We present a variational model for the quasi-static crack growth in hydraulic fracture in the framework of the energy formulation of rate-independent processes. The cracks are assumed to lie on a prescribed plane and to satisfy a very weak regularity assumption.

1 aAlmi, Stefano1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/20.500.11767/1735000819nas a2200157 4500008004100000022001400041245007800055210006900133260000800202300001400210490000700224520034300231100002100574700002000595856004600615 2014 eng d a1572-922200aQuasistatic Evolution in Perfect Plasticity as Limit of Dynamic Processes0 aQuasistatic Evolution in Perfect Plasticity as Limit of Dynamic cDec a915–9540 v263 aWe introduce a model of dynamic visco-elasto-plastic evolution in the linearly elastic regime and prove an existence and uniqueness result. Then we study the limit of (a rescaled version of) the solutions when the data vary slowly. We prove that they converge, up to a subsequence, to a quasistatic evolution in perfect plasticity.

1 aDal Maso, Gianni1 aScala, Riccardo uhttps://doi.org/10.1007/s10884-014-9409-701387nas a2200133 4500008004300000245008800043210006900131260001300200520093500213100002101148700002201169700002601191856003601217 2012 en_Ud 00aQuasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution0 aQuasistatic evolution for CamClay plasticity properties of the v bSpringer3 aCam-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/1963/367000550nas a2200109 4500008004300000245008300043210006900126520016900195100002100364700001900385856003600404 2010 en_Ud 00aQuasistatic crack growth in elasto-plastic materials: the two-dimensional case0 aQuasistatic crack growth in elastoplastic materials the twodimen3 aWe study a variational model for the quasistatic evolution of elasto-plastic materials with cracks in the case of planar small strain associative elasto-plasticity.1 aDal Maso, Gianni1 aToader, Rodica uhttp://hdl.handle.net/1963/296400595nas a2200109 4500008004300000245007600043210006900119520021600188100002100404700002400425856003600449 2010 en_Ud 00aQuasistatic crack growth in finite elasticity with non-interpenetration0 aQuasistatic crack growth in finite elasticity with noninterpenet3 aWe present a variational model to study the quasistatic growth of brittle cracks in hyperelastic materials, in the framework of finite elasticity, taking\\ninto account the non-interpenetration condition.

1 aDal Maso, Gianni1 aLazzaroni, Giuliano uhttp://hdl.handle.net/1963/339701311nas 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/1963/367100735nas a2200109 4500008004300000245009500043210006900138520033900207100002100546700002200567856003600589 2009 en_Ud 00aQuasistatic evolution for Cam-Clay plasticity: examples of spatially homogeneous solutions0 aQuasistatic evolution for CamClay plasticity examples of spatial3 aWe 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.1 aDal Maso, Gianni1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/339500626nas a2200109 4500008004300000245008200043210006900125520024600194100002100440700001900461856003600480 2007 en_Ud 00aQuasistatic crack growth for a cohesive zone model with prescribed crack path0 aQuasistatic crack growth for a cohesive zone model with prescrib3 aIn this paper we study the quasistatic crack growth for a cohesive zone model. We assume that the crack path is prescribed and we study the time evolution of the crack in the framework of the variational theory of rate-independent processes.1 aDal Maso, Gianni1 aZanini, Chiara uhttp://hdl.handle.net/1963/168600558nas a2200121 4500008004300000245007600043210006900119520014800188100002100336700002100357700002200378856003600400 2007 en_Ud 00aQuasistatic evolution problems for pressure-sensitive plastic materials0 aQuasistatic evolution problems for pressuresensitive plastic mat3 aWe study quasistatic evolution problems for pressure-sensitive plastic materials in the context of small strain associative perfect plasticity.1 aDal Maso, Gianni1 aDemyanov, Alexey1 aDeSimone, Antonio uhttp://hdl.handle.net/1963/196201091nas a2200121 4500008004300000245008400043210006900127520066900196100002100865700002200886700002500908856003600933 2006 en_Ud 00aQuasistatic evolution problems for linearly elastic-perfectly plastic materials0 aQuasistatic evolution problems for linearly elasticperfectly pla3 aThe 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.1 aDal Maso, Gianni1 aDeSimone, Antonio1 aMora, Maria Giovanna uhttp://hdl.handle.net/1963/212900706nas a2200121 4500008004300000245005300043210005300096520033400149100002100483700002500504700001900529856003600548 2005 en_Ud 00aQuasistatic Crack Growth in Nonlinear Elasticity0 aQuasistatic Crack Growth in Nonlinear Elasticity3 aIn this paper, we prove a new existence result for a variational model of crack growth in brittle materials proposed in [15]. We consider the case of $n$-dimensional finite elasticity, for an arbitrary $n\\\\ge1$, with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads, both depending on time.1 aDal Maso, Gianni1 aFrancfort, Gilles A.1 aToader, Rodica uhttp://hdl.handle.net/1963/229300759nas a2200121 4500008004300000245007800043210006900121520034600190100002100536700002500557700001900582856003600601 2004 en_Ud 00aQuasi-static evolution in brittle fracture: the case of bounded solutions0 aQuasistatic evolution in brittle fracture the case of bounded so3 aThe main steps of the proof of the existence result for the quasi-static evolution of cracks in brittle materials, obtained in [7] in the vector case and for a general quasiconvex elastic energy, are presented here under the simplifying assumption that the minimizing sequences involved in the problem are uniformly bounded in $L^\\\\infty$.1 aDal Maso, Gianni1 aFrancfort, Gilles A.1 aToader, Rodica uhttp://hdl.handle.net/1963/2229