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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

A finite viscoelastic constitutive model for low to high strain rate response of elastomers with application of strain rate-induced glass transition

Amorphous elastomers exhibit significant rate-stiffening and unique viscous flow characteristics across a wide range of strain rates, often undergoing glass transition above a strain rate threshold. We have developed a thermodynamically-consistent and micromechanically-inspired constitutive model for soft elastomeric materials to capture the rate-dependent stress-strain behavior and hysteresis when subjected to low to high strain rates. Here, our proposed constitutive model encapsulates the viscous flow of materials through molecular motion at low strain rates and local rearrangement and alignment of the molecules trying to overcome the intermolecular resistance at high strain rates, essentially covering the glass transition. We applied our constitutive model to uniaxial compression experiments performed at low and high strain rates for polyborosiloxane (PBS) to identify the material parameters, and subsequently, performed numerical simulations of single and multi-cycle compression, stress relaxation, and small amplitude oscillatory tension-compression. Our analyses indicate that the model predicts higher total energy dissipation with increasing strain rate; however, dissipation associated with molecular relaxation decreases (forming a cusp) because, beyond a crossover strain rate, intermolecular rearrangement and alignment become dominant, which is consistent with the onset of the glass transition. For cyclic loading-unloading, we observed that dissipation over a cycle remains constant at low strain rates but decreases non-monotonically at high strain rates before becoming constant, with the peak stress over the cycle becoming higher, which can be interpreted as more loading being carried elastically by the polymer network as the intermolecular rearrangement process occurs. Additionally, our model was able to predict the qualitative nature of the storage modulus and loss modulus in the limit of small strain over a wide range of frequency sweeps.

36 MATERIALS SCIENCE↗
NASA NTRS2000

Viscoelastic flow modeling in the extrusion of a dough-like fluid

This work attempts to investigate the effect of viscoelasticity and three-dimensional geometry in screw channels. The Phan-Thien Tanner (PTT) constitutive equation with simplified model parameters was solved in conjunction with the flow equations. Polyflow, a commercially available finite element code was used to solve the resulting nonlinear partial differential equations. The PTT model predicted one log scale lower pressure buildup compared to the equivalent Newtonian results. However, the velocity profile did not show significant changes for the chosen PTT model parameters. Past Researchers neglected viscoelastic effects and also the three dimensional nature of the flow in extruder channels. The results of this paper provide a starting point for further simulations using more realistic model parameters, which may enable the food engineer to more accurately scale-up and design extrusion processes.

NASA Discipline Life Support Systems↗
NASA NTRS1995

Time-domain approach for the transient responses in stratified viscoelastic Earth models

We have developed the numerical algorithm for the computation of transient viscoelastic responses in the time domain for a radially stratified Earth model. Stratifications in both the elastic parameters and the viscosity profile have been considered. The particular viscosity profile employed has a viscosity maximum with a constrast of O(100) in the mid lower mantle. The distribution of relaxation times reveals the presence of a continuous spectrum situated between O(100) and O(exp 4) years. The principal mode is embedded within this continuous spectrum. From this initial-value approach we have found that for the low degree harmonics the non-modal contributions are comparable to the modal contributions. For this viscosity model the differences between the time-domain and normal-mode results are found to decrease strongly with increasing angular order. These calculations also show that a time-dependent effective relaxation time can be defined, which can be bounded by the relaxation times of the principal modes.

Hanyk, L.↗
NASA NTRS1973

Rheological effects on friction in elastohydrodynamic lubrication

An analytical and experimental investigation is presented of the friction in a rolling and sliding elastohydrodynamic lubricated contact. The rheological behavior of the lubricant is described in terms of two viscoelastic models. These models represent the separate effects of non-Newtonian behavior and the transient response of the fluid. A unified description of the non-Newtonian shear rate dependence of the viscosity is presented as a new hyperbolic liquid model. The transient response of viscosity, following the rapid pressure rise encountered in the contact, is described by a compressional viscoelastic model of the volume response of a liquid to an applied pressure step. The resulting momentum and energy equations are solved by an iterative numerical technique, and a friction coefficient is calculated. The experimental study was performed, with two synthetic paraffinic lubricants, to verify the friction predictions of the analysis. The values of friction coefficient from theory and experiment are in close agreement.

