01427nas a2200145   4500008004300000245012100043210006900164260001300233520090600246653002401152100002101176700002201197700002601219856003601245       2011                        en_Ud  00aQuasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling0 aQuasistatic evolution for CamClay plasticity a weak formulation   bSpringer3 a<p>Cam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in [4] and [6], the proposed solution may be discontinuous with respect to the original time. Our formulation allows to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.</p>10aCam-Clay plasticity1 aDal Maso, Gianni1 aDeSimone, Antonio1 aSolombrino, Francesco  uhttp://hdl.handle.net/1963/367001311nas a2200121   4500008004300000245008200043210006900125520088800194653002401082100002101106700002601127856003601153       2010                        en_Ud  00aQuasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case0 aQuasistatic evolution for CamClay plasticity the spatially homog3 a<p>We study the spatially uniform case of the problem of quasistatic evolution in small strain nonassociative elastoplasticity (Cam-Clay model). Through the introdution of a viscous approximation, the problem reduces to determine the limit behavior of the solutions of a singularly perturbed system of ODE\\\'s in a finite dimensional Banach space. Depending on the sign of two explicit scalar indicators, we see that the limit dynamics presents, under quite generic assumptions, the alternation of three possible regimes: the elastic regime, when the limit equation is just the equation of linearized elasticity, the slow dynamics, when the strain evolves smoothly on the yield surface and plastic flow is produced, and the fast dynamics, which may happen only in the softening regime, where\\nviscous solutions exhibit a jump across a heteroclinic orbit of an auxiliary system.</p>10aCam-Clay plasticity1 aDal Maso, Gianni1 aSolombrino, Francesco  uhttp://hdl.handle.net/1963/3671