Related papers: Connecting disclinations by ridges
A new energy functional for pure traction problems in elasticity has been deduced in [23] as the variational limit of nonlinear elastic energy functional for a material body subject to an equilibrated force field: a sort of Gamma limit with…
In the limit of vanishing lattice spacing we provide a rigorous variational coarse-graining result for a next-to-nearest neighbor lattice model of a simple crystal. We show that the $\Gamma$-limit of suitable scaled versions of the model…
In this paper we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics \cite{Silling2000} or nonlocal diffusion models \cite{Rossi}. We derive nonlocal versions…
The dynamics of defect excitations in crystalline solids is necessary to understand the macroscopic low-energy properties of elastic media. We use fracton-elasticity duality to systematically study the defect dynamics and interactions in…
We study the transition from flat to wrinkled region in uniaxially stretched thin elastic film. We set up a model variational problem, and study energy of its ground state. Using known scaling bounds for the minimal energy, the minimal…
We study a variational model for transition layers in thin ferromagnetic films with an underlying functional that combines an Allen-Cahn type structure with an additional nonlocal interaction term. The model represents the magnetisation by…
In this work, we establish that discontinuous Galerkin methods are capable of producing reliable approximations for a broad class of nonlinear variational problems. In particular, we demonstrate that these schemes provide essential…
We prove the existence of minimizers for some constrained variational problems on $BV(\Omega)$, under subcritical and critical restrictions, involving the affine energy introduced by Zhang in \cite{Z}. Related functionals have non-coercive…
The subject of this paper is the study of the asymptotic behaviour of the equilibrium configurations of a nonlinearly elastic thin rod, as the diameter of the cross-section tends to zero. Convergence results are established assuming…
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 the global Lipschitz character of minimisers of the Dirichlet energy of diffeomorphisms between doubly connected domains with smooth boundaries from Riemann surfaces. The key point of the proof is the fact that minimisers are…
We consider periodic homogenization of nonlinearly elastic composite materials. Under suitable assumptions on the stored energy function (frame indifference; minimality, non-degeneracy and smoothness at identity; $p\geq d$-growth from…
The study of elastic membranes carrying topological defects has a longstanding history, going back at least to the 1950s. When allowed to buckle in three-dimensional space, membranes with defects can totally relieve their in-plane strain,…
We consider the problem of matching two shapes assuming these shapes are related by an elastic deformation. Using linearized elasticity theory and the finite element method we seek an elastic deformation that is caused by simple external…
We study self-contact phenomena in elastic rods that are constrained to lie on a cylinder. By choosing a particular set of variables to describe the rod centerline the variational setting is made particularly simple: the strain energy is a…
We consider the problem of distortion minimal morphing of $n$-dimensional compact connected oriented smooth manifolds without boundary embedded in $\R^{n+1}$. Distortion involves bending and stretching. In this paper, minimal distortion…
For thin networked materials, which are spatial discrete structures constructed by continuum components, a paradox on the effective thickness defined by the in-plane and out-of-plane stiffnesses is found, i.e. the effective thickness is not…
We introduce a simplified model for the minimization of the elastic energy in thin shells. This model is not obtained by an asymptotic analysis. The thickness of the shell remains a parameter as in Reisner-Mindlin's model for plates and…
Amontons' law postulates a monotonic relationship between frictional force and the normal load applied to a sliding contact. This empirical rule, however, fails in systems where internal degrees of freedom - such as structural or electronic…
We rephrase Monge's optimal transportation (OT) problem with quadratic cost--via a Monge-Amp\`ere equation--as an infinite-dimensional optimization problem, which is in fact a convex problem when the target is a log-concave measure with…