122 research outputs found
Cancellation of vorticity in steady-state non-isentropic flows of complex fluids
In steady-state non-isentropic flows of perfect fluids there is always
thermodynamic generation of vorticity when the difference between the product
of the temperature with the gradient of the entropy and the gradient of total
enthalpy is different from zero. We note that this property does not hold in
general for complex fluids for which the prominent influence of the material
substructure on the gross motion may cancel the thermodynamic vorticity. We
indicate the explicit condition for this cancellation (topological transition
from vortex sheet to shear flow) for general complex fluids described by
coarse-grained order parameters and extended forms of Ginzburg-Landau energies.
As a prominent sample case we treat first Korteweg's fluid, used commonly as a
model of capillary motion or phase transitions characterized by diffused
interfaces. Then we discuss general complex fluids. We show also that, when the
entropy and the total enthalpy are constant throughout the flow, vorticity may
be generated by the inhomogeneous character of the distribution of material
substructures, and indicate the explicit condition for such a generation. We
discuss also some aspects of unsteady motion and show that in two-dimensional
flows of incompressible perfect complex fluids the vorticity is in general not
conserved, due to a mechanism of transfer of energy between different levels.Comment: 12 page
Special solutions in a generalized theory of nematics
Abstract: Using a model of a nematic liquid crystal which extends Ericksen’s
and allows for biaxiality, we solve two simple problems for a slab of a nematic with
strong anchoring conditions on the boundary planes. We show that, as the anchoring
angle changes, a first-order transition between two solution types would be predicted
on the basis of the Frank’s and Ericksen’s models, whereas, when biaxiality is allowed,
the transition predicted is second-order, but with a non-smooth transition mode of the
chevron type
Thermoelastic Waves in Microstructured Solids
Thermoelastic wave propagation suggests a coupling between elastic deformation and heat conduction in a body. Microstructure of the body influences the both processes. Since energy is conserved in elastic deformation and heat conduction is always dissipative, the generalization of classical elasticity theory and classical heat conduction is performed differently. It is shown in the paper that a hyperbolic evolution equation for microtemperature can be obtained in the framework of the dual internal variables approach keeping the parabolic equation for the macrotemperature. The microtemperature is considered as a macrotemperature fluctuation. Numerical simulations demonstrate the formation and propagation of thermoelastic waves in microstructured solids under thermal loading
Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations
In 1922, Cartan introduced in differential geometry, besides the Riemannian
curvature, the new concept of torsion. He visualized a homogeneous and
isotropic distribution of torsion in three dimensions (3d) by the "helical
staircase", which he constructed by starting from a 3d Euclidean space and by
defining a new connection via helical motions. We describe this geometric
procedure in detail and define the corresponding connection and the torsion.
The interdisciplinary nature of this subject is already evident from Cartan's
discussion, since he argued - but never proved - that the helical staircase
should correspond to a continuum with constant pressure and constant internal
torque. We discuss where in physics the helical staircase is realized: (i) In
the continuum mechanics of Cosserat media, (ii) in (fairly speculative) 3d
theories of gravity, namely a) in 3d Einstein-Cartan gravity - this is Cartan's
case of constant pressure and constant intrinsic torque - and b) in 3d Poincare
gauge theory with the Mielke-Baekler Lagrangian, and, eventually, (iii) in the
gauge field theory of dislocations of Lazar et al., as we prove for the first
time by arranging a suitable distribution of screw dislocations. Our main
emphasis is on the discussion of dislocation field theory.Comment: 31 pages, 8 figure
Multiscale analysis of materials with anisotropic microstructure as micropolar continua
Multiscale procedures are often adopted for the continuum modeling of materials composed of a specific micro-structure. Generally, in mechanics of materials only two-scales are linked. In this work the original (fine) micro-scale description, thought as a composite material made of matrix and fibers/particles/crystals which can interact among them, and a scale-dependent continuum (coarse) macro-scale are linked via an energy equivalence criterion. In particular the multiscale strategy is proposed for deriving the constitutive relations of anisotropic composites with periodic microstructure and allows us to reduce the typically high computational cost of fully microscopic numerical analyses. At the microscopic level the material is described as a lattice system while at the macroscopic level the continuum is a micropolar continuum, whose material particles are endowed with orientation besides position. The derived constitutive relations account for shape, texture and orientation of inclusions as well as internal scale parameters, which account for size effects even in the elastic regime in the presence of geometrical and/or load singularities. Applications of this procedure concern polycrystals, wherein an important descriptor of the underlying microstructure gives the orientation of the crystal lattice of each grain, fiber reinforced composites, as well as masonry-like materials. In order to investigate the effects of micropolar constants in the presence of material non central symmetries, some numerical finite element simulations, with elements specifically formulated for micropolar media, are presented. The performed simulations, which extend several parametric analyses earlier performed [1], involve two-dimensional media, in the linear framework, subjected to compression loads distributed in a small portion of the medium
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