Related papers: Variational problems in thin elastic structures
Shell structure in the single particle spectrum of deformed harmonic oscillator potentials when a term proportional to $(\vec L)^2$ is added is analyzed for a large particle number. A scaling law which gives a dividing line between regular…
A weak notion of elastic energy for (not necessarily regular) rectifiable curves in any space dimension is proposed. Our $p$-energy is defined through a relaxation process, where a suitable $p$-rotation of inscribed polygonals is adopted.…
Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a…
A sheet of elastic foil rolled into a cylinder and deformed between two parallel plates acts as a non-Hookean spring if deformed normally to the axis. For large deformations the elastic force shows an interesting inverse squares dependence…
We use high resolution numerical simulations over several hundred of turnover times to study the influence of small scale dissipation onto vortex statistics in 2D decaying turbulence. A self-similar scaling regime is detected when the…
Two-dimensional (2D) nanomaterials exhibit unique properties that are promising for diverse applications, including those relevant to concentration-gradient-driven transport of electrolyte solutions through porous membranes made from these…
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…
We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling…
We deduce a 1D model of elastic planar rods starting from the F\"{o}ppl--von K\'{a}rm\'{a}n model of thin shells. Such model is enhanced by additional kinematical descriptors that keep explicit track of the compatibility condition requested…
We review different (reduced) models for thin structures using bending as principal mechanism to undergo large deformations. Each model consists in the minimization of a fourth order energy, potentially subject to a nonconvex constraint.…
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…
Partial complementary energy densities are introduced through partial Legendre transforms from the strain energy density of linear elasticity. They have mixed components of the strain and stress tensors. Mixed variational principles based…
In this work we introduce a procedure to find localized structures with finite energy. We start dealing with global monopoles, and add a new contribution to the potential of the scalar fields, to balance the contribution of the angular…
This work introduces the Hookean-Voronoi energy, a minimal model for the packing of soft, deformable balls. This is motivated by recent studies of quasi-periodic equilibria arising from dense packings of diblock and star polymers.…
A rectangular plate of dielectric elastomer exhibiting gradients of material properties through its thickness will deform inhomogeneously when a potential difference is applied to compliant electrodes on its major surfaces, because each…
The asymptotic behaviour of solutions of three-dimensional nonlinear elastodynamics in a thin shell is considered, as the thickness $h$ of the shell tends to zero. Given the appropriate scalings of the applied force and of the initial data…
Colliding high energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced. We consider the latter case here. Although inelastic processes dominate at high…
We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
This paper investigates, without any regularization or penalization procedure, a shape optimization problem involving a simplified friction phenomena modeled by a scalar Tresca friction law. Precisely, using tools from convex and…
We study the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable layer (e.g., bedrock).…