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We study the elasticity of a two-dimensional random network of rigid rods (``Mikado model''). The essential features incorporated into the model are the anisotropic elasticity of the rods and the random geometry of the network. We show that…
Soft dielectric elastomers that can exhibit extremely large deformations under the action of an electric field enable applications such as soft robotics, biomedical devices, energy harvesting among others. A key impediment in the use of…
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple…
Flutter instability in elastic structures subject to follower load, the most important cases being the famous Beck's and Pfluger's columns (two elastic rods in a cantilever configuration, with an additional concentrated mass at the end of…
The 'elastic capacitor' (EC) model was first introduced in studies of lipid bilayers (the major components of biological membranes). This electro-elastic model accounted for the compression of a membrane under applied voltage and allowed…
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…
The dynamics of elastocapillary thinning in high molecular weight polymer solutions are re-examined using high-speed digital video microscopy. At long times, the evolution of the viscoelastic thread deviates from self-similar exponential…
The nonconservative elastic responses of active solids have driven a recent explosion of interest in two-dimensional "odd" elasticity: small, linear deformations of these Cauchy elastic solids enable new behaviour absent from classical,…
We study the elastic behaviour of a supercoiled DNA molecule. The simplest model is that of a rod like chain, involving two elastic constants, the bending and the twist rigidities. We show that this model is singular and needs a small…
In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational…
In the literature, for semidynamical systems in infinite dimensional phase spaces, different topological structures are used (Hilbert, Banach, Sobolev, locally convex, Hausdorf topology etc.). That is because there are neither set rules nor…
We consider two-parameter bifurcation of equilibrium states of an elastic rod on a deformable foundation. Our main theorem shows that bifurcation occurs if and only if the linearization of our problem has nontrivial solutions. In fact our…
The study is devoted to mathematical modeling and optimal control design of longitudinal motions of a rectilinear elastic rod. The control inputs are a force, which is normal to the cross section and distributed piecewise constantly along…
We formulate a cut finite element method for linear elasticity based on higher order elements on a fixed background mesh. Key to the method is a stabilization term which provides control of the jumps in the derivatives of the finite element…
Unlike most synthetic materials, biological materials often stiffen as they are deformed. This nonlinear elastic response, critical for the physiological function of some tissues, has been documented since at least the 19th century, but the…
The linear (Winkler) foundation is a simple model widely used for decades to account for the surface response of elastic bodies. It models the response as purely local, linear, and perpendicular to the surface. We extend this model to the…
The tribology of a sliding elastic continuum in contact with a disordered substrate is investigated analytically and numerically via a bead-spring model. The deterministic dynamics of this system exhibits a depinning transition at a finite…
Many mechanical structures, both engineered and biological, combine heavy rigid elements such as bones and beams with lightweight flexible ones such as cables and membranes. These are referred to as tensegrities, reflecting that cables can…
This work investigates the morphological stability of a soft body composed of two heavy elastic layers, attached to a rigid surface and subjected only to the bulk gravity force. Using theoretical and computational tools, we characterize the…
Euler solved the problem of the collapse of tall thin columns under unexpectedly small loads in 1744. The analogous problem of the collapse of circular elastic rings or tubes under external pressure was mathematically intractable and only…