Trachman, E. G.↗
NASA NTRS1981

Nonlinear viscoelastic characterization of thin polyethylene film

In order to understand the state of stress and strain in a typical balloon fabricated from thin polyethylene film, experiment data in the literature reviewed. It was determined that the film behaves as a nonlinear viscoelasticity material and should be characterized accordingly. A simple uniaxial, nonlinear viscoelastic model was developed for predicting stress given a certain strain history. The simple model showed good qualitative agreement with results of constant rate, uniaxial accurately predicting stresses for cyclic strain histories typical of balloon flights. A program was outlined which will result in the development of a more complex nonlinear viscoelastic model.

Wilbeck, J. S.↗
NASA NTRSDate not supplied

A Nonlinear Viscoelastic-Viscoplastic Constitutive Model for Epoxy Polymers

The objective of this paper is to develop a nonlinear viscoelastic–viscoplastic constitutive model for epoxy polymers. The classic nonlinear viscoelasticity model is reformulated to yield a closed-form incremental constitutive relation, which relates the stress increments to the viscoelastic strain increments. A viscoplasticity model, which consists of the Drucker–Prager yield function, nonlinear isotropic and kinematic hardening laws, and the Perzyna viscosity function, is subsequently developed. The nonlinear viscoelasticity and the vis-coplasticity models are then implemented in a radial return algorithm. A closed-form algorithmic tangent operator is derived to facilitate model implementation. The nonlinear viscoelasticity model is validated by reproducing the test data for polymethyl methacrylate(PMMA). The present constitutive model’s capabilities are demonstrated through modeling viscoelastic–viscoplastic PMMA loaded at different strain rates. The mechanics of structure genome-based micromechanics approach, embedded with the present constitutive model, is used to homogenize a unidirectional fiber-reinforced composite with a PMMA matrix, subjected to uniaxial and shear loading at different strain rates. The viscoelastic characterization of PMT-F7 epoxy is evaluated by comparing the predicted creep–recovery responses by the present constitutive model with the experimental ones.

Liang Zhang↗
NASA NTRS1976

Development of a solid propellant viscoelastic dynamic model

The results of a one year study to develop a dynamic response model for the Space Shuttle Solid Rocket Motor (SRM) propellant are presented. An extensive literature survey was conducted, from which it was concluded that the only significant variables affecting the dynamic response of the SRM propellant are temperature and frequency. Based on this study, and experimental data on propellants related to the SRM propellant, a dynamic constitutive model was developed in the form of a simple power law with temperature incorporated in the form of a modified power law. A computer program was generated which performs a least-squares curve-fit of laboratory data to determine the model parameters and it calculates dynamic moduli at any desired temperature and frequency. Additional studies investigated dynamic scaling laws and the extent of coupling between the SRM propellant and motor cases. It was found, in agreement with other investigations, that the propellant provides all of the mass and damping characteristics whereas the case provides all of the stiffness.

Hufferd, W. L.↗
NASA NTRS2005

A K-BKZ Formulation for Soft-Tissue Viscoelasticity

A viscoelastic model of the K-BKZ (Kaye 1962; Bernstein et al. 1963) type is developed for isotropic biological tissues, and applied to the fat pad of the human heel. To facilitate this pursuit, a class of elastic solids is introduced through a novel strain-energy function whose elements possess strong ellipticity, and therefore lead to stable material models. The standard fractional-order viscoelastic (FOV) solid is used to arrive at the overall elastic/viscoelastic structure of the model, while the elastic potential via the K-BKZ hypothesis is used to arrive at the tensorial structure of the model. Candidate sets of functions are proposed for the elastic and viscoelastic material functions present in the model, including a regularized fractional derivative that was determined to be the best. The Akaike information criterion (AIC) is advocated for performing multi-model inference, enabling an objective selection of the best material function from within a candidate set.

Freed, Alan D.↗
NASA NTRS1996

A viscoelastic higher-order beam finite element

A viscoelastic internal variable constitutive theory is applied to a higher-order elastic beam theory and finite element formulation. The behavior of the viscous material in the beam is approximately modeled as a Maxwell solid. The finite element formulation requires additional sets of nodal variables for each relaxation time constant needed by the Maxwell solid. Recent developments in modeling viscoelastic material behavior with strain variables that are conjugate to the elastic strain measures are combined with advances in modeling through-the-thickness stresses and strains in thick beams. The result is a viscous thick-beam finite element that possesses superior characteristics for transient analysis since its nodal viscous forces are not linearly dependent an the nodal velocities, which is the case when damping matrices are used. Instead, the nodal viscous forces are directly dependent on the material's relaxation spectrum and the history of the nodal variables through a differential form of the constitutive law for a Maxwell solid. The thick beam quasistatic analysis is explored herein as a first step towards developing more complex viscoelastic models for thick plates and shells, and for dynamic analyses. The internal variable constitutive theory is derived directly from the Boltzmann superposition theorem. The mechanical strains and the conjugate internal strains are shown to be related through a system of first-order, ordinary differential equations. The total time-dependent stress is the superposition of its elastic and viscous components. Equations of motion for the solid are derived from the virtual work principle using the total time-dependent stress. Numerical examples for the problems of relaxation, creep, and cyclic creep are carried out for a beam made from an orthotropic Maxwell solid.

