks due to uncertainties in boundary conditions and geometries are relatively small, except for a few cases in the annulus experiment. The output uncertainty of the natural circulation model is quantified by considering the measurement error in boundary conditions, and it is shown that the output uncertainty ranges are relatively small for the range of conditions considered. Through this work, a clear pathway is provided for validation of RELAP7 once the code is available.

42 ENGINEERING↗
DOE OSTI2025

A comparison of surrogate constitutive models for viscoplastic creep simulation of HT-9 steel

Mechanistic microstructure-informed constitutive models for the mechanical response of polycrystals are a cornerstone of computational materials science. However, as these models become increasingly more complex – often involving coupled differential equations describing the effect of specific deformation modes – their associated computational costs can become prohibitive, particularly in optimization or uncertainty quantification tasks that require numerous model evaluations. To address this challenge, surrogate constitutive models that balance accuracy and computational efficiency are highly desirable. Data-driven surrogate models, that learn the constitutive relation directly from data, have emerged as a promising solution. In this work, we develop two local surrogate models for the viscoplastic response of a steel: a piecewise response surface method and a mixture of experts model. These surrogates are designed to adapt to complex material behavior, which may vary with material parameters or operating conditions. The surrogate constitutive models are applied to creep simulations of HT-9 steel, an alloy of considerable interest to the nuclear energy sector due to its high tolerance to radiation damage, using training data generated from viscoplastic self-consistent (VPSC) simulations. In conclusion, we define a set of test metrics to numerically assess the accuracy of our surrogate models for predicting viscoplastic material behavior, and show that the mixture of experts model outperforms the piecewise response surface method in terms of accuracy.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Revealing Defect-Seeded and Interfacial Generation Mechanisms of Photoinduced Coherent Phonons with 4D Ultrafast Electron Microscopy

Ultrafast photoexcitation of coherent phonons is driven by an impulsive, collective displacement of constituent atoms from their average equilibrium lattice positions [1]. Models describing the generation of coherent acoustic modes typically invoke the creation of an anisotropic strain profile arising from the relatively instantaneous absorption of an ultrafast laser pulse [2]. If the skin depth is shallow relative to the specimen thickness, a steep tensile strain gradient perpendicular to the surface ($\frac{∂ε}{∂z}$) results. Initial relaxation occurs via rapid contraction of the surface layers followed by subsequent coherent oscillations of the lattice and launch of a train of coherent elastic strain waves [i.e., coherent acoustic phonons (CAPs)]. Macroscopically, responses are generally well-described by constitutive relations as gleaned from data gathered using ultrasonic methods or ultrafast spectroscopies. Furthermore, at the atomic to nanoscale level, individual lattice discontinuities and their impact on CAP behaviors can be modeled using multiscale methods [3,4]. Further, average unit-cell level responses on ultrafast timescales can be probed using femtosecond electron and X-ray scattering [5,6].

Flannigan, David J. [University of Minnesota, Minn↗
DOE OSTI2023

Crystal plasticity model of BCC metals from large-scale MD simulations

Accurate crystal plasticity models that faithfully capture the behavior of single crystals under a wide range of loading conditions, such as loading direction, strain rate, and temperature, are still lacking. Here we introduce a novel approach in which a crystal plasticity (CP) model is informed directly from and calibrated to large-scale quantum-accurate MD simulations in which single crystal BCC Ta serves as a testbed material. By analyzing our large set of MD simulations several key insights are obtained leading us to modify constitutive assumptions in order to address deficiencies of existing CP models. Importantly, we observe that the standard notion of fixed slip systems – pairs of slip directions and slip planes – is inadequate for describing high-rate plasticity in BCC tantalum at room temperature. Instead, pencil glide defined as dislocation motion in the maximum resolved shear stress planes (MRSSP) of each Burgers vector is fully consistent with our MD simulation data while providing significant simplifications of the constitutive relations. Herein, our resulting new CP model closely matches the behavior of single crystals observed in high-rate MD simulations while being fully consistent with lower rate experimental results.

