@article {2012, title = {Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution}, journal = {Calculus of variations and partial differential equations 44 (2012) 495-541}, number = {SISSA;46/2010/M}, year = {2012}, publisher = {Springer}, abstract = {

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.

}, doi = {10.1007/s00526-011-0443-6}, url = {http://hdl.handle.net/1963/3900}, author = {Gianni Dal Maso and Antonio DeSimone and Francesco Solombrino} } @article {2011, title = {Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications}, journal = {Journal of the Mechanics and Physics of Solids 59 (2011) 787-803}, number = {SISSA;62/2010/M}, year = {2011}, abstract = {We provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the interpretation of mechanical experiments.}, url = {http://hdl.handle.net/1963/4065}, author = {Pierluigi Cesana and Antonio DeSimone} } @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 = {

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.

}, 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 {2011, title = {Quasistatic evolution of sessile drops and contact angle hysteresis}, journal = {Arch. Rational Mech. Anal. 202 (2011) 295-348}, year = {2011}, publisher = {Springer}, abstract = {We consider the classical model of capillarity coupled with a rate-independent dissipation mechanism due to frictional forces acting on the contact line, and prove the existence of quasistatic evolutions with prescribed initial configuration. We also discuss in detail some explicit solutions to show that the model does account for contact angle hysteresis, and to compare its predictions with experimental observations.}, doi = {10.1007/s00205-011-0427-x}, url = {http://hdl.handle.net/1963/4912}, author = {Giovanni Alberti and Antonio DeSimone} } @article {2009, title = {Quasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions}, journal = {Math. Models Methods Appl. Sci. 19 (2009) 1643-1711}, number = {SISSA;78/2008/M}, year = {2009}, abstract = {We study a quasistatic evolution problem for Cam-Clay plasticity under a special loading program which leads to spatially homogeneous solutions. Under some initial conditions, the solutions exhibit a softening behaviour and time discontinuities.\\nThe behavior of the solutions at the jump times is studied by a viscous approximation.}, doi = {10.1142/S0218202509003942}, url = {http://hdl.handle.net/1963/3395}, author = {Gianni Dal Maso and Antonio DeSimone} } @article {2007, title = {Quasistatic evolution problems for pressure-sensitive plastic materials}, journal = {Milan J. Math. 75 (2007) 117-134}, number = {SISSA;27/2007/M}, year = {2007}, abstract = {We study quasistatic evolution problems for pressure-sensitive plastic materials in the context of small strain associative perfect plasticity.}, doi = {10.1007/s00032-007-0071-y}, url = {http://hdl.handle.net/1963/1962}, author = {Gianni Dal Maso and Alexey Demyanov and Antonio DeSimone} } @article {2006, title = {Quasistatic evolution problems for linearly elastic-perfectly plastic materials}, journal = {Arch. Ration. Mech. Anal. 180 (2006) 237-291}, number = {arXiv.org;math/0412212v1}, year = {2006}, abstract = {The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental variational problems in spaces of functions with bounded deformation. This provides a new approximation result for the solutions of the quasistatic evolution problem, which are shown to be absolutely continuous in time. Four equivalent formulations of the problem in rate form are derived. A strong formulation of the flow rule is obtained by introducing a precise definition of the stress on the singular set of the plastic strain.}, doi = {10.1007/s00205-005-0407-0}, url = {http://hdl.handle.net/1963/2129}, author = {Gianni Dal Maso and Antonio DeSimone and Maria Giovanna Mora} }