Johnson, Arthur R.↗
NASA NTRS1979

Postseismic viscoelastic deformation and stress. Part 2: Stress theory and computation; dependence of displacement, strain, and stress on fault parameters

A viscoelastic model for deformation and stress associated with earthquakes is reported. The model consists of a rectangular dislocation (strike slip fault) in a viscoelastic layer (lithosphere) lying over a viscoelastic half space (asthenosphere). The time dependent surface stresses are analyzed. The model predicts that near the fault a significant fraction of the stress that was reduced during the earthquake is recovered by viscoelastic softening of the lithosphere. By contrast, the strain shows very little change near the fault. The model also predicts that the stress changes associated with asthenospheric flow extend over a broader region than those associated with lithospheric relaxation even though the peak value is less. The dependence of the displacements, stresses on fault parameters studied. Peak values of strain and stress drop increase with increasing fault height and decrease with fault depth. Under many circumstances postseismic strains and stresses show an increase with decreasing depth to the lithosphere-asthenosphere boundary. Values of the strain and stress at distant points from the fault increase with fault area but are relatively insensitive to fault depth.

Cohen, S. C.↗
NASA NTRS1993

The analytical representation of viscoelastic material properties using optimization techniques

This report presents a technique to model viscoelastic material properties with a function of the form of the Prony series. Generally, the method employed to determine the function constants requires assuming values for the exponential constants of the function and then resolving the remaining constants through linear least-squares techniques. The technique presented here allows all the constants to be analytically determined through optimization techniques. This technique is employed in a computer program named PRONY and makes use of commercially available optimization tool developed by VMA Engineering, Inc. The PRONY program was utilized to compare the technique against previously determined models for solid rocket motor TP-H1148 propellant and V747-75 Viton fluoroelastomer. In both cases, the optimization technique generated functions that modeled the test data with at least an order of magnitude better correlation. This technique has demonstrated the capability to use small or large data sets and to use data sets that have uniformly or nonuniformly spaced data pairs. The reduction of experimental data to accurate mathematical models is a vital part of most scientific and engineering research. This technique of regression through optimization can be applied to other mathematical models that are difficult to fit to experimental data through traditional regression techniques.

Hill, S. A.↗
DOE OSTI2026

Influence of Numerical Modeling Approaches on Damped Behavior of Flexible Beams: Preprint

Composites structures are widely used in aerospace and wind energy applications for their excellent stiffness and strength-to-weight properties. In these structures, structural damping is critical to predict vibration amplitudes, performance, and reliability. Structural damping is of particular interest for slender wings, rotorcraft blades, and wind turbine blades that can exhibit complex vibration phenomena and are frequently modeled with geometrically exact beam theory (GEBT). Standard approaches of stiffness proportional or modal damping merely assign user defined values and cannot predict damping behavior. This work compares stiffness proportional damping to two more advanced damping approaches: modal strain energy and Prony series. The modal strain energy approach uses a sectional analysis tool to calculate the beam stiffness and postprocess internal stresses from GEBT simulations. The internal stresses are then used to calculate modal damping factors. The Prony series is implemented within GEBT to directly model viscoelastic behavior of the composites. These approaches are compared by modeling the evolution of the damping factors of a realistic flexible wind turbine blade with varying rotational speed. Discrepancies between the approaches suggest areas for future modeling development, but differences in nonlinear damping values are less than current uncertainties about the magnitude of structural damping.

17 WIND ENERGY↗
NASA NTRS1997

A General Reversible Hereditary Constitutive Model: Application to a Titanium Alloy - Part 2

Given the mathematical framework and specific viscoelastic model in Part 1 our primary goal in this second part is focused on model characterization and assessment for the specific titanium alloy, TIMETAL 21S. The model is motivated by experimental evidence suggesting the presence of significant rate/time effects in the so-called quasilinear, reversible, material response range. An explanation of the various experiments performed and their corresponding results are also included. Finally, model correlations and predictions are presented for a wide temperature range.

