Catálogo de publicaciones - libros

Nearly all technologically useful materials are polycrystalline. Their ability to meet system level specifications of performance and reliability is influenced by the types of grain boundaries present and their connectivity. To engineer the grain boundary network to achieve these objectives, we seek predictive models of growth at various mesoscale levels. Here we discuss a master equation description of normal grain growth derived from large scale simulations and compare the results with recent experiments.

We study the homogenization of a linearly elastic energy defined on a periodic collection of disconnected sets with a unilateral condition on the contact region between two such sets, with the model of a brick wall in mind. Using the language of Γ-convergence we show that the limit homogenized behavior of such an energy can be described on the space of functions with bounded deformation using the masonry-type functionals studied by Anzellotti, Giaquinta and Giusti. In this case, the limit energy density is given by the homogenization formula related to the brick-wall type energy.

We study variational problems involving the measure of level sets, or more precisely the push-forward of the Lebesgue measure. This problem generalizes variational problems with finitely many (discrete) volume constraints. We obtain existence results for this general framework. Moreover, we show the surprising existence of asymmetric solutions to symmetric variational problems with this type of volume constraints.

A unified treatment of several aspects of material behavior is provided by a one-dimensional model based on the decomposition of the energy of a body into the sum of two parts, bulk and cohesive. This note deals with a specific form of the cohesive energy, called . Using the example of a bar subject to axial elongation, it is shown that a cohesive energy of this form captures two aspects of material response which, at a first glance, look very different: stress oscillation, and damage.

We propose a criterion to find the symmetric tricritical points of an ordering phase transition in liquid crystals described by more than one scalar order parameter. Our criterion extends the one already put forward in the literature, which is based on the classical Griffiths’s criterion valid when all phases are described by a single order parameter. When applied to a recently proposed model for biaxial liquid crystals, the criterion presented here predicts the existence of a new tricritical point.

We present a result of variational convergence for Ginzburg-Landau type energies having “supercritical” growth, under a prescribed Dirichlet boundary condition. This is obtained modifying our previous result proved in [] about the Γ-convergence of the unconstrained functionals, and allows us to obtain the asymptotic behavior of minimizers.

These notes attempt a simple introduction to H-measures (microlocal defect measures), a tool designed independently by P. and by L. to compute weak limits of quadratic products of oscillating fields. The canvas around which the concepts are presented is that of the linear wave equation with smooth coefficients and rapidly oscillating initial data. The weak limit of the energy density is computed and a compactness result of the -norm of the field (in ℝ) at each time is established.

Let be an open bounded interval of ℝ and a non-negative continuous function vanishing only at ∈ ℝ. We investigate the asymptotic behavior in terms of Γ-convergence of the following functional , as ɛ → 0.

We show that minimizers of elastic-plastic energies dependent on jump integrals are smooth provided a smallness condition is fulfilled by the load. We examine also the structure of extremals when this smallness condition is violated.

Three examples of equilibrium problems are presented where arise to guarantee partwise equilibrium. In the first example, a concentrated force is applied at the boundary of a half plane, and the stress field has an integrable singularity at the point where the force is applied. Suturing two such stress fields so as to have a mirror-symmetric stress field in the whole plane produces a second example of concentrated contact interactions. For a third example, a concentrated couple is applied at the boundary of a half plane, and the standard stress field has a nonintegrable singularity at the point where the couple is applied, whereas the associated hyperstress field, although still singular, is integrable.