Related papers: Elastic membranes spanning deformable boundaries
A method is described for embedding a deformable, elastic, membrane within a lattice Boltzmann fluid. The membrane is represented by a set of massless points which advect with the fluid and which impose forces on the fluid which are derived…
We describe a numerical method to simulate an elastic shell immersed in a viscous incompressible fluid. The method is developed as an extension of the immersed boundary method using shell equations based on the Kirchhoff-Love and the planar…
We put forward a variational framework suitable for the study of curves whose energies depend on their bend and twist degrees of freedom. By employing the material curvatures to describe such elastic deformation modes, we derive the…
Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies,…
The theory of irreversible thermodynamics for arbitrarily curved lipid membranes is presented here. The coupling between elastic bending and irreversible processes such as intra-membrane lipid flow, intra-membrane phase transitions, and…
A remarkable property of flexible self-avoiding elastic surfaces (membranes) is that they remain flat at all temperatures, even in the absence of a bending rigidity or in the presence of active fluctuations. Here, we report numerical…
We examine the equilibrium and stability of an elastocapillary system to model drying-induced structural failures. The model comprises a circular elastic membrane with a hole at the center that is deformed by the capillary pressure of…
We investigate the equilibrium configurations of closed planar elastic curves of fixed length, whose stiffness, also known as the bending rigidity, depends on an additional density variable. The underlying variational model relies on the…
In this paper we derive a general linearized theory for first-order continuum dynamics on manifolds with particular application to incompatible elasticity. We adopt a global approach viewing the equations of motion as a $1$-form on the…
We consider the steady-state analysis of a pinned elastic plate lying on the free surface of a thin viscous fluid, forced by the motion of a bottom substrate moving at constant speed. A mathematical model incorporating elasticity,…
We discuss a 1D variational problem modeling an elastic sheet on water, lifted at one end. Its terms include the membrane and bending energy of the sheet as well as terms due to gravity and surface tension. By studying a suitable…
The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which…
We derive the equations of motion for relativistic elastic membranes, that is, two-dimensional elastic bodies whose internal energy depends only on their stretching, starting from a variational principle. We show how to obtain conserved…
The fluctuations of two-dimensional extended objects membranes is a rich and exciting field with many solid results and a wide range of open issues. We review the distinct universality classes of membranes, determined by the local order,…
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…
Using classical differential geometry, the problem of elastic curves and surfaces in the presence of long-range interactions $\Phi$, is posed. Starting from a variational principle, the balance of elastic forces and the corresponding…
We amplify previous arguments why mean curvature should be used as measure of integration in calculating the effective bending rigidity of fluid membranes subjected to a weak background curvature. The stiffening of the membrane by its…
Effective interface conditions for a periodically voided thin layer separating two homogeneous bulk regions are derived for the elastic wave equation by taking the simultaneous limit of vanishing layer periodicity and layer thickness. The…
Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In the real-life applications like blood flow, there is often an additional complexity of vorticity being…
Cells and other soft particles are often forced to flow in confined geometries in both laboratory and natural environments, where the elastic deformation induces an additional drag and pressure drop across the particle. In contrast with…