Matteo Negri

Junction-aware extraction and regularization of urban road networks in high-resolution SAR images

A general processing framework for urban road network extraction in high-resolution synthetic aperture radar images is proposed. It is based on novel multiscale detection of street candidates, followed by optimization using a Markov random field description of the road network. The latter step, in the path of recent technical literature, is enriched by the inclusion of a priori knowledge about road junctions and the automatic choice of most of the involved parameters. Advantages over existing and previous extraction and optimization procedures are proved by comparison using data from different sensors and locations

Linearized Elasticity as Γ-Limit of Finite Elasticity

Linearized elastic energies are derived from rescaled nonlinear energies by means of Γ-convergence. For Dirichlet and mixed boundary value problems in a Lipschitz domain Ω, the convergence of minimizers takes place in the weak topology of H1(Ω,Rn) and in the strong topology of W1,q(Ω,Rn) for 1≤q<2.

The anisotropy introduced by the mesh in the finite element approximation of the mumford-shah functional

We compute explicitly the anisotropy effect in the H 1 term, generated in the approximation of the Mumford-Shah functional by finite element spaces defined on structured triangulations.

A finite element approximation of the Griffith's model in fracture mechanics

Summary.The Griffith model for the mechanics of fractures in brittle materials is consider in the weak formulation of SBD spaces. We suggest an approximation, in the sense of Γ−convergence, by a sequence of discrete functionals defined on finite elements spaces over structured and adaptive triangulations. The quasi-static evolution for boundary value problems is also taken into account and some numerical results are shown.

A comparative analysis on variational models for quasi-static brittle crack propagation

Abstract We consider a brittle material under displacement control with a mode III crack running in quasi-static regime along a straight line. Several definitions of propagation, based on variational criteria, have been proposed in the last decade. Our aim is a detailed study of their properties, in particular as far as energy, energy release rate and jump discontinuities is concerned. In order to make similarities and differences appear more clearly, the analysis of the evolutions follows a common structure and theoretical results are illustrated by a prototype numerical example.

Convergence analysis for a smeared crack approach in brittle fracture

Our analysis focuses on the mechanical energies involved in the propagation of fractures: the elastic energy, stored in the bulk, and the fracture energy, concentrated in the crack. We consider a finite element model based on a smeared crack approach: the fracture is approximated geometrically by a stripe of elements and mechanically by a softening constitutive law. We define in this way a discrete free energyGh (h being the element size) which accounts for both elastic displacements and fractures. Our main interest is the behaviour of Gh as h ! 0. We prove that, for a suitable choice of the (mesh dependent) constitutive law, Gh converges to a limit functional G with a positive (anisotropic) term concentrated on the crack. We discuss the mesh bias and compute it explicitly in the case of a structured triangulation.

Convergence of Nonlocal Finite Element Energies for Fracture Mechanics

Usually, smeared crack techniques are based on the following features: the fracture is represented by means of a band of finite elements and by a softening constitutive law of damage type. Often, these methods are implemented with nonlocal operators that control the localization effects and reduce the mesh bias. We consider a nonlocal smeared crack energy defined for a finite element space on a structured grid. We characterize the limit energy as the mesh size h tends to zero and we establish a precise link between the discrete and continuum formulations of the fracture energies, showing the correct scaling and the explicit form of the mesh bias.

Scaling in fracture mechanics by Bažant law: From finite to linearized elasticity

We consider crack propagation in brittle nonlinear elastic materials in the context of quasi-static evolutions of energetic type. Given a sequence of self-similar domains nΩ on which the imposed boundary conditions scale according to Bažants law, we show, in agreement with several experimental data, that the corresponding sequence of evolutions converges (for n → ∞) to the evolution of a crack in a brittle linear-elastic material.

Convergence of alternate minimization schemes for phase field

We consider time-discrete evolutions for a phase-field model (for fracture and damage) obtained by alternate minimization schemes. First, we characterize their time-continuous limit in terms of parametrized BV-evolutions, introducing a suitable family of “intrinsic energy norms”. Further, we show that the limit evolution satisfies Griffith’s criterion, for a phase-field energy release, and that the irreversibility constraint is thermodynamically consistent.

Quasi-Static Evolutions in Brittle Fracture Generated by Gradient Flows: Sharp Crack and Phase-Field Approaches

In this paper we will describe how gradient flows, in a suitable norm, are natural and helpful to generate quasi-static evolutions in brittle fracture. First, we will consider the case of a brittle crack running along a straight line according to Griffith’s law. Then, we will see how the same approach leads to quasi-static evolutions in the phase field setting, taking into account the alternate minimization scheme. In the latter, the norm associated to the gradient flow is not “user supplied”, however, the algorithm itself together with the separate quadratic structure of the energy defines a family of norms which, in the limit, characterizes the quasi-static evolution. Mathematically speaking, all of these evolutions are (parametrized) BV-evolutions.