A fItrite element scheme (together with a conjugate gradient algorithmj is demonstrated to be a very effective method for analyzing general elastoplastic torsion of prismatic bars posed as quadratic programming problems. Solutions for bars with elliptical and Sokolovsky’s oval cross-sections are presented. The solutions for the elliptical bars agree with the existing elastic and limit plastic s...

We study the mechanical response of elastic rods bent into open knots, focusing on the case of trefoil and cinquefoil topologies. The limit of a weak applied tensile force is studied both analytically and experimentally: the Kirchhoff equations with self-contact are solved by means of matched asymptotic expansions; predictions on both the geometrical and mechanical properties of the elastic equ...

Phase-field-crystal (PFC) models constitute a field theoretical approach to solidification, melting, and related phenomena at atomic length and diffusive time scales. One of the advantages of these models is that they naturally contain elastic excitations associated with strain in crystalline bodies. However, instabilities that are diffusively driven towards equilibrium are often orders of magn...

We give results for the Γ-limit of a scaled elastic energy of a film as the thickness h > 0 converges to zero. The elastic energy density models materials with multiple phases or variants and is thus non-convex. The model includes an interfacial energy that allows sharp interfaces between the phases and variants and is proportional to the total variation of the deformation gradient.

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 physical growth conditions for the elastic energy density and suitable scalings of the applied loads, that correspond at the limit to different rod models: the cons...

We study the macroscopic behavior of an elastic-viscoelastic mixture, in the non penodic case The oscillating problem présents an elastic term and a short memory term At the macroscopic level a long memory term, of the convolution type, also appears The mam re suit consists in establishing the limit équation and charactenzing Us coefficients in terms of the oscillations of the domains occupied ...

The curvature elastic energy of bilayer vesicles formed by a mixture of two surfactants, which individually form either micelles or lamellar bilayer phases is described theoretically. In the limit of large bending elastic modulus K being much greater than the temperature T, the free energy is minimized by vesicles with different concentrations of the two surfactants in each monolayer of the bil...