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QUASISTATIC EVOLUTION FOR CAMCLAY PLASTICITY: A WEAK FORMULATION VIA VISCOPLASTIC REGULARIZATION AND TIME RESCALING
"... Abstract. CamClay 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 viscoplast ..."
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Abstract. CamClay 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 energydissipation 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: CamClay plasticity, softening behaviour, nonassociative plasticity, pressuresensitive
Nonsmooth analysis of doubly nonlinear evolution equations
 Calc. Var. Partial Differential Equations
, 2012
"... Abstract. In this paper we analyze a broad class of abstract doubly nonlinear evolution equations in Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general sufficient conditions, on the dissipation potential and the energy functional, for existence of solutions to the re ..."
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Cited by 12 (5 self)
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Abstract. In this paper we analyze a broad class of abstract doubly nonlinear evolution equations in Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general sufficient conditions, on the dissipation potential and the energy functional, for existence of solutions to the related Cauchy problem. We prove our main existence result by passing to the limit in a timediscretization scheme with variational techniques. Finally, we discuss an application to a material model in finitestrain elasticity. AMS Subject Classication: 35A15, 35K50, 35K85 49Q20, 58E99. Key words: doubly nonlinear equations, differential inclusions, generalized gradient flows,
Adhesive contact of viscoelastic bodies and defect measures arising by vanishing viscosity
 SIAM J Math Anal
"... Abstract: An adhesive unilateral contact of elastic bodies with a small viscosity in the linear KelvinVoigt rheology at small strains is scrutinized. The flowrule for debonding the adhesive is considered rateindependent and unidirectional. The asymptotics for the viscosity or for external loadin ..."
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Cited by 8 (1 self)
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Abstract: An adhesive unilateral contact of elastic bodies with a small viscosity in the linear KelvinVoigt rheology at small strains is scrutinized. The flowrule for debonding the adhesive is considered rateindependent and unidirectional. The asymptotics for the viscosity or for external loading speed approaching zero is proved in some special cases, in particular when inertia is neglected or when delamination is in Mode II (pure shear). The solutions thus obtained involve certain defectlike measures recording in some sense natural additional energy dissipated in the bulk due to (vanishing) viscosity. Reflecting also the conventional engineering concept, the delamination is thus driven rather by stress than energy. An explicit example leading to a nontrivial defect measure is given.
QUASISTATIC EVOLUTION IN PERFECT PLASTICITY AS LIMIT OF DYNAMIC PROCESSES
, 2013
"... We introduce a model of dynamic viscoelastoplastic evolution in the linearly elastic regime and we 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 quasista ..."
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Cited by 2 (0 self)
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We introduce a model of dynamic viscoelastoplastic evolution in the linearly elastic regime and we 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.
Globally stable quasistatic evolution for a coupled elastoplasticdamage model
 ESAIM Control Optim. Calc. Var. DOI
, 2015
"... Abstract. We show the existence of globally stable quasistatic evolutions for a rateindependent material model with elastoplasticity and incomplete damage, in small strain assumptions. The main feature of our model is that the scalar internal variable which describes the damage affects both the ela ..."
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Abstract. We show the existence of globally stable quasistatic evolutions for a rateindependent material model with elastoplasticity and incomplete damage, in small strain assumptions. The main feature of our model is that the scalar internal variable which describes the damage affects both the elastic tensor and the plastic yield surface. It is also possible to require that the history of plastic strain up to the current state influences the future evolution of damage.
Convergence of interactiondriven evolutions of dislocations with Wasserstein dissipation and slipplane confinement, (in preparation
"... Abstract. We consider systems of n parallel edge dislocations in a single slip system, represented by points in a twodimensional domain; the elastic medium is modelled as a continuum. We formulate the energy of this system in terms of the empirical measure of the dislocations, and prove several co ..."
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Cited by 1 (0 self)
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Abstract. We consider systems of n parallel edge dislocations in a single slip system, represented by points in a twodimensional domain; the elastic medium is modelled as a continuum. We formulate the energy of this system in terms of the empirical measure of the dislocations, and prove several convergence results in the limit n→∞. The main aim of the paper is to study the convergence of the evolution of the empirical measure as n→∞. We consider rateindependent, quasistatic evolutions, in which the motion of the dislocations is restricted to the same slip plane. This leads to a formulation of the quasistatic evolution problem in terms of a modified Wasserstein distance, which is only finite when the transport plan is slipplaneconfined. Since the focus is on interaction between dislocations, we renormalize the elastic energy to remove the potentially large self or core energy. We prove Gammaconvergence of this renormalized energy, and we construct joint recovery sequences for which both the energies and the modified distances converge. With this augmented Gammaconvergence we prove the convergence of the quasistatic evolutions as n→∞. 1.
Quasistatic delamination of sandwichlike KirchhoffLove plates
"... Abstract. A quasistatic rateindependent adhesive delamination problem of laminated plates with a finite thickness is considered. By letting the thickness of the plates go to zero, a rateindependent delamination model for a laminated KirchhoffLove plate is obtained as limit of these quasistatic pr ..."
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Abstract. A quasistatic rateindependent adhesive delamination problem of laminated plates with a finite thickness is considered. By letting the thickness of the plates go to zero, a rateindependent delamination model for a laminated KirchhoffLove plate is obtained as limit of these quasistatic processes. The same dimension reduction procedure is eventually applied to processes which are sensitive to delamination modes, namely opening vs. shearing is distinguished.
WeierstraßInstitut für Angewandte Analysis und Stochastik A vanishing viscosity approach to a rateindependent damage model
, 2010
"... Abstract We analyze a rateindependent model for damage evolution in elastic bodies. The central quantities are a stored energy functional and a dissipation functional, which is assumed to be positively homogeneous of degree one. Since the energy is not simultaneously (strictly) convex in the damag ..."
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Abstract We analyze a rateindependent model for damage evolution in elastic bodies. The central quantities are a stored energy functional and a dissipation functional, which is assumed to be positively homogeneous of degree one. Since the energy is not simultaneously (strictly) convex in the damage variable and the displacements, solutions may have jumps as a function of time. The latter circumstance makes it necessary to recur to suitable notions of weak solution. However, the bynow classical concept of global energetic solution fails to describe accurately the behavior of the system at jumps. Hence, we consider rateindependent damage models as limits of systems driven by viscous, ratedependent dissipation. We use a technique for taking the vanishing viscosity limit, which is based on arclength reparameterization. In this way, in the limit we obtain a novel formulation for the rateindependent damage model, which highlights the interplay of viscous and rateindependent effects in the jump regime, and provides a better description of the energetic behavior of the system at jumps.