Arnold, S. M.↗
NASA NTRS1999

Comparison of observed rheological properties of hard wheat flour dough with predictions of the Giesekus-Leonov, White-Metzner and Phan-Thien Tanner models

The measured rheological behavior of hard wheat flour dough was predicted using three nonlinear differential viscoelastic models. The Phan-Thien Tanner model gave good zero shear viscosity prediction, but overpredicted the shear viscosity at higher shear rates and the transient and extensional properties. The Giesekus-Leonov model gave similar predictions to the Phan-Thien Tanner model, but the extensional viscosity prediction showed extension thickening. Using high values of the mobility factor, extension thinning behavior was observed but the predictions were not satisfactory. The White-Metzner model gave good predictions of the steady shear viscosity and the first normal stress coefficient but it was unable to predict the uniaxial extensional viscosity as it exhibited asymptotic behavior in the tested extensional rates. It also predicted the transient shear properties with moderate accuracy in the transient phase, but very well at higher times, compared to the Phan-Thien Tanner model and the Giesekus-Leonov model. None of the models predicted all observed data consistently well. Overall the White-Metzner model appeared to make the best predictions of all the observed data.

Non-NASA Center↗
NASA NTRS2002

Finite-Strain Fractional-Order Viscoelastic (FOV) Material Models and Numerical Methods for Solving Them

Fraction-order viscoelastic (FOV) material models have been proposed and studied in 1D since the 1930's, and were extended into three dimensions in the 1970's under the assumption of infinitesimal straining. It was not until 1997 that Drozdov introduced the first finite-strain FOV constitutive equations. In our presentation, we shall continue in this tradition by extending the standard, FOV, fluid and solid, material models introduced in 1971 by Caputo and Mainardi into 3D constitutive formula applicable for finite-strain analyses. To achieve this, we generalize both the convected and co-rotational derivatives of tensor fields to fractional order. This is accomplished by defining them first as body tensor fields and then mapping them into space as objective Cartesian tensor fields. Constitutive equations are constructed using both variants for fractional rate, and their responses are contrasted in simple shear. After five years of research and development, we now possess a basic suite of numerical tools necessary to study finite-strain FOV constitutive equations and their iterative refinement into a mature collection of material models. Numerical methods still need to be developed for efficiently solving fraction al-order integrals, derivatives, and differential equations in a finite element setting where such constitutive formulae would need to be solved at each Gauss point in each element of a finite model, which can number into the millions in today's analysis.

Freed, Alan D.↗
NASA NTRS2002

Transients in Pacific/North American Plate Boundary Deformation: Synthesis and Modeling of GPS and Borehole Strain Observations

This is the Final Technical Report on research conducted between 1 June 1997 and 14 September 2001 entitled "Transients in Pacific/North American plate boundary deformation: Synthesis and modeling of GPS and borehole strain observations." As the project title implies, our effort involved a geodetic study of strain transients, i.e., temporal variations in deformation rates, that occur within plate boundary zones and their relationship to earthquakes and plate motions. Important transients occur during and following large earthquakes, and there are also strain transients not apparently associated with earthquakes. A particularly intriguing class of transients, for which there is a modest but growing list of examples, are preseismic anomalies. Such earthquake precursors, if further documented and understood, would have obvious importance for earthquake hazard mitigation. Because the timescales for these diverse transients range over at least 6 orders of magnitude (minutes to years), no single geodetic technique is optimum. We therefore undertook a systematic synthesis of Global Positioning Satellite (GPS) and borehole strainmeter data in three areas in California where there are adequate numbers of both types of instruments (or their equivalent): the San Francisco Bay region (within the Bay Area Regional Deformation network), southern California (within the Southern California Integrated GPS Network), and Parkfield (where a two-color laser system provides a proxy for continuous GPS measurements). An integral component of our study was the elucidation of the physical mechanisms by which such transients occur and propagate. We therefore initiated the development of multiple forward models, using two independent approaches. In the first, we explored the response to specified earthquake slip in viscoelastic models that incorporated failure criteria and the geometry of major faults in California. In the second approach, we examined the dynamical response of a complex rheological medium to the application of a far-field stress imposed by plate motions. The forward models were used both to gain insight into the range of strain transients to be expected under different assumed mechanical conditions and to develop representations for strain fields that allow GPS, borehole, and other strain data to be combined in a self-consistent, yet well-determined, manner. The models also provided a basis for hypothesis testing, by which data from a strain transient well characterized by GPS and borehole observations were utilized to distinguish among competing candidates for the causative physical mechanism and the governing physical characteristics. During the three years of this project, continued to a fourth year through a no-cost extension of the grant, we published 14 papers and presented or co-authored 37 papers at national scientific meetings.

Solomon, Sean C.↗