Search NASA⌕ Search

SEARCH · Search NASA

Results for “constitutive equations”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Symbolic generation of constitutive equations

The use of the symbolic manipulation program MACSYMA for the automatic generation of constitutive equations describing the thermomechanical behavior of complex materials such as metal-matrix composites is demonstrated. Problem-specific algorithms are developed; e.g., for partial differentiation by the chain rule, automatic generation of tree structures, special tensor analysis, and the simplification of expressions. The resulting subprogram package, SDICE, is shown to be fully applicable to both isotropic and anisotropic materials; its potential usefulness as a basis for FEM analyses is indicated.

Tan, H. Q.↗
NASA NTRS1989

Computer simulation of the mathematical modeling involved in constitutive equation development: Via symbolic computations

Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation.

Arnold, S. M.↗
NASA NTRS1997

Constitutive Equations: Plastic and Viscoelastic Properties. (Latest citations from the Aerospace Database)

The bibliography contains citations concerning analytical techniques using constitutive equations, applied to materials under stress. The properties explored with these techniques include viscoelasticity, thermoelasticity, and plasticity. While many of the references are general as to material type, most refer to specific metals or composites, or to specific shapes, such as flat plate or spherical vessels.

VISCOELASTICITY↗
NASA NTRS1996

Constitutive Equations: Plastic and Viscoelastic Properties. (Latest Citations from the Aerospace Database)

The bibliography contains citations concerning analytical techniques using constitutive equations, applied to materials under stress. The properties explored with these techniques include viscoelasticity, thermoelasticity, and plasticity. While many of the references are general as to material type, most refer to specific metals or composites, or to specific shapes, such as flat plate or spherical vessels. (Contains 50-250 citations and includes a subject term index and title list.)

BIBLIOGRAPHIES↗
NASA NTRS1985

On thermomechanical testing in support of constitutive equation development for high temperature alloys

Three major categories of testing are identified that are necessary to provide support for the development of constitutive equations for high temperature alloys. These are exploratory, charactrization and verification tests. Each category is addressed and specific examples of each are given. An extensive, but not exhaustive, set of references is provided concerning pertinent experimental results and their relationships to theoretical development. This guide to formulating a meaningful testing effort in support of consitutive equation development can also aid in defining the necessary testing equipment and instrumentation for the establishment of a deformation and structures testing laboratory.

Robinson, D. N.↗
NASA NTRS1983

A Potential Function Derivation of a Constitutive Equation for Inelastic Material Response

Physical and thermodynamic concepts are used to develop a potential function for application to high temperature polycrystalline material response. Inherent in the formulation is a differential relationship between the potential function and constitutive equation in terms of the state variables. Integration of the differential relationship produces a state variable evolution equation that requires specification of the initial value of the state variable and its time derivative. It is shown that the initial loading rate, which is directly related to the initial hardening rate, can significantly influence subsequent material response. This effect is consistent with observed material behavior on the macroscopic and microscopic levels, and may explain the wide scatter in response often found in creep testing.

Stouffer, D. C.↗
NASA NTRS1985

On the use of internal state variables in thermoviscoplastic constitutive equations

The general theory of internal state variables are reviewed to apply it to inelastic metals in use in high temperature environments. In this process, certain constraints and clarifications will be made regarding internal state variables. It is shown that the Helmholtz free energy can be utilized to construct constitutive equations which are appropriate for metallic superalloys. Internal state variables are shown to represent locally averaged measures of dislocation arrangement, dislocation density, and intergranular fracture. The internal state variable model is demonstrated to be a suitable framework for comparison of several currently proposed models for metals and can therefore be used to exhibit history dependence, nonlinearity, and rate as well as temperature sensitivity.

Allen, D. H.↗
NASA NTRS1984

Dynamics of coupled ice-ocean system in the marginal ice zone: Study of the mesoscale processes and of constitutive equations for sea ice

This study is aimed at the modelling of mesoscale processed such as up/downwelling and ice edge eddies in the marginal ice zones. A 2-dimensional coupled ice-ocean model is used for the study. The ice model is coupled to the reduced gravity ocean model (f-plane) through interfacial stresses. The constitutive equations of the sea ice are formulated on the basis of the Reiner-Rivlin theory. The internal ice stresses are important only at high ice concentrations (90-100%), otherwise the ice motion is essentially free drift, where the air-ice stress is balanced by the ice-water stress. The model was tested by studying the upwelling dynamics. Winds parallel to the ice edge with the ice on the right produce upwilling because the air-ice momentum flux is much greater that air-ocean momentum flux, and thus the Ekman transport is bigger under the ice than in the open water. The upwelling simulation was extended to include temporally varying forcing, which was chosen to vary sinusoidally with a 4 day period. This forcing resembles successive cyclone passings. In the model with a thin oceanic upper layer, ice bands were formed.

