Related papers: Snapping of elastic strips with controlled ends
We investigate the morphology and mechanics of a naturally curved elastic arch loaded at its center and frictionally supported at both ends on a flat, rigid substrate. Through systematic numerical simulations, we classify the observed…
Many elastic structures have two possible equilibrium states: from umbrellas that become inverted in a sudden gust of wind, to nano-electromechanical switches, origami patterns and the hopper popper, which jumps after being turned…
Dynamic buckling may occur when a load is rapidly applied to, or removed from, an elastic object at rest. In contrast to its static counterpart, dynamic buckling offers a wide range of accessible patterns depending on the parameters of the…
The morphology of an elastic strip subject to vertical compressive stress on a frictional rigid substrate is investigated by a combination of theory and experiment. We find a rich variety of morphologies, which -when the bending elasticity…
Snap-fits are versatile mechanical designs in industrial products, which enable the repeated assembling and disassembling of two solid parts. This important property is attributed to a fine balance between geometry, friction, and bending…
Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of…
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…
Athermal (i.e. zero-temperature) under-constrained systems are typically floppy, but they can be rigidified by the application of external strain, which is theoretically well understood. Here and in the companion paper, we extend this…
The paper is devoted to the study of a stabilization problem for the 2D incompressible Euler system in an infinite strip with boundary controls. We show that for any stationary solution (c, 0) of the Euler system there is a control which is…
Euler buckling epitomises mechanical instabilities: An inextensible straight elastic line buckles under compression when the compressive force reaches a critical value $F_\ast>0$. Here, we extend this classical, planar instability to the…
Two mathematical models are developed within the theoretical framework of large strain elasticity for the determination of upper and lower bounds on the total strain energy of a finitely deformed hyperelastic body in unilateral contact with…
We investigate the possibility of a striped inhomoegenous phase occurring as an electronic system with an order parameter linearly coupled to the elastic degrees of freedom is tuned through the electronic phase transition. We find that in…
Many physical systems can be modelled as parameter-dependent variational problems. In numerous cases, multiple equilibria co-exist, requiring the evaluation of their stability, and the monitoring of transitions between them. Generally, the…
Bistability and snap-through instabilities are central to various mechanisms in nature and engineering, enabling rapid movement and large shape changes with minimal energy input. These phenomena are easily demonstrated by bending a piece of…
The equations of a planar elastica under pressure can be rewritten in a useful form by parametrising the variables in terms of the local orientation angle, $\theta$, instead of the arc length. This ``$\theta$-formulation'' lends itself to a…
A generalization of the Euler's elastic problem, i.e., finding a stationary configuration (planar elastica) of the Bernoulli's thin ideal elastic rod with boundary conditions defined through fixed endpoints and/or tangents at the endpoints,…
We present a new one-dimensional model for elastic strips based on a nondevelopable ruled surface. An auxiliary field regularizes the Sadowsky narrow-strip model to allow nonzero twist with vanishing curvature. The energy exhibits the…
The depinning of an elastic line in a random medium is studied via an extremal model. The latter gives access to the instantaneous depinning force for each successive conformation of the line. Based on conditional statistics the universal…
Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical…
A class of isotropic and scale invariant strain energy functions is given for which the corresponding spherically symmetric elastic motion includes bodies whose diameter becomes infinite with time or collapses to zero in finite time,…