Lorenzo Freddi
University of Udine
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Publication
Featured researches published by Lorenzo Freddi.
Journal of Elasticity | 2001
Elio Cabib; Lorenzo Freddi; Antonino Morassi; Danilo Percivale
The three-dimensional elasticity energy for a notched rod under axial loads is shown to converge in a variational sense to a class of one-dimensional models with a localized compliance when the beam becomes very slender and when the ratio between the depth and the width of each notch vanishes in a suitable way. Also the case of notched thermal conductors is considered, in a parallel treatment, because it falls in a similar but simpler framework.
Interfaces and Free Boundaries | 2004
Lorenzo Freddi; Roberto Paroni
Martensitic thin films have recently attracted much interest because of their applications in the construction of actuators, sensors and micromachines. These technological applications have generated a new interest in nonlinear membranes theories. The purpose of the present paper is to obtain, by means of a rigorous dimension reduction, the energy density of a thin film, and hence to deduce a membrane model capable of describing the microstructure observed in martensitic materials. Phase transformations have been successfully modelled within the theory of non-linear elasticity by Ball and James [5]. Within this approach, equilibrium configurations are found by minimizing the total free energy of the body. In the spirit of the works on dimension reduction (see for instance [1, 3]) we start by considering the total free energy
Asymptotic Analysis | 2010
Lorenzo Freddi; Roberto Paroni; Chiara Zanini
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.
Siam Journal on Mathematical Analysis | 2009
Lorenzo Freddi; Franco Is Murat; Roberto Paroni
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
Mathematical Models and Methods in Applied Sciences | 2012
Lorenzo Freddi; Maria Giovanna Mora; Roberto Paroni
\varepsilon
Siam Journal on Mathematical Analysis | 2016
Lorenzo Freddi; Peter Hornung; Maria Giovanna Mora; Roberto Paroni
and
Journal of Optimization Theory and Applications | 1997
Giuseppe Buttazzo; M. E. Drakhlin; Lorenzo Freddi; E. Stepanov
\varepsilon^2
Archive | 1999
Giuseppe Buttazzo; Lorenzo Freddi
and clamped on one of its bases. The sequence of solutions
Asymptotic Analysis | 2010
Lorenzo Freddi; Franã§ois Murat; Roberto Paroni
u^\varepsilon
Mathematics and Mechanics of Solids | 2013
Luca Della Longa; Lorenzo Freddi; Alessandro Londero; Roberto Paroni
of the equilibrium problem is shown to converge in an appropriate topology, as