The use of simple viscoelastic models in stress analysis
Mathematical model for viscoelastic stress analysis
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Mathematical model for viscoelastic stress analysis
Thermal effects in model viscoelastic solids
Drag reduction prediction in turbulent flow with viscoelastic model, discussing solutions exhibiting elastic properties in laminar flow
Arterial model with effects of thick walls, linear viscoelasticity and wall tethering for studying arterial mechanics
Nonlinear viscoelastic and thermoelastic characterization procedures were applied to a rubber toughened adhesive that is commercially available as FM-300. Long time (accelerated testing) predictions on the basis of stress-time-superposition and time-temperature-superposition were compared with actual long term data. Good verification was obtained.
An analytic approximation to the Green's function for the displacements due to a strike slip point source in an elastic layer over a viscoelastic half-space is developed. This approximate Green's function is useful because it can be analytically integrated over the fault surface. Comparison with a numerical integration of the exact solution integral indicates that the approximation is quite good. The approximate Green's function is integrated analytically to obtain the displacements due to a finite rectangular strike slip fault in an elastic layer over a viscoelastic half-space. Ground displacements and angle changes from a model survey net are computed to illustrate the viscoelastic relaxation which follows a fracture in the elastic region.
Dynamic plane shear of incompressible viscoelastic material with temperature dependent viscosity determined, using electric transmission line analog
Analytic model resembling thick walled ellipsoid of revolution incorporating three dimensional shape of human left ventricle and ventricular wall thickness effects
The deformation of Io, the tidal dissipation rate, and its interior spatial distribution are investigated by means of numerical simulations based on (1) a three-layer model (with dissipation in the mantle) or (2) a four-layer model (with dissipation in the asthenosphere). The mathematical derivation of the models is outlined; the selection of the input-parameter values is explained; the results are presented in extensive graphs and contour maps; and the constraints imposed on the models by observational data on the hot-spot distribution, tidal deformation, and gravity field are discussed in detail. It is found that both dissipation mechanisms may play a role on Io: model (2) is better able to explain the concentration of hot spots near the equator, while the presence of a large hot spot near the south pole (if confirmed by observations) would favor model (1).
The crustal deformation patterns associated with the earthquake cycle can depend strongly on the rheological properties of subcrustal material. Substantial deviations from the simple patterns for a uniformly elastic earth are expected when viscoelastic flow of subcrustal material is considered. The detailed description of the deformation pattern and in particular the surface displacements, displacement rates, strains, and strain rates depend on the structure and geometry of the material near the seismogenic zone. The origin of some of these differences are resolved by analyzing several different linear viscoelastic models with a common finite element computational technique. The models involve strike-slip faulting and include a thin channel asthenosphere model, a model with a varying thickness lithosphere, and a model with a viscoelastic inclusion below the brittle slip plane. The calculations reveal that the surface deformation pattern is most sensitive to the rheology of the material that lies below the slip plane in a volume whose extent is a few times the fault depth. If this material is viscoelastic, the surface deformation pattern resembles that of an elastic layer lying over a viscoelastic half-space. When the thickness or breath of the viscoelastic material is less than a few times the fault depth, then the surface deformation pattern is altered and geodetic measurements are potentially useful for studying the details of subsurface geometry and structure. Distinguishing among the various models is best accomplished by making geodetic measurements not only near the fault but out to distances equal to several times the fault depth. This is where the model differences are greatest; these differences will be most readily detected shortly after an earthquake when viscoelastic effects are most pronounced.
The crustal deformation patterns associated with the earthquake cycle can depend strongly on the rheological properties of subcrustal material. Substantial deviations from the simple patterns for a uniformly elastic earth are expected when viscoelastic flow of subcrustal material is considered. The detailed description of the deformation pattern and in particular the surface displacements, displacement rates, strains, and strain rates depend on the structure and geometry of the material near the seismogenic zone. The origin of some of these differences are resolved by analyzing several different linear viscoelastic models with a common finite element computational technique. The models involve strike-slip faulting and include a thin channel asthenosphere model, a model with a varying thickness lithosphere, and a model with a viscoelastic inclusion below the brittle slip plane. The calculations reveal that the surface deformation pattern is most sensitive to the rheology of the material that lies below the slip plane in a volume whose extent is a few times the fault depth. If this material is viscoelastic, the surface deformation pattern resembles that of an elastic layer lying over a viscoelastic half-space. When the thickness or breath of the viscoelastic material is less than a few times the fault depth, then the surface deformation pattern is altered and geodetic measurements are potentially useful for studying the details of subsurface geometry and structure. Distinguishing among the various models is best accomplished by making geodetic measurements not only near the fault but out to distances equal to several times the fault depth. This is where the model differences are greatest; these differences will be most readily detected shortly after an earthquake when viscoelastic effects are most pronounced.
A viscoelastic relaxation model is used to interpret postseismic surface deformation for the large-magnitude Aleutian earthquakes of 1957 and 1965. The lithosphere and asthenosphere are modeled as elastic solids with an anomalous viscoelastic inclusion below the island arc volcanoes. It is found that the observed postseismic surface deformation is a corollary of the known island arc structure. A satisfactory fit to the uplift following the 1957 earthquake is found for a viscoelastic volume with 80-km width extending from a depth of 50 to 200 km.
A viscoelastic stiffness model of seismicity is developed by introducing a viscoelastic element into the stiffness model for fault dynamics. The introduction of this element permits modeling of transient anelastic deformations in response to stress loading and relaxation and provides a mechanism for partial stress recovery following an earthquake. As a consequence, several phenomena not present in elastic stiffness theory emerge. These include postseismic creep, foreshocks, and aftershocks. Numerical simulations of fault motion also reveal episodes of stable sliding, tertiary creep preceeding earthquakes, and long-term aseismic creep.
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.
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.
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.
Photoviscoelastic method for stress analysis of two dimensional viscoelastic models
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.