00727nas a2200121 4500008004300000245006600043210006400109260003400173520032000207100002000527700002200547856003600569 2002 en_Ud 00aCurvature theory of boundary phases: the two-dimensional case0 aCurvature theory of boundary phases the twodimensional case bEuropean Mathematical Society3 aWe describe the behaviour of minimum problems involving non-convex surface integrals in 2D, singularly perturbed by a curvature term. We show that their limit is described by functionals which take into account energies concentrated on vertices of polygons. Non-locality and non-compactness effects are highlighted.1 aBraides, Andrea1 aMalchiodi, Andrea uhttp://hdl.handle.net/1963/353700481nas a2200121 4500008004300000245011600043210006900159260003000228100002000258700002400278700002100302856003600323 2002 en_Ud 00aThe passage from nonconvex discrete systems to variational problems in Sobolev spaces: the one-dimensional case0 apassage from nonconvex discrete systems to variational problems bMAIK Nauka/Interperiodica1 aBraides, Andrea1 aGelli, Maria Stella1 aSigalotti, Mario uhttp://hdl.handle.net/1963/313001405nas a2200133 4500008004300000245009900043210006900142260001300211520094900224100002001173700002101193700002101214856003601235 1999 en_Ud 00aVariational formulation of softening phenomena in fracture mechanics. The one-dimensional case0 aVariational formulation of softening phenomena in fracture mecha bSpringer3 aStarting from experimental evidence, the authors justify a variational model for softening phenomena in fracture of one-dimensional bars where the energy is given by the contribution and interaction of two terms: a typical bulk energy term depending on elastic strain and a discrete part that depends upon the jump discontinuities that occur in fracture. A more formal, rigorous derivation of the model is presented by examining the $\\\\Gamma$-convergence of discrete energy functionals associated to an array of masses and springs. Close attention is paid to the softening and fracture regimes. \\nOnce the continuous model is derived, it is fully analyzed without losing sight of its discrete counterpart. In particular, the associated boundary value problem is studied and a detailed analysis of the stationary points under the presence of a dead load is performed. A final, interesting section on the scale effect on the model is included.1 aBraides, Andrea1 aDal Maso, Gianni1 aGarroni, Adriana uhttp://hdl.handle.net/1963/337100446nas a2200121 4500008004100000245009900041210006900140260001800209100002000227700002000247700002100267856003600288 1998 en d00aSpecial functions with bounded variation and with weakly differentiable traces on the jump set0 aSpecial functions with bounded variation and with weakly differe bSISSA Library1 aAmbrosio, Luigi1 aBraides, Andrea1 aGarroni, Adriana uhttp://hdl.handle.net/1963/1025