Fatigue Effects in Elastic Materials with Variational Damage Models: A Vanishing Viscosity Approach View Full Text


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Article Info

DATE

2018-11-11

AUTHORS

Roberto Alessi, Vito Crismale, Gianluca Orlando

ABSTRACT

We study the existence of quasistatic evolutions for a family of gradient damage models which take into account fatigue, that is the process of weakening in a material due to repeated applied loads. The main feature of these models is the fact that damage is favoured in regions where the cumulation of the elastic strain (or other relevant variables, depending on the model) is higher. To prove the existence of a quasistatic evolution, we follow a vanishing viscosity approach based on two steps: we first let the time step τ of the time discretisation and later the viscosity parameter ε go to zero. As τ→0, we find ε-approximate viscous evolutions; then, as ε→0, we find a rescaled approximate evolution satisfying an energy-dissipation balance. More... »

PAGES

1-54

References to SciGraph publications

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  • 2011-01. Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 2009. Fatigue of Structures and Materials in NONE
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  • 2002. Non-Smooth Thermomechanics in NONE
  • 2006-09. A Variational View of Partial Brittle Damage Evolution in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2018-02. Viscous Corrections of the Time Incremental Minimization Scheme and Visco-Energetic Solutions to Rate-Independent Evolution Problems in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2016-06. Fracture models for elasto-plastic materials as limits of gradient damage models coupled with plasticity: the antiplane case in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 2017-04. Globally stable quasistatic evolution for strain gradient plasticity coupled with damage in ANNALI DI MATEMATICA PURA ED APPLICATA (1923 -)
  • 2016-02. Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
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  • 2018-04. A Reshetnyak-type lower semicontinuity result for linearised elasto-plasticity coupled with damage in W1,n in NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS NODEA
  • 2014-11. Gradient Damage Models Coupled with Plasticity and Nucleation of Cohesive Cracks in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00332-018-9511-9

    DOI

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    DIMENSIONS

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