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13
A vanishing viscosity approach to quasistatic evolution in plasticity with softening, preprint, (see http://cvgmt.sns.it/papers/daldesmor06/DMDeSMorMor.pdf
"... Abstract. We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rateindependent proble ..."
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Cited by 41 (4 self)
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Abstract. We deal with quasistatic evolution problems in plasticity with softening, in the framework of small strain associative elastoplasticity. The presence of a nonconvex term due to the softening phenomenon requires a nontrivial extension of the variational framework for rateindependent problems to the case of a nonconvex energy functional. We argue that, in this case, the use of global minimizers in the corresponding incremental problems is not justified from the mechanical point of view. Thus, we analize a different selection criterion for the solutions of the quasistatic evolution problem, based on a viscous approximation. This leads to a generalized formulation in terms of Young measures, developed in the first part of the paper. In the second part we apply our approach to
Morini M.: Globally stable quasistatic evolution in plasticity with softening
 Netw. Heterog. Media
"... Abstract. We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global st ..."
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Cited by 18 (3 self)
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Abstract. We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is characterized by the following properties: global stability at each time and energy balance on each time interval. An example developed in detail compares the solutions obtained by this method with the ones provided by a vanishing viscosity approximation, and shows that only the latter capture a decreasing branch in the stressstrain response.
A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy
"... Abstract. We study a quasistatic evolution problem for a nonconvex elastic energy functional. Due to lack of convexity, the natural energetic formulation can be obtained only in the framework of Young measures. Since the energy functional may present multiple wells, an evolution driven by global min ..."
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Cited by 7 (0 self)
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Abstract. We study a quasistatic evolution problem for a nonconvex elastic energy functional. Due to lack of convexity, the natural energetic formulation can be obtained only in the framework of Young measures. Since the energy functional may present multiple wells, an evolution driven by global minimizers may exhibit unnatural jumps from one well to another one, which overcome large potential barriers. To avoid this phenomenon, we study a notion of solution based on a viscous regularization. Finally we
A young measure approach to quasistatic evolution for a class of material models with nonconvex elastic energies
, 2008
"... Abstract. Rateindependent evolution for material models with nonconvex elastic energies is studied without any spatial regularization of the inner variable; due to lack of convexity, the model is developed in the framework of Young measures. An existence result for the quasistatic evolution is obta ..."
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Cited by 4 (2 self)
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Abstract. Rateindependent evolution for material models with nonconvex elastic energies is studied without any spatial regularization of the inner variable; due to lack of convexity, the model is developed in the framework of Young measures. An existence result for the quasistatic evolution is obtained in terms of compatible systems of Young measures. We also show as this result can be equivalently reformulated with probabilistic language and leads to the description of the quasistatic evolution in terms of stochastic processes on a suitable probability space.
Youngmeasure quasistatic damage evolution
, 2012
"... Abstract. An existence result for the quasistatic evolution of incomplete damage in elastic materials is presented. The absence of gradient terms in the damage variable causes a critical lack of compactness. Therefore, the analysis is developed in the framework of Young measures, where a notion of ..."
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Cited by 4 (0 self)
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Abstract. An existence result for the quasistatic evolution of incomplete damage in elastic materials is presented. The absence of gradient terms in the damage variable causes a critical lack of compactness. Therefore, the analysis is developed in the framework of Young measures, where a notion of solution is defined, presenting some improvements with respect to previous contributions. The main new feature in the proof of the existence result regards a delicate construction of the jointrecovery sequence. 1.
RATEINDEPENDENT PHASE TRANSITIONS IN ELASTIC MATERIALS: A YOUNGMEASURE APPROACH.
"... Abstract. A quasistatic evolution problem for a phase transitions model with nonconvex energy density is considered in terms of Young measures. We focus on the particular case of a finite number of phases. The new feature consists in the usage of suitable regularity arguments in order to prove an ex ..."
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Cited by 1 (1 self)
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Abstract. A quasistatic evolution problem for a phase transitions model with nonconvex energy density is considered in terms of Young measures. We focus on the particular case of a finite number of phases. The new feature consists in the usage of suitable regularity arguments in order to prove an existence result for the a notion of evolution presenting some improvements with respect to the one defined in [9], for infinitely many phases.
BICS Bath Institute for Complex Systems Evolutionary problems in nonreflexive spaces
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ON CERTAIN CONVEX COMPACTIFICATIONS FOR RELAXATION IN EVOLUTION PROBLEMS
"... On certain convex compactifications for relaxation in evolution problems ..."
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