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Register a new userCoupled electro-elastic deformation and instabilities of a toroidal membrane
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We analyse here the problem of large deformation of dielectric elastomeric membranes under coupled electromechanical loading. Extremely large deformations (enclosed volume changes of 100 times and greater) of a toroidal membrane are studied by the use of a variational formulation that accounts for the total energy due to mechanical and electrical fields. A modified shooting method is adopted to solve the resulting system of coupled and highly nonlinear ordinary differential equations. We demonstrate the occurrence of limit point, wrinkling, and symmetry-breaking buckling instabilities in the solution of this problem. Onset of each of these reversible instabilities depends significantly on the ratio of the mechanical load to the electric load, thereby providing a control mechanism for state switching.
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We discuss the electrostatic contribution to the elastic moduli of a cell or artificial membrane placed in an electrolyte and driven by a DC electric field. The field drives ion currents across the membrane, through specific channels, pumps or natural pores. In steady state, charges accumulate in the Debye layers close to the membrane, modifying the membrane elastic moduli. We first study a model of a membrane of zero thickness, later generalizing this treatment to allow for a finite thickness and finite dielectric constant. Our results clarify and extend the results presented in [D. Lacoste, M. Cosentino Lagomarsino, and J. F. Joanny, Europhys. Lett., {bf 77}, 18006 (2007)], by providing a physical explanation for a destabilizing term proportional to $kps^3$ in the fluctuation spectrum, which we relate to a nonlinear ($E^2$) electro-kinetic effect called induced-charge electro-osmosis (ICEO). Recent studies of ICEO have focused on electrodes and polarizable particles, where an applied bulk field is perturbed by capacitive charging of the double layer and drives flow along the field axis toward surface protrusions; in contrast, we predict reverse ICEO flows around driven membranes, due to curvature-induced tangential fields within a non-equilibrium double layer, which hydrodynamically enhance protrusions. We also consider the effect of incorporating the dynamics of a spatially dependent concentration field for the ion channels.
The paper investigates localized deformation patterns resulting from the onset of instabilities in lattice structures. The study is motivated by previous observations on discrete hexagonal lattices, where the onset of non-uniform, quasi-static deformation patterns was associated with the loss of convexity of the interaction potential, and where a variety of localized deformations were found depending on loading configuration, lattice parameters and boundary conditions. These observations are here conducted on other lattice structures, with the goal of identifying models of reduced complexity that are able to provide insight into the key parameters that govern the onset of instability-induced localization. To this end, we first consider a two-dimensional square lattice consisting of point masses connected by in-plane axial springs and vertical ground springs. Results illustrate that depending on the choice of spring constants and their relative values, the lattice exhibits in-plane or out-of plane instabilities leading to folding and unfolding. This model is further simplified by considering the one-dimensional case of a spring-mass chain sitting on an elastic foundation. A bifurcation analysis of this lattice identifies the stable and unstable branches and illustrates its hysteretic and loading path-dependent behaviors. Finally, the lattice is further reduced to a minimal four mass model which undergoes a folding/unfolding process qualitatively similar to the same process in the central part of a longer chain, helping our understanding of localization in more complex systems. In contrast to the widespread assumption that localization is induced by defects or imperfections in a structure, this work illustrates that such phenomena can arise in perfect lattices as a consequence of the mode-shapes at the bifurcation points.
The buckling and twisting of slender, elastic fibers is a deep and well-studied field. A slender elastic rod that is twisted with respect to a fixed end will spontaneously form a loop, or hockle, to relieve the torsional stress that builds. Further twisting results in the formation of plectonemes -- a helical excursion in the fiber that extends with additional twisting. Here we use an idealized, micron-scale experiment to investigate the energy stored, and subsequently released, by hockles and plectonemes as they are pulled apart, in analogy with force spectroscopy studies of DNA and protein folding. Hysteresis loops in the snapping and unsnapping inform the stored energy in the twisted fiber structures.
Using numerical simulations, we characterized the behavior of an elastic membrane immersed in an active fluid. Our findings reveal a nontrivial folding and re-expansion of the membrane that is controlled by the interplay of its resistance to bending and the self-propulsion strength of the active components in solution. We show how flexible membranes tend to collapse into multi-folded states, whereas stiff membranes oscillates between an extended configuration and a singly folded state. This study provides a simple example of how to exploit the random motion of active particles to perform mechanical work at the micro-scale.
In this study, micro-droplets are placed on thin, glassy, free-standing films where the Laplace pressure of the droplet deforms the free-standing film, creating a bulge. The films tension is modulated by changing temperature continuously from well below the glass transition into the melt state of the film. The contact angle of the liquid droplet with the planar film as well as the angle of the bulge with the film are measured and found to be consistent with the contact angles predicted by a force balance at the contact line.
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