TY - JOUR
T1 - Curvature theory of boundary phases: the two-dimensional case
JF - Interfaces Free Bound. 7 (2002) 345-370
Y1 - 2002
A1 - Andrea Braides
A1 - Andrea Malchiodi
AB - 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.
PB - European Mathematical Society
UR - http://hdl.handle.net/1963/3537
U1 - 1164
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - The passage from nonconvex discrete systems to variational problems in Sobolev spaces: the one-dimensional case
JF - Proc. Steklov Inst. Math. 236 (2002) 395-414
Y1 - 2002
A1 - Andrea Braides
A1 - Maria Stella Gelli
A1 - Mario Sigalotti
PB - MAIK Nauka/Interperiodica
UR - http://hdl.handle.net/1963/3130
U1 - 1203
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Variational formulation of softening phenomena in fracture mechanics. The one-dimensional case
JF - Arch. Ration. Mech. Anal. 146 (1999), no. 1, 23--58
Y1 - 1999
A1 - Andrea Braides
A1 - Gianni Dal Maso
A1 - Adriana Garroni
AB - 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.
PB - Springer
UR - http://hdl.handle.net/1963/3371
U1 - 959
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Special functions with bounded variation and with weakly differentiable traces on the jump set
JF - NoDEA Nonlinear Differential Equations Appl. 5 (1998), no. 2, 219--243
Y1 - 1998
A1 - Luigi Ambrosio
A1 - Andrea Braides
A1 - Adriana Garroni
PB - SISSA Library
UR - http://hdl.handle.net/1963/1025
U1 - 2831
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -