1,721,128 research outputs found
Circularly polarized wave propagation in a class of bodies defined by a new class of implicit constitutive relations
No full textIn this paper, we show that circularly polarized transverse stress waves, standing shear stress waves, and oscillatory
shear stress waves can propagate in a new class of viscoelastic solid bodies which are a subclass of bodies described by
implicit constitutive theories. The class of models that is being considered includes as sub-classes, the classical Kelvin–Voigt
model, the new models introduced by Rajagopal wherein the Cauchy–Green tensor is a non-linear function of the stress,
and the Navier–Stokes fluid model. The solutions established in this paper are generalizations of solutions that have been
established within the context of nonlinear elasticity by Carroll, and Destrade and Saccomandi, to the new class of elastic
and viscoelastic bodies that are being considered
Response of an Elastic Body whose Heat Conduction Is Pressure Dependent
No full texthe properties of many real materials such as the viscosity, thermal and electrical conductivity, specific heat, relaxation time, as well as optical properties, depend upon the pressure to which the body is subject. For instance, the viscosity of fluids can vary by several orders of magnitude due to the variation in the pressure. In this paper we investigate the change in the response of an elastic solid due to the thermal conductivity being pressure dependent. It is well known that higher pressure leads to reduced molecular mobility, in rubber-like materials, leading in turn to higher cross-linking reaction rates. We find that the response of the solid is quite different from the classical response that is obtained by using Fourier's law of heat conduction. The theoretical predictions according to the assumption that the thermal conductivity is pressure dependent, are in keeping with experimental results concerning the vulcanization of rubbers wherein one observes the conduction to be dependent on the pressure. To our knowledge, this is the first theoretical study that evaluates the response of non-linear elastic solids due the thermal conductivity depending on the pressure
Unsteady motions of a new class of elastic solids
No full textIn this short paper we study unsteady motions of a new class of elastic solids, wherein one can justify a non-linear relationship between the linearized strain and the stress, an impossibility
within the classical construct of elasticity. For the class of materials concerned, one has to solve simultaneously the balance of mass, balance of linear momentum and the constitutive relation. In general, one has ten scalar unknowns, i.e., density ρ, the components of Cauchy stress T and displacement u, and ten scalar algebraic–partial differential equations,
the balance of mass (1), the balance of linear momentum (3) and the constitutive equation (6). The stress wave that is generated is quite distinct from what one observes within the context of the classical theory
Flow of fluids with pressure- and shear-dependent viscosity down an inclined plane
Full text linkIn this paper we consider a fluid whose viscosity depends on both the mean normal stress and the shear rate flowing down an inclined plane. Such flows have relevance to geophysical flows. In order to make the problem amenable to analysis, we consider a generalization of the lubrication approximation for the flows of such fluids based on the development of the generalization of the Reynolds equation for such flows. This allows us to obtain analytical solutions to the problem of propagation of waves in a fluid flowing down an inclined plane. We find that the dependence of the viscosity on the pressure can increase the breaking time by an order of magnitude or more than that for the classical Newtonian fluid. In the viscous regime, we find both upslope and downslope travelling wave solutions, and these solutions are quantitatively and qualitatively different from the classical Newtonian solutions
On the nonlinear stability of onedimensional granular flows
No full textProceedings of A.S.M.E. conferenc
On the conditional stability of the rest state of a fluid of second grade in unbounded domains
No full textThe conditional stability of the rest state of a fluid of second grade
in unbounded domains is studied, some stability theorems are proven
Unsteady flows of fluids with pressure dependent viscosity
No full textIn this short paper we consider the unsteady flows of fluids with pressure dependent viscosities when the effect of gravity has to be taken into account. Such a situation presents itself in many technologically relevant flows. After developing the appropriate governing equations, we establish qualitative results concerning the nature of the solutions to the governing equations as well as uniqueness results. We then obtain explicit exact solutions for two initial-boundary value problems, namely modified Stokes’ first and second problems. Such explicit solutions serve a dual purpose, they present exact results for idealized problems that reflect practical situations, and they provide a means for checking the numerical schemes that are developed for flows in more complex situations
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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