%0 Journal Article
%J Interfaces Free Bound. 7 (2002) 345-370
%D 2002
%T Curvature theory of boundary phases: the two-dimensional case
%A Andrea Braides
%A Andrea Malchiodi
%X We 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.
%B Interfaces Free Bound. 7 (2002) 345-370
%I European Mathematical Society
%G en_US
%U http://hdl.handle.net/1963/3537
%1 1164
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2009-02-23T15:34:33Z\\nNo. of bitstreams: 1\\n2001BM.pdf: 361945 bytes, checksum: eb748fdc7f69d6fef497ebaf68f155a6 (MD5)
%0 Journal Article
%J Proc. Steklov Inst. Math. 236 (2002) 395-414
%D 2002
%T The passage from nonconvex discrete systems to variational problems in Sobolev spaces: the one-dimensional case
%A Andrea Braides
%A Maria Stella Gelli
%A Mario Sigalotti
%B Proc. Steklov Inst. Math. 236 (2002) 395-414
%I MAIK Nauka/Interperiodica
%G en_US
%U http://hdl.handle.net/1963/3130
%1 1203
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-10-16T15:53:06Z\\nNo. of bitstreams: 1\\npassage.pdf: 242138 bytes, checksum: 1874bdb2ad8c185c3fe84d7deb988b5b (MD5)
%0 Journal Article
%J Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58
%D 1999
%T Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case
%A Andrea Braides
%A Gianni Dal Maso
%A Adriana Garroni
%X Starting 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.
%B Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58
%I Springer
%G en_US
%U http://hdl.handle.net/1963/3371
%1 959
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-11-28T17:18:31Z\\nNo. of bitstreams: 1\\nVariational_formulation.pdf: 2100868 bytes, checksum: 88bfc4cfb6072391f1c6d7cd06e7b8ec (MD5)
%R 10.1007/s002050050135
%0 Journal Article
%J NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243
%D 1998
%T Special functions with bounded variation and with weakly differentiable traces on the jump set
%A Luigi Ambrosio
%A Andrea Braides
%A Adriana Garroni
%B NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243
%I SISSA Library
%G en
%U http://hdl.handle.net/1963/1025
%1 2831
%2 Mathematics
%3 Functional Analysis and Applications
%$ Made available in DSpace on 2004-09-01T12:41:50Z (GMT). No. of bitstreams: 0\\n Previous issue date: 1995