Cam-Clay plasticity is a well established model for the description of the mechanics of fine grained soils. As solutions can develop discontinuities in time, a weak notion of solution, in terms of a rescaled time s , has been proposed in [8] to give a meaning to this discontinuous evolution. In this paper we first prove that this rescaled evolution satisfies the flow-rule for the rate of plastic strain, in a suitable measure-theoretical sense. In the second part of the paper we consider the behavior of the evolution in terms of the original time variable t . We prove that the unrescaled solution satisfies an energy-dissipation balance and an evolution law for the internal variable, which can be expressed in terms of integrals depending only on the original time. Both these integral identities contain terms concentrated on the jump times, whose size can only be determined by looking at the rescaled formulation.

1 aDal Maso, Gianni1 aDeSimone, Antonio1 aSolombrino, Francesco uhttp://hdl.handle.net/1963/390001427nas 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 aCam-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.

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 aWe 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.

10aCam-Clay plasticity1 aDal Maso, Gianni1 aSolombrino, Francesco uhttp://hdl.handle.net/1963/367101168nas a2200157 4500008004100000022001400041245008800055210006900143300000900212490000700221520061900228653003000847653003100877100002600908856007600934 2010 eng d a1078-094700aQuasistatic evolution for plasticity with softening: The spatially homogeneous case0 aQuasistatic evolution for plasticity with softening The spatiall a11890 v273 aThe spatially uniform case of the problem of quasistatic evolution in small strain associative elastoplasticity with softening is studied. Through the introdution of a viscous approximation, the problem reduces to determine the limit behaviour of the solutions of a singularly perturbed system of ODE's in a finite dimensional Banach space. We see that the limit dynamics presents, for a generic choice of the initial data, the alternation of three possible regimes (elastic regime, slow dynamics, fast dynamics), which is determined by the sign of two scalar indicators, whose explicit expression is given.

10aplasticity with softening10arate independent processes1 aSolombrino, Francesco uhttp://aimsciences.org//article/id/4c2301d8-f553-493e-b672-b4f76a3ede2f01324nas a2200121 4500008004100000245008000041210006900121300001300190490000700203520085200210100002601062856011401088 2009 eng d00aQuasistatic evolution problems for nonhomogeneous elastic plastic materials0 aQuasistatic evolution problems for nonhomogeneous elastic plasti a89–1190 v163 aThe paper studies the quasistatic evolution for elastoplastic materials when the yield surface depends on the position in the reference configuration. The main results are obtained when the yield surface is continuous with respect to the space variable. The case of piecewise constant dependence is also considered. The evolution is studied in the framework of the variational formulation for rate independent problems developed by Mielke. The results are proved by adapting the arguments introduced for a constant yield surface, using some properties of convex valued semicontinuous multifunctions. A strong formulation of the problem is also obtained, which includes a pointwise version of the plastic flow rule. Some examples are considered, which show that strain concentration may occur as a consequence of a nonconstant yield surface.

1 aSolombrino, Francesco uhttps://www.math.sissa.it/publication/quasistatic-evolution-problems-nonhomogeneous-elastic-plastic-materials