36 MATERIALS SCIENCE↗
NASA NTRS2000

Constitutive and Stability Behavior of Soils in Microgravity Environment

All aspects of soil stability, bearing capacity, slope stability, the supporting capacity of deep foundations, and penetration resistance depend on soil strength. The stress-deformation and stress-deformation-time behavior of soils are of importance in any problem where ground movements are of interest. In most engineering materials, the strength is derived from internal chemical and physico-chemical forces of interaction, which bond the atoms, molecules, and particles together. In soils, the constitutive relations are mainly derived from interparticle friction between particles and particle groups and dilatancy, and to a lesser extent from particle bonding by weak electrostatic, physico-chemical, and coulomb forces. For engineering purposes, soils are classified as cohesive (clays and silts; typical particle sizes range from 10 nm to 10 micrometers) and cohesionless (sand and gravel; typical particle sizes range from 10 micrometers to 75 mm). The mechanical or constitutive properties of cohesionless soils or granular materials are highly fabric-dependent, highly non-linear, and non-conservative with engineering properties primarily depending on the effects of gravity through self-weight and on the tractions or forces applied to the soil mass. Under moderate-to-high stress levels, the influence of gravity on the behavior of laboratory test specimens may not be pronounced and, therefore, the test results in terrestrial (1-g) environment may be sufficiently conclusive. However at low interparticle stresses, which can result either from low applied (confining) stresses or from excess pore fluid pressures developed within the soil mass without corresponding changes in the applied stresses, the presence of gravitational body forces acting on solid particles and interstitial fluids exerts a pronounced influence on movement of individual particles or particle groups. Such motions, in turn, cause changes in soil fabric which results in significant changes in the interparticle friction forces contributing to the soil's strength and deformation characteristics.

Alshibli, Khalid A.↗
NASA NTRS1991

Stirling engine: Available tools for long-life assessment

A review is presented for the durability approaches applicable to long-time life assessment of Stirling engine hot-section components. The crucial elements are experimental techniques for generating long-time materials property data (both monotonic and cyclic flow and failure properties); analytic representations of slow strain rate material stress-strain response characteristics (monotonic and cyclic constitutive relations) at high temperatures and low stresses and strains; analytic creep-fatigue-environmental interaction life prediction methods applicable to long lifetimes at high temperatures and small stresses and strains; and experimental verification of life predictions. Long-lifetime design criteria for materials of interest are woefully lacking. Designing against failures due to creep, creep-rupture, fatigue, environmental attack, and creep-fatigue-environmental interaction will require considerable extrapolation. Viscoplastic constitutive models and time-temperature parameters will have to be calibrated for the hot-section materials of interest. Analysis combined with limited verification testing in a short-time regime will be required to build confidence in long-lifetime durability models.

Halford, Gary R.↗
NASA NTRS1991

Stirling engine - Available tools for long-life assessment

A review is presented for the durability approaches applicable to long-time life assessment of Stirling engine hot-section components. The crucial elements are experimental techniques for generating long-time materials property data (both monotonic and cyclic flow and failure properties); analytic representations of slow strain rate material stress-strain response characteristics (monotonic and cyclic constitutive relations) at high temperatures and low stresses and strains; analytic creep-fatigue-environmental interaction life prediction methods applicable to long lifetimes at high temperatures and small stresses and strains; and experimental verification of life predictions. Long-lifetime design criteria for materials of interest are woefully lacking. Designing against failures due to creep, creep-rupture, fatigue, environmental attack, and creep-failure-environmental interaction will require considerable extrapolation. Viscoplastic constitutive models and time-temperature parameters will have to be calibrated for the hot-section materials of interest. Analysis combined with limited verification testing in a short-time regime will be required to build confidence in long-lifetime durability models.

Halford, Gary R.↗
NASA NTRS1996

First Cycle Heterogeneous Deformation Behavior and Cyclic Shakedown Phenomena of Nitinol Near A(sub f) Temperatures

Experimental observations on the cyclic behavior of a NiTi alloy (Nitinol) at temperatures in the neighborhood of the A(sub f) (austenite finish) temperature are presented. The strongly heterogeneous nature of the deformation behavior of this material at temperatures within this regime during the first cycle is examined with emphasis placed on the difficulties that the existence of such phenomena pose on the formulation of realistic constitutive relations. It is further demonstrated that this heterogeneity of deformation persists on subsequent cycles with the result that the hysteretic cyclic behavior of these alloys can exhibit a point to point variation in an otherwise uniform geometry. The experimental observations on the deformation behavior of this alloy show that it is strongly dependent on temperature and prior deformation history of the sample, thus resulting in an almost intractable problem with respect to capturing an adequate constitutive description from either experiment or modeling.

Jones, H. N.↗
NASA NTRS2002

A Thermodynamic Theory of Solid Viscoelasticity. Part 3: Nonlinear Glassy Viscoelasticity, Stability Constraints, Specifications

This paper, the last in the series, continues developing the nonlinear constitutive relations for non-isothermal, compressible, solid viscoelasticity. We initially discuss a single integral approach, more suitable for the glassy state of rubber-like materials, with basic functionals involved in the thermodynamic description for this type of viscoelasticity. Then we switch our attention to analyzing stability constraints, imposed on the general formulation of the nonlinear theory of solid viscoelasticity. Finally, we discuss specific (known from the literature or new) expressions for material functions that are involved in the constitutive formulations of both the rubber-like and glassy-like, complementary parts of the theory.

Freed, Alan↗