4,229 research outputs found
High frequency homogenisation for elastic lattices
A complete methodology, based on a two-scale asymptotic approach, that
enables the homogenisation of elastic lattices at non-zero frequencies is
developed. Elastic lattices are distinguished from scalar lattices in that two
or more types of coupled waves exist, even at low frequencies. Such a theory
enables the determination of effective material properties at both low and high
frequencies. The theoretical framework is developed for the propagation of
waves through lattices of arbitrary geometry and dimension. The asymptotic
approach provides a method through which the dispersive properties of lattices
at frequencies near standing waves can be described; the theory accurately
describes both the dispersion curves and the response of the lattice near the
edges of the Brillouin zone. The leading order solution is expressed as a
product between the standing wave solution and long-scale envelope functions
that are eigensolutions of the homogenised partial differential equation. The
general theory is supplemented by a pair of illustrative examples for two
archetypal classes of two-dimensional elastic lattices. The efficiency of the
asymptotic approach in accurately describing several interesting phenomena is
demonstrated, including dynamic anisotropy and Dirac cones.Comment: 24 pages, 7 figure
Dynamical approach to the Casimir effect
Casimir forces can appear between intrusions placed in different media driven
by several fluctuation mechanisms, either in equilibrium or out of it. Herein,
we develop a general formalism to obtain such forces from the dynamical
equations of the fluctuating medium, the statistical properties of the driving
noise, and the boundary conditions of the intrusions (which simulate the
interaction between the intrusions and the medium). As a result, an explicit
formula for the Casimir force over the intrusions is derived. This formalism
contains the thermal Casimir effect as a particular limit and generalizes the
study of the Casimir effect to such systems through their dynamical equations,
with no appeal to their Hamiltonian, if any exists. In particular, we study the
Casimir force between two infinite parallel plates with Dirichlet or Neumann
boundary conditions, immersed in several media with finite correlation lengths
(reaction--diffusion system, liquid crystals, and two coupled fields with
non-Hermitian evolution equations). The driving Gaussian noises have vanishing
or finite spatial or temporal correlation lengths; in the first case,
equilibrium is reobtained and finite correlations produce nonequilibrium
dynamics. The results obtained show that, generally, nonequilibrium dynamics
leads to Casimir forces, whereas Casimir forces are obtained in equilibrium
dynamics if the stress tensor is anisotropic.Comment: 12 pages, 1 figur
On three-dimensional singular stress/residual stress fields at the front of a crack/anticrack in an orthotropic/orthorhombic plate under anti-plane shear loading
Journal ArticleA novel eigenfunction expansion technique, based in part on separation of the thickness-variable, is developed to derive three-dimensional asymptotic stress field in the vicinity of the front of a semi-infinite through-thickness crack/anticrack weakening/reinforcing an infinite orthotropic/orthorhombic plate, of finite thickness and subjected to far-field anti-plane shear loading. Crack/anticrack-face boundary conditions and those that are prescribed on the top and bottom (free, fixed and lubricated) surfaces of the orthotropic plate are exactly satisfied. Five different through-thickness crack/anticrack-face boundary conditions are considered: (i) slit crack, (ii) anticrack or perfectly bonded rigid inclusion, (iii) transversely rigid inclusion (longitudinal slip permitted), (iv) rigid inclusion in part perfectly bonded, the remainder with slip, and (v) rigid inclusion located alongside a crack. Explicit expressions for the singular stress fields in the vicinity of the fronts of the through-thickness cracks, anticracks or mixed crack-anticrack type discontinuities, weakening/reinforcing orthotropic/orthorhombic plates, subjected to far-field anti-plane shear (mode III) loadings, are presented. In addition, singular residual stress fields in the vicinity of the fronts of these cracks, anticracks and similar discontinuities are also discussed
Mechanically coupled laminates with balanced plain weave
