TY - JOUR
T1 - A variational model for quasistatic crack growth in nonlinear elasticity: some qualitative properties of the solutions
JF - Boll. Unione Mat. Ital. (9) 2 (2009) 371-390
Y1 - 2009
A1 - Gianni Dal Maso
A1 - Alessandro Giacomini
A1 - Marcello Ponsiglione
UR - http://hdl.handle.net/1963/2675
U1 - 1425
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - A vanishing viscosity approach to quasistatic evolution in plasticity with softening
JF - Arch. Ration. Mech. Anal. 189 (2008) 469-544
Y1 - 2008
A1 - Gianni Dal Maso
A1 - Antonio DeSimone
A1 - Maria Giovanna Mora
A1 - Massimiliano Morini
AB - We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rate-independent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to some concrete examples.
UR - http://hdl.handle.net/1963/1844
U1 - 2373
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - RPRT
T1 - Variational problems in fracture mechanics
Y1 - 2006
A1 - Gianni Dal Maso
AB - We present some recent existence results for the variational model of crack growth in brittle materials proposed by Francfort and Marigo in 1998. These results, obtained in collaboration with Francfort and Toader, cover the case of arbitrary space dimension with a general quasiconvex bulk energy and with prescribed boundary deformations and applied loads.
UR - http://hdl.handle.net/1963/1816
U1 - 2398
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Value Functions for Bolza Problems with Discontinuous Lagrangians and Hamilton-Jacobi inequalities
JF - ESAIM Control Optim. Calc. Var., 5 (2000), n. 5, p. 369-393.
Y1 - 2000
A1 - Gianni Dal Maso
A1 - Helene Frankowska
PB - SISSA Library
UR - http://hdl.handle.net/1963/1514
U1 - 2649
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 - A variational method in image segmentation: existence and approximation result
JF - Acta Math. 168 (1992), no.1-2, p. 89-151
Y1 - 1992
A1 - Gianni Dal Maso
A1 - Jean-Michel Morel
A1 - Sergio Solimini
PB - SISSA Library
UR - http://hdl.handle.net/1963/808
U1 - 2983
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Variational inequalities for the biharmonic operator with variable obstacles.
JF - Ann. Mat. Pura Appl. (4) 153 (1988), 203-227 (1989)
Y1 - 1988
A1 - Gianni Dal Maso
A1 - Gabriella Paderni
PB - SISSA Library
UR - http://hdl.handle.net/1963/531
U1 - 3373
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -