15,020 research outputs found
Subdivision Shell Elements with Anisotropic Growth
A thin shell finite element approach based on Loop's subdivision surfaces is
proposed, capable of dealing with large deformations and anisotropic growth. To
this end, the Kirchhoff-Love theory of thin shells is derived and extended to
allow for arbitrary in-plane growth. The simplicity and computational
efficiency of the subdivision thin shell elements is outstanding, which is
demonstrated on a few standard loading benchmarks. With this powerful tool at
hand, we demonstrate the broad range of possible applications by numerical
solution of several growth scenarios, ranging from the uniform growth of a
sphere, to boundary instabilities induced by large anisotropic growth. Finally,
it is shown that the problem of a slowly and uniformly growing sheet confined
in a fixed hollow sphere is equivalent to the inverse process where a sheet of
fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless,
quasi-static, elastic limit.Comment: 20 pages, 12 figures, 1 tabl
Folds and Buckles at the Nanoscale: Experimental and Theoretical Investigation of the Bending Properties of Graphene Membranes
The elastic properties of graphene crystals have been extensively investigated, revealing unique properties in the linear and nonlinear regimes, when the membranes are under either stretching or bending loading conditions. Nevertheless less knowledge has been developed so far on folded graphene membranes and ribbons. It has been recently suggested that fold-induced curvatures, without in-plane strain, can affect the local chemical reactivity, the mechanical properties, and the electron transfer in graphene membranes. This intriguing perspective envisages a materials-by-design approach through the engineering of folding and bending to develop enhanced nano-resonators or nano-electro-mechanical devices. Here we present a novel methodology to investigate the mechanical properties of folded and wrinkled graphene crystals, combining transmission electron microscopy mapping of 3D curvatures and theoretical modeling based on continuum elasticity theory and tight-binding atomistic simulations
Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems
Voltage-dependent ion channels determine the electric properties of axonal
cell membranes. They not only allow the passage of ions through the cell
membrane but also contribute to an additional charging of the cell membrane
resulting in the so-called capacitance loading. The switching of the channel
gates between an open and a closed configuration is intrinsically related to
the movement of gating charge within the cell membrane. At the beginning of an
action potential the transient gating current is opposite to the direction of
the current of sodium ions through the membrane. Therefore, the excitability is
expected to become reduced due to the influence of a gating current. Our
stochastic Hodgkin-Huxley like modeling takes into account both the channel
noise -- i.e. the fluctuations of the number of open ion channels -- and the
capacitance fluctuations that result from the dynamics of the gating charge. We
investigate the spiking dynamics of membrane patches of variable size and
analyze the statistics of the spontaneous spiking. As a main result, we find
that the gating currents yield a drastic reduction of the spontaneous spiking
rate for sufficiently large ion channel clusters. Consequently, this
demonstrates a prominent mechanism for channel noise reduction.Comment: 18 page
Trends of mechanical consequences and modeling of a fibrous membrane around femoral hip prostheses
In the present study, the effects of a fibrous membrane between cement and bone in a femoral total hip replacement were investigated. The study involved the problem of modeling this fibrous membrane in finite-element analyses, and its global consequences for the load-transfer mechanism and its resulting stress patterns. A finite-element model was developed, suitable to describe nonlinear contact conditions in combination with nonlinear material properties of the fibrous membrane. The fibrous tissue layer was described as a highly compliant material with little resistance against tension and shear. The analysis showed that the load transfer mechanism from stem to bone changes drastically when such a membrane is present. These effects are predominantly caused by tensile loosening and slip at the interface, and are enhanced by the nonlinear membrane characteristics.\ud
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Using parametric analysis, it was shown that these effects on the load-transfer mechanism cannot be described satisfactorily with linear elastic models.\ud
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Most importantly, the fibrous tissue interposition causes excessive stress concentrations in bone and cement, and relatively high relative displacements between these materials
Bistable forespore engulfment in Bacillus subtilis by a zipper mechanism in absence of the cell wall
To survive starvation, the bacterium Bacillus subtilis forms durable spores.
The initial step of sporulation is asymmetric cell division, leading to a large
mother-cell and a small forespore compartment. After division is completed and
the dividing septum is thinned, the mother cell engulfs the forespore in a slow
process based on cell-wall degradation and synthesis. However, recently a new
cell-wall independent mechanism was shown to significantly contribute, which
can even lead to fast engulfment in 60 of the cases when the cell
wall is completely removed. In this backup mechanism, strong ligand-receptor
binding between mother-cell protein SpoIIIAH and forespore-protein SpoIIQ leads
to zipper-like engulfment, but quantitative understanding is missing. In our
work, we combined fluorescence image analysis and stochastic Langevin
simulations of the fluctuating membrane to investigate the origin of fast
bistable engulfment in absence of the cell wall. Our cell morphologies compare
favorably with experimental time-lapse microscopy, with engulfment sensitive to
the number of SpoIIQ-SpoIIIAH bonds in a threshold-like manner. By systematic
exploration of model parameters, we predict regions of osmotic pressure and
membrane-surface tension that produce successful engulfment. Indeed, decreasing
the medium osmolarity in experiments prevents engulfment in line with our
predictions. Forespore engulfment may thus not only be an ideal model system to
study decision-making in single cells, but its biophysical principles are
likely applicable to engulfment in other cell types, e.g. during phagocytosis
in eukaryotes
A Review on Mechanics and Mechanical Properties of 2D Materials - Graphene and Beyond
Since the first successful synthesis of graphene just over a decade ago, a
variety of two-dimensional (2D) materials (e.g., transition
metal-dichalcogenides, hexagonal boron-nitride, etc.) have been discovered.
Among the many unique and attractive properties of 2D materials, mechanical
properties play important roles in manufacturing, integration and performance
for their potential applications. Mechanics is indispensable in the study of
mechanical properties, both experimentally and theoretically. The coupling
between the mechanical and other physical properties (thermal, electronic,
optical) is also of great interest in exploring novel applications, where
mechanics has to be combined with condensed matter physics to establish a
scalable theoretical framework. Moreover, mechanical interactions between 2D
materials and various substrate materials are essential for integrated device
applications of 2D materials, for which the mechanics of interfaces (adhesion
and friction) has to be developed for the 2D materials. Here we review recent
theoretical and experimental works related to mechanics and mechanical
properties of 2D materials. While graphene is the most studied 2D material to
date, we expect continual growth of interest in the mechanics of other 2D
materials beyond graphene
An isogeometric finite element formulation for phase transitions on deforming surfaces
This paper presents a general theory and isogeometric finite element
implementation for studying mass conserving phase transitions on deforming
surfaces. The mathematical problem is governed by two coupled fourth-order
nonlinear partial differential equations (PDEs) that live on an evolving
two-dimensional manifold. For the phase transitions, the PDE is the
Cahn-Hilliard equation for curved surfaces, which can be derived from surface
mass balance in the framework of irreversible thermodynamics. For the surface
deformation, the PDE is the (vector-valued) Kirchhoff-Love thin shell equation.
Both PDEs can be efficiently discretized using -continuous interpolations
without derivative degrees-of-freedom (dofs). Structured NURBS and unstructured
spline spaces with pointwise -continuity are utilized for these
interpolations. The resulting finite element formulation is discretized in time
by the generalized- scheme with adaptive time-stepping, and it is fully
linearized within a monolithic Newton-Raphson approach. A curvilinear surface
parameterization is used throughout the formulation to admit general surface
shapes and deformations. The behavior of the coupled system is illustrated by
several numerical examples exhibiting phase transitions on deforming spheres,
tori and double-tori.Comment: fixed typos, extended literature review, added clarifying notes to
the text, added supplementary movie file
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