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@ARTICLE{Fleck:19499,
      author       = {Fleck, M. and Pilipenko, D. and Spatschek, R. and Brener,
                      E. A.},
      title        = {{B}rittle fracture in viscoelastic materials as a
                      pattern-formation process},
      journal      = {Physical review / E},
      volume       = {83},
      number       = {4},
      issn         = {1539-3755},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {PreJuSER-19499},
      pages        = {046213},
      year         = {2011},
      note         = {M. F. and D. P. are thankful for support by DFG Grant No.
                      SPP 1418 and R. S. for support by DFG Grant No. SPP 1296. E.
                      B. gratefully acknowledges support by the Erna and Jacob
                      Michael visiting professorship funds at the Weizmann
                      Institute of Science, Rehovot.},
      abstract     = {A continuum model of crack propagation in brittle
                      viscoelastic materials is presented and discussed. Thereby,
                      the phenomenon of fracture is understood as an elastically
                      induced nonequilibrium interfacial pattern formation
                      process. In this spirit, a full description of a propagating
                      crack provides the determination of the entire time
                      dependent shape of the crack surface, which is assumed to be
                      extended over a finite and self-consistently selected length
                      scale. The mechanism of crack propagation, that is, the
                      motion of the crack surface, is then determined through
                      linear nonequilibrium transport equations. Here we consider
                      two different mechanisms, a first-order phase transformation
                      and surface diffusion. We give scaling arguments showing
                      that steady-state solutions with a self-consistently
                      selected propagation velocity and crack shape can exist
                      provided that elastodynamic or viscoelastic effects are
                      taken into account, whereas static elasticity alone is not
                      sufficient. In this respect, inertial effects as well as
                      viscous damping are identified to be sufficient crack tip
                      selection mechanisms. Exploring the arising description of
                      brittle fracture numerically, we study steady-state crack
                      propagation in the viscoelastic and inertia limit as well as
                      in an intermediate regime, where both effects are important.
                      The arising free boundary problems are solved by phase field
                      methods and a sharp interface approach using a multipole
                      expansion technique. Different types of loading, mode I,
                      mode III fracture, as well as mixtures of them, are
                      discussed.},
      keywords     = {J (WoSType)},
      cin          = {PGI-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-2-20110106},
      pnm          = {Grundlagen für zukünftige Informationstechnologien},
      pid          = {G:(DE-Juel1)FUEK412},
      shelfmark    = {Physics, Fluids $\&$ Plasmas / Physics, Mathematical},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000290116400001},
      doi          = {10.1103/PhysRevE.83.046213},
      url          = {https://juser.fz-juelich.de/record/19499},
}