Definitive listings of laminate stacking sequences are derived for balanced plain weave laminated materials, assuming each layer is composed of the same material with constant thickness throughout and that standard ply angle orientations 0, 90, and ±45° are adopted; consistent with industrial design practice. A single layer of balanced plain weave material is shown to be immune to thermal distortion following a standard high temperature manufacturing process, which implies that all laminates constructed of this material possess what is commonly referred to as the hygro-thermally curvature-stable or warp-free condition, irrespective of the individual ply orientations used or the laminate stacking sequence definition. A single uncoupled parent laminate class is shown to contain sub-groups with extensionally isotropic and fully isotropic properties that are invariant with off-axis orientation of the principal material axes with respect to the system or structural axes. By contrast a single mechanically coupled parent laminate class is shown to give rise to seven unique forms of coupled laminate through judicious off-axis orientation. Invariant off-axis properties are also identified in coupled laminate designs. Finally, example calculations, abridged stacking sequence listings and design data are presented
The curved kinetic boundary layer of active matter
The finite reorient-time of swimmers leads to a finite run length and
the kinetic accumulation boundary layer on the microscopic length scale
on a non-penetrating wall. That boundary layer is the microscopic
origin of the swim pressure, and is impacted by the geometry of the boundary
[Yan \& Brady, \textit{J. Fluid. Mech.}, 2015, \textbf{785}, R1]. In this work
we extend the analysis to analytically solve the boundary layer on an
arbitrary-shaped body distorted by the local mean curvature. The solution gives
the swim pressure distribution and the total force (torque) on an arbitrarily
shaped body immersed in swimmers, with a general scaling of the curvature
effect
Effective slippage on superhydrophobic trapezoidal grooves
We study the effective slippage on superhydrophobic grooves with trapezoidal
cross-sections of various geometries (including the limiting cases of triangles
and rectangular stripes), by using two complementary approaches. First,
dissipative particle dynamics (DPD) simulations of a flow past such surfaces
have been performed to validate an expression [E.S.Asmolov and O.I.Vinogradova,
J. Fluid Mech. \textbf{706}, 108 (2012)] that relates the eigenvalues of the
effective slip-length tensor for one-dimensional textures. Second, we propose
theoretical estimates for the effective slip length and calculate it
numerically by solving the Stokes equation based on a collocation method. The
comparison between the two approaches shows that they are in excellent
agreement. Our results demonstrate that the effective slippage depends strongly
on the area-averaged slip, the amplitude of the roughness, and on the fraction
of solid in contact with the liquid. To interpret these results, we analyze
flow singularities near slipping heterogeneities, and demonstrate that they
inhibit the effective slip and enhance the anisotropy of the flow. Finally, we
propose some guidelines to design optimal one-dimensional superhydrophobic
surfaces, motivated by potential applications in microfluidics.Comment: 11 pages, 8 figures, submitted to J. Chem. Phy
Rheological Signatures in Limit Cycle Behaviour of Dilute, Active, Polar Liquid Crystalline Polymers in Steady Shear
We consider the dilute regime of active suspensions of liquid crystalline polymers (LCPs), addressing issues motivated by our kinetic model and simulations in Forest et al. (Forest et al. 2013 Soft Matter 9, 5207-5222 (doi:10.1039/c3sm27736d)). In particular, we report unsteady two-dimensional heterogeneous flow-orientation attractors for pusher nanorod swimmers at dilute concentrations where passive LCP equilibria are isotropic. These numerical limit cycles are analogous to longwave (homogeneous) tumbling and kayaking limit cycles and two-dimensional heterogeneous unsteady attractors of passive LCPs in weak imposed shear, yet these states arise exclusively at semi-dilute concentrations where stable equilibria are nematic. The results in Forest et al. mentioned above compel two studies in the dilute regime that complement recent work of Saintillan & Shelley (Saintillan & Shelley 2013 C. R. Physique 14, 497-517 (doi: 10.1016/j.crhy.2013.04.001)): linearized stability analysis of the isotropic state for nanorod pushers and pullers; and an analytical-numerical study of weakly and strongly sheared active polar nanorod suspensions to capture how particle-scale activation affects shear rheology. We find that weakly sheared dilute puller versus pusher suspensions exhibit steady versus unsteady responses, shear thickening versus thinning and positive versus negative first normal stress differences. These results further establish how sheared dilute nanorod pusher suspensions exhibit many of the characteristic features of sheared semi-dilute passive nanorod suspensions
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