Related papers: Elasticae and inradius
In this paper, we deal with an obstacle placement problem inside a disk, that can be formulated as an energy minimization problem with respect to the rotations of the obstacle about its center, with respect to the translations of the…
Energies and equilibrium equations for thin elastic plates are discussed, with emphasis on several issues pertinent to recent approaches in soft condensed matter. Consequences of choice of basis, choice of invariant strain measures, and of…
We consider the problem of minimizing the bending or elastic energy among Jordan curves confined in a given open set $\Omega$. We prove existence, regularity and some structural properties of minimizers. In particular, when $\Omega$ is…
We study an obstacle problem for the length-penalized elastic bending energy for open planar curves pinned at the boundary. We first consider the case without length penalization and investigate the role of global minimizers among graph…
This paper investigates the homogenization, dimension reduction, and linearization of a composite plate subjected to external loading within the framework of non-linear elasticity problem. The total elastic energy of the problem is of order…
For two different scenarios regarding thin elastic structures, described by 2d-F\"oppl-von K\'arm\'an plate models, we obtain energy scaling laws. Firstly, assuming the reference geometry being that of a singular excess-cone, we obtain…
The problem of the sudden growth and coalescence of voids in elastic media is considered. The Dirichlet energy is minimized among incompressible and invertible Sobolev deformations of a two-dimensional domain having $n$ microvoids of radius…
Elastic turbulence is the chaotic fluid motion resulting from elastic instabilities due to the addition of polymers in small concentrations at very small Reynolds ($\mbox{Re}$) numbers. Our direct numerical simulations show that elastic…
The crumpling of a thin sheet can be understood as the condensation of elastic energy into a network of ridges which meet in vertices. Elastic energy condensation should occur in response to compressive strain in elastic objects of any…
Motivated by experiments and formal asymptotic expansions in the physics literature, Maor and Shachar (J. Elasticity 134 (2019), 149-173) studied the behaviour of a model elastic energy of maps between manifolds with incompatible metrics.…
In this paper we show the emergence of polycrystalline structures as a result of elastic energy minimisation. For this purpose, we introduce a variational model for two-dimensional systems of edge dislocations, within the so-called core…
We consider a single disclination in a thin elastic sheet of thickness $h$. We prove ansatz-free lower bounds for the free elastic energy in three different settings: First, for a geometrically fully non-linear plate model, second, for…
We consider elastic flows of closed curves in Euclidean space. We obtain optimal energy thresholds below which elastic flows preserve embeddedness of initial curves for all time. The obtained thresholds take different values between…
We reconsider the geometrically nonlinear Cosserat model for a uniformly convex elastic energy and write the equilibrium problem as a minimization problem. Applying the direct methods of the calculus of variations we show the existence 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 nonlinear elasticity, finding the deformation of a material which minimizes a given stored energy density is a challenging calculus of variations problem which may fail to have minimizers: the energy optimal material forms infinitely…
We consider a class of models motivated by previous numerical studies of wrinkling in highly stretched, thin rectangular elastomer sheets. The model used is characterized by a finite-strain hyperelastic membrane energy perturbed by small…
A numerical scheme for computing arc-length parametrized curves of low bending energy that are confined to convex domains is devised. The convergence of the discrete formulations to a continuous model and the unconditional stability of an…
Minimizing the so-called "Dirichlet energy" with respect to the domain under a volume constraint is a standard problem in shape optimization which is now well understood. This article is devoted to a prototypal non-linear version of the…
A controversy exists among literature reports of constraints on elastic constants. In particular, it has been reported that embedded atom method (EAM) potentials generally impose three constraints on elastic constants of crystals that are…