TY - JOUR
T1 - Globally stable quasistatic evolution in plasticity with softening
JF - Netw. Heterog. Media 3 (2008) 567-614
Y1 - 2008
A1 - Gianni Dal Maso
A1 - Antonio DeSimone
A1 - Maria Giovanna Mora
A1 - Massimiliano Morini
AB - We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each\\ntime interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stress-strain response.
UR - http://hdl.handle.net/1963/1965
U1 - 2228
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -
TY - JOUR
T1 - Global calibrations for the non-homogeneous Mumford-Shah functional
JF - Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1 (2002) 603-648
Y1 - 2002
A1 - Massimiliano Morini
AB - Using a calibration method we prove that, if $\\\\Gamma\\\\subset \\\\Omega$ is a closed regular hypersurface and if the function $g$ is discontinuous along $\\\\Gamma$ and regular outside, then the function $u_{\\\\beta}$ which solves $$ \\\\begin{cases} \\\\Delta u_{\\\\beta}=\\\\beta(u_{\\\\beta}-g)& \\\\text{in $\\\\Omega\\\\setminus\\\\Gamma$} \\\\partial_{\\\\nu} u_{\\\\beta}=0 & \\\\text{on $\\\\partial\\\\Omega\\\\cup\\\\Gamma$} \\\\end{cases} $$ is in turn discontinuous along $\\\\Gamma$ and it is the unique absolute minimizer of the non-homogeneous Mumford-Shah functional $$ \\\\int_{\\\\Omega\\\\setminus S_u}|\\\\nabla u|^2 dx +{\\\\cal H}^{n-1}(S_u)+\\\\beta\\\\int_{\\\\Omega\\\\setminus S_u}(u-g)^2 dx, $$ over $SBV(\\\\Omega)$, for $\\\\beta$ large enough. Applications of the result to the study of the gradient flow by the method of minimizing movements are shown.
PB - Scuola Normale Superiore di Pisa
UR - http://hdl.handle.net/1963/3089
U1 - 1244
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -