Related papers: Elastic Curves with Variable Bending Stiffness
The buckling instabilities of core-shell systems, comprising an interior elastic sphere, attached to an exterior shell, have been proposed to underlie myriad biological morphologies. To fully discuss such systems, however, it is important…
We study wrinkling patterns in a thin elastic annulus subjected to radial stretching within the framework of the F\"oppl--von K\'arm\'an theory. Building on the analysis of the Lam\'e problem in Bella and Kohn, we investigate the asymptotic…
Elastic strips provide a canonical system for studying the mechanisms governing elastic shape transitions. Buckling, linear snap-through, and nonlinear snap-through have been observed in boundary-actuated strips and linked to the type of…
We report evidence of irregular unsteady flow of two-dimensional polymer solutions in the absence of inertia in cross-slot geometry using numerical simulations of Oldroyd-B model. By exploring the transition to time-dependent flow versus…
We investigate the finite bending and the associated bending instability of an incompressible dielectric slab subject to a combination of applied voltage and axial compression, using nonlinear electro-elasticity theory and its incremental…
The patterns arising from the differential swelling of gels are investigated experimentally and theoretically as a model for the differential growth of living tissues. Two geometries are considered: a thin strip of soft gel clamped to a…
Linearized elasticity models are derived, via Gamma-convergence, from suitably rescaled nonlinear energies when the corresponding energy densities have a multiwell structure and satisfy a weak coercivity condition, in the sense that the…
We investigate the dependence of the hardness of materials on their elastic stiffness. This is possible by constructing a series of model potentials of the Morse type; starting on modelling natural Cu, the model potential exhibit an…
We study equilibrium configurations for the Euler-Plateau energy with elastic modulus, which couples an energy functional of Euler-Plateau type with a total curvature term often present in models for the free energy of biomembranes. It is…
Minute amount of long chain flexible polymer dissolved in a turbulent flow can drastically change flow properties, such as reducing the drag and enhancing mixing. One fundamental riddle is how these polymer additives interact with the…
Quasi-static strain-controlled measurements of stress vs strain curves in macroscopic amorphous solids result in a nonlinear looking curve that ends up either in mechanical collapse or in a steady-state with fluctuations around a mean…
Elastic turbulence is a spatially and temporally disordered flow state appearing in viscoelastic fluids at vanishing fluid inertia and large elasticity. The resulting flows have broad technological interest, particularly to enhance mixing…
The interplay among the spectrum, geometry and magnetic field in tubular neighbourhoods of curves in Euclidean spaces is investigated in the limit when the cross section shrinks to a point. Proving a norm resolvent convergence, we derive…
We study investigate a long, thin rectangular elastic membrane that is bent through an angle $2 \alpha$, using the Foppl--von Karman ansatz in a geometrically linear setting. We study the associated variational problem, and show the…
We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a complete proof of global existence and…
Entangled networks of stiff biopolymers exhibit complex dynamic response, emerging from the topological constraints that neighboring filaments impose upon each other. We propose a class of reference models for entanglement dynamics of stiff…
We consider a curve with boundary points free to move on a line in $\mathbb R^2$, which evolves by the $L^2$--gradient flow of the elastic energy, that is a linear combination of the Willmore and the length functional. For such planar…
In this paper we study the homogenization effects on the model of elastic plate in the bending regime, under the assumption that the energy density (material) oscillates in the direction of thickness. We study two different cases. First, we…
A convergence result is proved for the equilibrium configurations of a three-dimensional thin elastic beam, as the diameter h of the cross-section goes to zero. More precisely, we show that stationary points of the nonlinear elastic…
A confined incompressible elastic film does not deform uniformly when subjected to adhesive interfacial stresses but with undulations which have a characteristic wavelength scaling linearly with the thickness of the film. In the classical…