72 research outputs found
Encasement as a morphogenetic mechanism: The case of bending
We study how the encasement of a growing elastic bulk within a possibly
differently growing elastic coat may induce mechanical instabilities in the
equilibrium shape of the combined body. The inhomogeneities induced in an
incompressible bulk during growth are also discussed. These effects are
illustrated through a simple example in which a growing elastic cylinder may
undergo a shape transition towards a bent configuration.Comment: 17 pages, 3 figure
Liquid relaxation: A new Parodi-like relation for nematic liquid crystals
We put forward a hydrodynamic theory of nematic liquid crystals that includes
both anisotropic elasticity and dynamic relaxation. Liquid remodeling is
encompassed through a continuous update of the shear-stress free configuration.
The low-frequency limit of the dynamical theory reproduces the classical
Ericksen-Leslie theory, but it predicts two independent identities between the
six Leslie viscosity coefficients. One replicates Parodi's relation, while the
other-which involves five Leslie viscosities in a nonlinear way-is new. We
discuss its significance, and we test its validity against evidence from
physical experiments, independent theoretical predictions, and
molecular-dynamics simulations.Comment: 6 pages, 1 figure, 2 table
Bulk and surface biaxiality in nematic liquid crystals
Nematic liquid crystals possess three different phases: isotropic, uniaxial,
and biaxial. The ground state of most nematics is either isotropic or uniaxial,
depending on the external temperature. Nevertheless, biaxial domains have been
frequently identified, especially close to defects or external surfaces. In
this paper we show that any spatially-varying director pattern may be a source
of biaxiality. We prove that biaxiality arises naturally whenever the symmetric
tensor \Sb=(\grad \nn)(\grad \nn)^T possesses two distinct nonzero
eigenvalues. The eigenvalue difference may be used as a measure of the expected
biaxiality. Furthermore, the corresponding eigenvectors indicate the directions
in which the order tensor \QQ is induced to break the uniaxial symmetry about
the director \nn. We apply our general considerations to some examples. In
particular we show that, when we enforce homeotropic anchoring on a curved
surface, the order tensor become biaxial along the principal directions of the
surface. The effect is triggered by the difference in surface principal
curvatures
Intermittency in crystal plasticity informed by lattice symmetry
We develop a nonlinear, three-dimensional phase field model for crystal
plasticity which accounts for the infinite and discrete symmetry group G of the
underlying periodic lattice. This generates a complex energy landscape with
countably-many G-related wells in strain space, whereon the material evolves by
energy minimization under the loading through spontaneous slip processes
inducing the creation and motion of dislocations without the need of auxiliary
hypotheses. Multiple slips may be activated simultaneously, in domains
separated by a priori unknown free boundaries. The wells visited by the strain
at each position and time, are tracked by the evolution of a G-valued discrete
plastic map, whose non-compatible discontinuities identify lattice
dislocations. The main effects in the plasticity of crystalline materials at
microscopic scales emerge in this framework, including the long-range elastic
fields of possibly interacting dislocations, lattice friction, hardening,
band-like vs. complex spatial distributions of dislocations. The main results
concern the scale-free intermittency of the flow, with power-law exponents for
the slip avalanche statistics which are significantly affected by the symmetry
and the compatibility properties of the activated fundamental shears.Comment: 13 pages, 4 figure
Strain intermittency in shape-memory alloys
We study experimentally the intermittent progress of the mechanically induced
martensitic transformation in a Cu-Al-Be single crystal through a full-field
measurement technique: the grid method. We utilize an in- house, specially
designed gravity-based device, wherein a system controlled by water pumps
applies a perfectly monotonic uniaxial load through very small force
increments. The sample exhibits hysteretic superelastic behavior during the
forward and reverse cubic-monoclinic transformation, produced by the evolution
of the strain field of the phase microstructures. The in-plane linear strain
components are measured on the sample surface during the loading cycle, and we
characterize the strain intermittency in a number of ways, showing the
emergence of power-law behavior for the strain avalanching over almost six
decades of magnitude. We also describe the nonstationarity and the asymmetry
observed in the forward versus reverse transformation. The present experimental
approach, which allows for the monitoring of the reversible martensitic
transformation both locally and globally in the crystal, proves useful and
enhances our capabilities in the analysis and possible control of
transition-related phenomena in shape-memory alloys.Comment: Four supplementary video
Expansion of Two-Dimensional Models in the Scaling Region
The main technical and conceptual features of the lattice expansion in
the scaling region are discussed in the context of a two-parameter
two-dimensional spin model interpolating between and
models, with standard and improved lattice actions. We show how to
perform the asymptotic expansion of effective propagators for small values of
the mass gap and how to employ this result in the evaluation of physical
quantities in the scaling regime. The lattice renormalization group
function is constructed explicitly and exactly to .Comment: 6 pages, report no. IFUP-TH 49/9
Telephone-cord instabilities in thin smectic capillaries
Telephone-cord patterns have been recently observed in smectic liquid crystal
capillaries. In this paper we analyse the effects that may induce them. As long
as the capillary keeps its linear shape, we show that a nonzero chiral
cholesteric pitch favors the SmA*-SmC* transition. However, neither the
cholesteric pitch nor the presence of an intrinsic bending stress are able to
give rise to a curved capillary shape.
The key ingredient for the telephone-cord instability is spontaneous
polarization. The free energy minimizer of a spontaneously polarized SmA* is
attained on a planar capillary, characterized by a nonzero curvature. More
interestingly, in the SmC* phase the combined effect of the molecular tilt and
the spontaneous polarization pushes towards a helicoidal capillary shape, with
nonzero curvature and torsion.Comment: Submitte
Finite-temperature avalanches in 2D disordered Ising models
We study the qualitative and quantitative properties of the Barkhausen noise
emerging at finite temperatures in random Ising models. The random-bond Ising
Model is studied with a Wolff cluster Monte-Carlo algorithm to monitor the
avalanches generated by an external driving magnetic field. Satisfactory
power-law distributions are found which expand over five decades, with a
temperature-dependent critical exponent which matches the existing experimental
measurements. We also focus on a Ising system in which a finite fraction of
defects is quenched. Also the presence of defects proves able to induce a
critical response to a slowly oscillating magnetic field, though in this case
the critical exponent associated with the distributions obtained with different
defect fractions and temperatures seems to belong to the same universality
class, with a critical exponent equal to 1.Comment: 12 pages, 5 figure
Ericksen-Landau Modular Strain Energies for Reconstructive Phase Transformations in 2D crystals
By using modular functions on the upper complex half-plane, we study a class
of strain energies for crystalline materials whose global invariance originates
from the full symmetry group of the underlying lattice. This follows Ericksen's
suggestion which aimed at extending the Landau-type theories to encompass the
behavior of crystals undergoing structural phase transformation, with twinning,
microstructure formation, and possibly associated plasticity effects. Here we
investigate such Ericksen-Landau strain energies for the modelling of
reconstructive transformations, focusing on the prototypical case of the
square-hexagonal phase change in 2D crystals. We study the bifurcation and
valley-floor network of these potentials, and use one in the simulation of a
quasi-static shearing test. We observe typical effects associated with the
micro-mechanics of phase transformation in crystals, in particular, the bursty
progression of the structural phase change, characterized by intermittent
stress-relaxation through microstructure formation, mediated, in this
reconstructive case, by defect nucleation and movement in the lattice.Comment: 17 pages, 6 figures, links to 4 supplementary video
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