Related papers: Elasticae and inradius
The problem of determining the thermomechanical characteristics of the system of closely spaced bodies considered by many authors. For scalar problems, such as problems of heat, electrostatic, etc., the localization effect was found (so…
Frustration arises for a broad class of physical systems where confinement (geometric) or the presence of a perturbation (kinematic) prevents equilibration to a minimum energy state. By varying the diameter ratio and packing fraction in…
We consider a setting in which an evolving surface is implicitly characterized as the zero level of a level set function. Such an implicit surface does not encode any information about the path of a single point on the evolving surface. In…
We study stationary points of the bending energy of curves $\gamma\colon[a,b]\to\mathbb{R}^n$ subject to constraints on the arc-length and the curve's holonomy while simultaneously allowing for a variable bending stiffness along the…
The asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness $h$ of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional $\mathcal…
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…
Current quadratic smoothness energies for curved surfaces either exhibit distortions near the boundary due to zero Neumann boundary conditions, or they do not correctly account for intrinsic curvature, which leads to unnatural-looking…
We provide an approximation result for the pure traction problem of linearized elasticity in terms of local minimizers of finite elasticity, under the constraint of vanishing average curl for admissible deformation maps. When suitable…
We consider models for elastic liquids, such as solutions of flexible polymers. They introduce a relaxation time $\lambda$ into the system, over which stresses relax. We study the kinematics of the problem, and clarify the relationship…
We explore the nonlinear variational modelling of two-dimensional (2D) crystal plasticity based on strain energies which are invariant under the full symmetry group of 2D lattices. We use a natural parameterization of strain space via the…
A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…
A model (further referred to as the enhanced vector-based model or EVM) for elastic bonds in solids, composed of bonded particles is presented. The model can be applied for a description of elastic deformation of rocks, ceramics, concrete,…
We study the $\Gamma$-convergence of a class of elastica-type energies defined on immersed planar curves and depending on a small positive parameter $\epsilon$. As $\epsilon\to 0^+$, sequences with equibounded energy develop concentration…
In this paper, I mainly prove the following results. For every energy value below the minimum of the first, second and third critical value, each bounded component of the regularized energy hypersurface of the Lagrange problem under some…
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 extend the theory of structured deformations to the setting of linearized elasticity by providing an integral representation for the underlying energy that features bulk and surface contributions. Our derivation is obtained both via a…
We consider a parabolic obstacle problem for Euler's elastic energy of graphs with fixed ends. We show global existence, well-posedness and subconvergence provided that the obstacle and the initial datum are suitably 'small'. For symmetric…
In this paper we formulate the theory of nonlinear elasticity in a geometrically intrinsic manner using exterior calculus and bundle-valued differential forms. We represent kinematics variables, such as velocity and rate-of-strain, as…
We consider the topic of linearization of finite elasticity for pure traction problems. We characterize the variational limit for the approximating sequence of rescaled nonlinear elastic energies. We show that the limiting minimal value can…
The deep energy method (DEM) has been used to solve the elastic deformation of structures with linear elasticity, hyperelasticity, and strain-gradient elasticity material models based on the principle of minimum potential energy. In this…