Peter Hornung

Infinitesimal Isometries on Developable Surfaces and Asymptotic Theories for Thin Developable Shells

We perform a detailed analysis of first order Sobolev-regular infinitesimal isometries on developable surfaces without affine regions. We prove that given enough regularity of the surface, any first order infinitesimal isometry can be matched to an infinitesimal isometry of an arbitrarily high order. We discuss the implications of this result for the elasticity of thin developable shells.

Continuation of Infinitesimal Bendings on Developable Surfaces and Equilibrium Equations for Nonlinear Bending Theory of Plates

We introduce a natural concept of stationarity for the nonlinear bending theory of elastic plates, and we derive the equilibrium equations satisfied by stationary points. A key ingredient is a geometric result about the continuation of infinitesimal bendings on developable surfaces.

A variational model for anisotropic and naturally twisted ribbons

We consider thin plates whose energy density is a quadratic function of the difference between the second fundamental form of the deformed configuration and a natural curvature tensor. This tensor either denotes the second fundamental form of the stress-free configuration, if it exists, or a target curvature tensor. In the latter case, residual stress arises from the geometrical frustration involved in the attempt to achieve the target curvature: as a result, the plate is naturally twisted, even in the absence of external forces or prescribed boundary conditions. Here, starting from this kind of plate energy, we derive a new variational one-dimensional model for naturally twisted ribbons by means of

A Γ-convergence result for thin martensitic films in linearized elasticity

\Gamma

Intrinsically biharmonic maps into homogeneous spaces

-convergence. Our result generalizes, and corrects, the classical Sadowsky energy to geometrically frustrated anisotropic ribbons with a narrow, possibly curved, reference configuration.

A remark on constrained von Kármán theories

The elastic energy of a thin film

Global structure of the singular set of energy minimising bendings

\Omega_h

Approximation of Flat W2,2 Isometric Immersions by Smooth Ones

of thickness h with displacement

Euler-Lagrange Equation and Regularity for Flat Minimizers of the Willmore Functional

u:\Omega_h\to\RR^3

Fine Level Set Structure of Flat Isometric Immersions

is given by the functional