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Networks and Heterogeneous Media

2008, Volume 3, Issue 3: 567-614. doi: 10.3934/nhm.2008.3.567
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Globally stable quasistatic evolution in plasticity with softening

  • 1.
    SISSA-International School for Advanced Studies, Via Beirut 2-4, 34014, Trieste
  • 2.
    SISSA-International School for Advanced Studies, Via Beirut 2-4, 34014 Trieste
  • 3.
    SISSA-International School for Advanced Studies, Via Beirut 2-4,, 34014, Trieste
  • Received: 01 February 2008

  • Primary: 74C05; Secondary: 28A33, 74G65, 49J45, 35Q72.

  • 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 stress-strain response.

    Citation: G. Dal Maso, Antonio DeSimone, M. G. Mora, M. Morini. Globally stable quasistatic evolution in plasticity with softening[J]. Networks and Heterogeneous Media, 2008, 3(3): 567-614. doi: 10.3934/nhm.2008.3.567

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  • 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 stress-strain response.


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  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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    沈阳化工大学材料科学与工程学院 沈阳 110142

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