A vanishing viscosity approach to a rate-independent damage model (Articolo in rivista)

Type
Label
  • A vanishing viscosity approach to a rate-independent damage model (Articolo in rivista) (literal)
Anno
  • 2013-01-01T00:00:00+01:00 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#doi
  • 10.1142/S021820251250056X (literal)
Alternative label
  • Dorothee Knees; Riccarda Rossi; Chiara Zanini (2013)
    A vanishing viscosity approach to a rate-independent damage model
    in Mathematical models and methods in applied sciences; World Scientific Publishing Co, Singapore (Singapore)
    (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#autori
  • Dorothee Knees; Riccarda Rossi; Chiara Zanini (literal)
Pagina inizio
  • 565 (literal)
Pagina fine
  • 616 (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#url
  • http://www.worldscientific.com/doi/abs/10.1142/S021820251250056X (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroVolume
  • 23 (literal)
Rivista
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#numeroFascicolo
  • 4 (literal)
Note
  • Scopu (literal)
Http://www.cnr.it/ontology/cnr/pubblicazioni.owl#affiliazioni
  • Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin, Germany; Department of Mathematics, University of Brescia, Via Valotti 9, 25133 Brescia, Italy; Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy (literal)
Titolo
  • A vanishing viscosity approach to a rate-independent damage model (literal)
Abstract
  • We analyze a rate-independent 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 by-now classical concept of global energetic solution fails to describe accurately the behavior of the system at jumps. Hence, we consider rate-independent damage models as limits of systems driven by viscous, rate-dependent dissipation. We use a technique for taking the vanishing viscosity limit, which is based on arclength reparametrization. In this way, in the limit we obtain a novel formulation for the rate-independent damage model, which highlights the interplay of viscous and rate-independent effects in the jump regime, and provides a better description of the energetic behavior of the system at jumps. (literal)
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