Related papers: The elastica sling
This paper is devoted to describe the deformations and the elastic energy for structures made of straight rods of thickness $2\delta$ when $\delta$ tends to 0. This analysis relies on the decomposition of the large deformation of a single…
Mechanical interactions between rigid rings and flexible cables find broad application in both daily life (hanging clothes) and engineering systems (closing a tether-net). A reduced-order method for the dynamic analysis of sliding rings on…
An optimal control problem for longitudinal motions of a thin elastic rod is considered. We suppose that a normal force, which changes piecewise constantly along the rod's length, is applied to the cross-section so that the positions of…
The discovery of configurational forces acting on elastic structures and its initial applications are reviewed. Configurational forces are related to the possibility that an elastic structure can change its configuration, thus inducing a…
Recent experiments have shown that surface stresses in soft materials can have a significant strain-dependence. Here we explore the implications of this surface elasticity to show how, and when, we expect it to arise. We develop the…
We present the spectral analysis of three-dimensional dynamics of an elastic filament in a shear flow of a viscous fluid at a low Reynolds number in the absence of Brownian motion. The elastica model is used. The fiber initially is almost…
A challenge in soft robotics and soft actuation is the determination of an elastic system which spontaneously recovers its trivial path during postcritical deformation after a bifurcation. The interest in this behaviour is that a…
A linear elastic circular disc is analyzed under a self-equilibrated system of loads applied along its boundary. A distinctive feature of the investigation, conducted using complex variable analysis, is the assumption that the material is…
The problem of the rigorous derivation of one-dimensional models for nonlinearly elastic curved beams is studied in a variational setting. Considering different scalings of the three-dimensional energy and passing to the limit as the…
The choice of elastic energies for thin plates and shells is an unsettled issue with consequences for much recent modeling of soft matter. Through consideration of simple deformations of a thin body in the plane, we demonstrate that four…
The design and control of soft robots operating in fluid environments requires a careful understanding of the interplay between large elastic body deformations and hydrodynamic forces. Here we show that this interplay leads to novel…
Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a…
This work is focused on a nonlinear equation describing the oscillations of an extensible viscoelastic beam with fixed ends, subject to distributed elastic external force. For a general axial load $\beta$, the existence of a finite/infinite…
Single-loop elastic rings can be folded into multi-loop equilibrium configurations. In this paper, the stability of several such multi-loop states which are either circular or straight are investigated analytically and illustrated by…
We propose and analyze a mathematical model of the mechanics of gels, consisting of the laws of balance of mass and linear momentum. We consider a gel to be an immiscible and incompressible mixture of a nonlinearly elastic polymer and a…
The stability analysis of elastic rings subjected to various loading conditions is examined, focusing on stable and unstable configurations. The harmonic balance method is employed to investigate the stability range under different loading…
We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we…
Using dimensionally reduced models for the numerical simulation of thin objects is highly attractive as this reduces the computational work substantially. The case of narrow thin elastic bands is considered and a convergent finite element…
We study the problem of the rigorous derivation of one-dimensional models for a thin curved beam starting from three-dimensional nonlinear elasticity. We describe the limiting models obtained for different scalings of the energy. In…
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…