Browsing by Author "Mora, Maria Giovanna"

Now showing 1 - 4 of 4
  • Thumbnail Image
    Item
    Derivation of a rod theory for phase-transforming materials
    (2005) Mora, Maria Giovanna; Müller, Stefan; Mathematics; Functional Analysis and Applications
    A rigorous derivation is given of a rod theory for a multiphase material,starting from three-dimensional nonlinear elasticity. The stored energy density is supposed to be nonnegative and to vanish exactly on a set consisting of two copies of the group of rotations SO(3). The two potential wells correspond to the two crystalline configurations preferred by the material. We find the optimal scaling of the energy in terms of the diameter of the rod and we identify the limit, as the diameter goes to zero, in the sense of Gamma-convergence.
  • Thumbnail Image
    Item
    Nonlinear thin-walled beams with a rectangular cross-section - Part II
    (SISSA, 2011) Freddi, Lorenzo; Mora, Maria Giovanna; Paroni, Roberto; Mathematics; Functional Analysis and Applications
    In this paper we report the second part of our results concerning the rigorous derivation of a hierarchy of one-dimensional models for thin-walled beams with rectangular cross-section..
  • Thumbnail Image
    Item
    A Quasistatic evolution model for perfectly plastic plates derived by Gamma-convergence
    (SISSA, 2012-04) Davoli, Elisa; Mora, Maria Giovanna; Mathematics; Functional Analysis and Applications
    The subject of this paper is the rigorous derivation of a quasistatic evolution model for a linearly elastic - perfectly plastic thin plate. As the thickness of the plate tends to zero, we prove via Gamma-convergence techniques that solutions to the three-dimensional quasistatic evolution problem of Prandtl-Reuss elastoplasticity converge to a quasistatic evolution of a suitable reduced model. In this limiting model the admissible displacements are of Kirchhoff-Love type and the stretching and bending components of the stress are coupled through a plastic flow rule. Some equivalent formulations of the limiting problem in rate form are derived, together with some two-dimensional characterizations for suitable choices of the data.
  • Thumbnail Image
    Item
    Time-dependent systems of generalized Young measures
    (2005) Dal Maso, Gianni; DeSimone, Antonio; Mora, Maria Giovanna; Morini, Massimiliano; Mathematics; Functional Analysis and Applications
    In this paper some new tools for the study of evolution problems in the framework of Young measures are introduced. A suitable notion of time-dependent system of generalized Young measures is defined, which allows to extend the classical notions of total variation and absolute continuity with respect to time, as well as the notion of time derivative. The main results are a Helly type theorem for sequences of systems of generalized Young measures and a theorem about the existence of the time derivative for systems with bounded variation with respect to time.