@article {2011,
	title = {Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling},
	journal = {Calculus of Variations and Partial Differential Equations 40 (2011) 125-181},
	number = {SISSA;36/2009/M},
	year = {2011},
	publisher = {Springer},
	abstract = {<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>},
	keywords = {Cam-Clay plasticity},
	doi = {10.1007/s00526-010-0336-0},
	url = {http://hdl.handle.net/1963/3670},
	author = {Gianni Dal Maso and Antonio DeSimone and Francesco Solombrino}
}
@article {2010,
	title = {Quasistatic evolution for Cam-Clay plasticity: the spatially homogeneous case},
	journal = {Netw. Heterog. Media 5 (2010) 97-132},
	number = {SISSA;39/2009/M},
	year = {2010},
	abstract = {<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>},
	keywords = {Cam-Clay plasticity},
	doi = {10.3934/nhm.2010.5.97},
	url = {http://hdl.handle.net/1963/3671},
	author = {Gianni Dal Maso and Francesco Solombrino}
}