Hakkinen, S.↗
NASA NTRS2004

A Constitutive Equation for Stratospheric Balloon Materials

The selection of a suitable material for use as a reliable stratospheric balloon gas barrier and structural component is based on a variety of properties. Due to a more desirable combination of properties, the low density polyethylene that has been used for the last half century has been replaced during the last decade by linear low density polyethylene (LLDPE). This paper describes the effort to characterize the time dependent properties of a 38 micron coextrusion of LLDPE. The nonlinear viscoelastic constitutive equation presented may be used to accurately describe the creep and/or relaxation of this film when subjected to a biaxial state of stress, such as might be required for an extended balloon flight. Recent laboratory data have been used to mod@ an existing model of LLDPE to account for differences caused by the coextrusion process. The new model will facilitate structural design optimization and reliability assessment, and may be further utilized as a predictive tool to benefit in-flight operations. Current structural analysis tech&ques based on linear elastic properties have predicted stresses in excess of those which would actually exist.

Rand, J. L.↗
NASA NTRS1983

Constitutive Equations for Use in Design Analyses of Long-life Elevated Temperature Components

Design analysis needs and procedures relative to elevated temperature components in liquid metal fast breeder reactor (LMFBR) system were examined. The effects of the thermal transients on the pressure boundary components are enhanced by the excellent heat transfer properties of the liquid sodium coolant. Design criteria for high temperature nuclear reactor components recognize the potential occurrence of inelastic structural response. Specifically, criteria and limits were developed which reflect a recognition of this potential and employ design by analysis concepts that requires that inelastic (elastic-plastic and creep) analyses be performed. Constitutive equations to represent multiaxial time-dependent responses of LMFBR alloys are established. The development of equations applicable under cyclic loading conditions are outlined.

Pugh, C. E.↗
NASA NTRS1985

Thermodynamically consistent constitutive equations for nonisothermal large strain, elasto-plastic, creep behavior

The paper is concerned with the development of constitutive relations for large nonisothermal elastic-viscoplastic deformations for metals. The kinematics of elastic-plastic deformation, valid for finite strains and rotations, is presented. The resulting elastic-plastic uncoupled equations for the deformation rate combined with use of the incremental elasticity law permits a precise and purely deductive development of elastic-viscoplastic theory. It is shown that a phenomenological thermodynamic theory in which the elastic deformation and the temperature are state variables, including few internal variables, can be utilized to construct elastic-viscoplastic constitutive equations, which are appropriate for metals. The limiting case of inviscid plasticity is examined.

Riff, R.↗
NASA NTRS1985

Physical concepts in the development of constitutive equations

Proposed viscoplastic material models include in their formulation observed material response but do not generally incorporate principles from thermodynamics, statistical mechanics, and quantum mechanics. Numerous hypotheses were made for material response based on first principles. Many of these hypotheses were tested experimentally. The proposed viscoplastic theories and the experimental basis of these hypotheses must be checked against the hypotheses. The physics of thermodynamics, statistical mechanics and quantum mechanics, and the effects of defects, are reviewed for their application to the development of constitutive laws.

Cassenti, B. N.↗
NASA NTRS1983

Correlations Between Metallurgical Characterization Studies, Exploratory Mechanical Tests, and Continuum Mechanics Approaches to Constitutive Equations

Austenitic stainless steels, such as types 316 and 304, are widely used as pressure vessel materials in the temperature range of 425 to 650 C. Stainless steel specimens were tested to rupture at two different stress levels sigma and sigma 2 sigma 1 sigma 2) to establish the normal stain-time behavior. A subsequent test was performed in which the specimen was crept at the higher stress (sigma 1) to the beginning of the secondary stage of creep, presumed to be the strain/time conditions at which a steady state microstructure is developed, and then the stress was reduced to the lower level (sigma 2). The associated microstructure, and significance of this microstructure on the creep strain-hardening model for variable uniaxial loads were assesed and found to be consistent with the use of creep-recovery models at high stresses and temperatures and strain-hardening models at low stresses and tempertures.

Moteff, J.↗
NASA NTRS1986

Constitutive Equations of Aging in Polymers

Theoretical paper presents solutions of equations that describe polymeric aging. Solutions apply under such loading conditions as constant strain (stress relaxation), constant strain rate, and stress relaxation with sudden change of cross-link density. Theoretical models form framework for predicting chemomechanical aging behavior of elastomers and polymers.

Peng, S. T. J.↗