177,289 research outputs found
Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics
No full textThis note deals with the analysis of a model for partial damage, where the rate- independent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubicek [1, 2] with the methods from Lazzaroni/Rossi/Thomas/Toader [3]. The present analysis encompasses, differently from [2], the monotonicity in time of damage and the dependence of the viscous tensor on damage and temperature, and, unlike [3], a nonconstant heat capacity and a time-dependent Dirichlet loading
Limits of Dirichlet problems in perforated domains: a new formulation
No full textSia A un operatore ellittico lineare del secondo ordine con coefficienti
misurabili e limitati su un aperto limitato di
, sia
e sia un'arbitraria successione di sottoinsiemi aperti
di . Dimostriamo il seguente risultato di compattezza: esistono
una sottosuccessione, che indichiamo ancora con ed una
funzione w{*} K{*} tali che, per ogni f
, le soluzioni u delle
equazioni Au = f in , estese a zero su ,
convergano debolmente in all'unica
soluzione u del problema.
Studiamo inoltre in maniera sistematica le proprietà delle soluzioni
di tale equazione. Dimostriamo infine il seguente risultato di densità:
per ogni w{*}K{*} esiste una successione
di sottoinsiemi aperti di tali che per ogni f
le soluzioni u dell'equazione
Au=f in , estese a zero convergano
debolmente in alla soluzione di ({*}).Let A be a linear elliptic operator of the second order with bounded
measurable coefficients on a bounded open set of
, let
and let be an arbitrary sequence of open subsets of
. We prove the following compactness result: there exist
a subsequence, still denoted by and a function w{*}
K{*} such that, for every f
, the solutions u
of the equation Au = f in , extended by zero
on , converge weakly in
to the unique solution u of the problem.
We provide a self-contained study of the properties of the solutions
of ({*}). We prove also the following density result: for any w{*}K{*}
there exists a sequence of open subsets of
such that for every f the
solutions u of the
equation Au=f in , extended by zero on
converge weakly in to the solution
of ({*})
An artificial viscosity approach to quasistatic crack growth
No full textWe introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified epsilon-gradient flow of the energy functional, as the "viscosity" parameter epsilon tends to zero
Quasistatic crack growth in elasto-plastic materials: the two-dimensional case
No full textWe study a variational model for the quasistatic evolution of elasto-plastic materials with cracks in the case of planar small strain associative elasto-plasticity
Decomposition results for functions with bounded variation
No full textSome decomposition results for functions with bounded variation are obtained by using Gagliardo's Theorem on the surjectivity of the trace operator from W1,1(Ω) into L1(∂Ω). More precisely, we prove that every BV function can be written as the sum of a BV function without jumps and a BV function without Cantor part. Alternatively, it can be written as the sum of a BV function without jumps and a purely ingular BV function (i.e., a function whose gradient is singular with respect to the Lebesgue measure). It can also be decomposed as the sum of a purely singular BV function and a BV function without Cantor part. We also prove similar results for the space BD of functions with bounded deformation. In particular, we show that every BD function can be written as the sum of a BD function without jumps and a BV function without Cantor part. Therefore, every BD function without Cantor part is the sum of a function whose symmetrized gradient belongs to L1 and a BV function without Cantor part
On a notion of unilateral slope for the Mumford-Shah functional
No full textIn this paper we introduce a notion of unilateral slope for the Mumford-Shah functional, and provide an explicit formula in the case of smooth cracks. We show that the slope is not lower semicontinuous and study the corresponding relaxed functional
On the jerky crack growth in elastoplastic materials
No full textThe purpose of this paper is to show that in elastoplastic materials cracks can grow only in an intermittent way. This result is rigorously proved in the framework of a simplified model
A model for the quasi-static growth of brittle fractures: existence and approximation results
No full textWe give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G. A. Francfort and J.J. Marigo, and based on Griffith's theory of crack growth. In the two-dimensional case we prove an existence result for the quasi-static evolution and show that the total energy is an absolutely continuous function of time, although we cannot exclude the possibility that the bulk energy and the surface energy may present some jump discontinuities. This existence result is proved by a time-discretization process, where at each step a global energy minimization is performed, with the constraint that the new crack contains all cracks formed at the previous time steps. This procedure provides an effective way to approximate the continuous time evolution
Quasistatic crack evolution for a cohesive zone model with different response to loading and unloading: a Young measures approach
No full textA new approach to irreversible quasistatic fracture growth is given, by means of Young measures. The study concerns a cohesive zone model with prescribed crack path, when the material gives different responses to loading and unloading phases
Quasistatic crack growth in elasto-plastic materials with hardening: The antiplane case
No full textWe study a variational model for crack growth in elasto-plastic materials with hardening in the antiplane case. The main result is the existence of a solution to the initial value problem with prescribed time-dependent boundary conditions
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