59 research outputs found
Soft modes near the buckling transition of icosahedral shells
Icosahedral shells undergo a buckling transition as the ratio of Young's
modulus to bending stiffness increases. Strong bending stiffness favors smooth,
nearly spherical shapes, while weak bending stiffness leads to a sharply
faceted icosahedral shape. Based on the phonon spectrum of a simplified
mass-and-spring model of the shell, we interpret the transition from smooth to
faceted as a soft-mode transition. In contrast to the case of a disclinated
planar network where the transition is sharply defined, the mean curvature of
the sphere smooths the transitition. We define elastic susceptibilities as the
response to forces applied at vertices, edges and faces of an icosahedron. At
the soft-mode transition the vertex susceptibility is the largest, but as the
shell becomes more faceted the edge and face susceptibilities greatly exceed
the vertex susceptibility. Limiting behaviors of the susceptibilities are
analyzed and related to the ridge-scaling behavior of elastic sheets. Our
results apply to virus capsids, liposomes with crystalline order and other
shell-like structures with icosahedral symmetry.Comment: 28 pages, 6 figure
Different mechanics of snap-trapping in the two closely related carnivorous plants Dionaea muscipula and Aldrovanda vesiculosa
The carnivorous aquatic Waterwheel Plant (Aldrovanda vesiculosa L.) and the
closely related terrestrial Venus Flytrap (Dionaea muscipula SOL. EX J. ELLIS)
both feature elaborate snap-traps, which shut after reception of an external
mechanical stimulus by prey animals. Traditionally, Aldrovanda is considered as
a miniature, aquatic Dionaea, an assumption which was already established by
Charles Darwin. However, videos of snapping traps from both species suggest
completely different closure mechanisms. Indeed, the well-described snapping
mechanism in Dionaea comprises abrupt curvature inversion of the two trap
lobes, while the closing movement in Aldrovanda involves deformation of the
trap midrib but not of the lobes, which do not change curvature. In this paper,
we present the first detailed mechanical models for these plants, which are
based on the theory of thin solid membranes and explain this difference by
showing that the fast snapping of Aldrovanda is due to kinematic amplification
of the bending deformation of the midrib, while that of Dionaea unambiguously
relies on the buckling instability that affects the two lobes.Comment: accepted in Physical Review
A micro-mechanics based extension of the GTN continuum model accounting for random void distributions
Randomness in the void distribution within a ductile metal complicates
quantitative modeling of damage following the void growth to coalescence
failure process. Though the sequence of micro-mechanisms leading to ductile
failure is known from unit cell models, often based on assumptions of a regular
distribution of voids, the effect of randomness remains a challenge. In the
present work, mesoscale unit cell models, each containing an ensemble of four
voids of equal size that are randomly distributed, are used to find statistical
effects on the yield surface of the homogenized material. A yield locus is
found based on a mean yield surface and a standard deviation of yield points
obtained from 15 realizations of the four-void unit cells. It is found that the
classical GTN model very closely agrees with the mean of the yield points
extracted from the unit cell calculations with random void distributions, while
the standard deviation varies with the imposed stress state. It is
shown that the standard deviation is nearly zero for stress triaxialities
, while it rapidly increases for triaxialities above ,
reaching maximum values of about at . At even higher triaxialities it decreases slightly. The results indicate
that the dependence of the standard deviation on the stress state follows from
variations in the deformation mechanism since a well-correlated variation is
found for the volume fraction of the unit cell that deforms plastically at
yield. Thus, the random void distribution activates different complex
localization mechanisms at high stress triaxialities that differ from the
ligament thinning mechanism forming the basis for the classical GTN model. A
method for introducing the effect of randomness into the GTN continuum model is
presented, and an excellent comparison to the unit cell yield locus is
achieved
Programmed buckling by controlled lateral swelling in a thin elastic sheet
Recent experiments have imposed controlled swelling patterns on thin polymer
films, which subsequently buckle into three-dimensional shapes. We develop a
solution to the design problem suggested by such systems, namely, if and how
one can generate particular three-dimensional shapes from thin elastic sheets
by mere imposition of a two-dimensional pattern of locally isotropic growth.
Not every shape is possible. Several types of obstruction can arise, some of
which depend on the sheet thickness. We provide some examples using the
axisymmetric form of the problem, which is analytically tractable.Comment: 11 pages, 9 figure
Mechanical model of the ultra-fast underwater trap of Utricularia
The underwater traps of the carnivorous plants of the Utricularia species
catch their preys through the repetition of an "active slow deflation / passive
fast suction" sequence. In this paper, we propose a mechanical model that
describes both phases and strongly supports the hypothesis that the trap door
acts as a flexible valve that buckles under the combined effects of pressure
forces and the mechanical stimulation of trigger hairs, and not as a panel
articulated on hinges. This model combines two different approaches, namely (i)
the description of thin membranes as triangle meshes with strain and curvature
energy, and (ii) the molecular dynamics approach, which consists in computing
the time evolution of the position of each vertex of the mesh according to
Langevin equations. The only free parameter in the expression of the elastic
energy is the Young's modulus E of the membranes. The values for this parameter
are unequivocally obtained by requiring that the trap model fires, like real
traps, when the pressure difference between the outside and the inside of the
trap reaches about 15 kPa. Among other results, our simulations show that, for
a pressure difference slightly larger than the critical one, the door buckles,
slides on the threshold and finally swings wide open, in excellent agreement
with the sequence observed in high-speed videos.Comment: Accepted for publication in Physical Review
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