Roberto Paroni

Theory of Linearly Elastic Residually Stressed Plates

The equations of a plate for a linearly elastic monoclinic material with residual stress are here derived for the first time. By using techniques of Γ-convergence we show that also in the case with residual stress the displacements are of Kirchhoff-Love type. An improvement of the result of Man and Carlson on the existence of a solution for the three-dimensional problem of linear elasticity with residual stress is also obtained.

A JUSTIFICATION OF THE REISSNER–MINDLIN PLATE THEORY THROUGH VARIATIONAL CONVERGENCE

We provide a justification of the Reissner–Mindlin plate theory, using linear threedimensional elasticity as framework and Γ-convergence as technical tool. Essential to our developments is the selection of a transversely isotropic material class whose stored energy depends on (first and) second gradients of the displacement field. Our choices of a candidate Γ-limit and a scaling law of the basic energy functional in terms of a thinness parameter are guided by mechanical and formal arguments that our variational convergence theorem is meant to validate mathematically.

Dimension reduction of a crack evolution problem in a linearly elastic plate

A two-dimensional model which describes the evolution of a crack in a plate is deduced from a three-dimensional lin- early elastic Griffiths type model. The result is achieved by adopting the framework of energetic solutions for rate-independent processes, to model three-dimensional fracture evolution, in conjunction with a variational dimension reduction procedure.

ANISOTROPIC INHOMOGENEOUS RECTANGULAR THIN-WALLED BEAMS ∗

This paper is devoted to the asymptotic analysis of the problem of linear elasticity for an anisotropic and inhomogeneous body occupying, in its reference configuration, a cylindrical domain with a rectangular cross section with sides proportional to

Nonlinear thin-walled beams with a rectangular cross-section - Part II

varepsilon

On Korn’s constant for thin cylindrical domains

and

The Gaussian stiffness of graphene deduced from a continuum model based on Molecular Dynamics potentials

varepsilon^2

An existence theorem for inextensible nets with slack

and clamped on one of its bases. The sequence of solutions

A new material property of graphene: The bending Poisson coefficient

u^varepsilon

Saint-Venant's theory for beams with multi-connected cross-section: Justification and error estimate

of the equilibrium problem is shown to converge in an appropriate topology, as