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@ARTICLE{Brener:808658,
      author       = {Brener, Efim and Weikamp, Marc and Spatschek, Robert and
                      Bar-Sinai, Yohai and Bouchbinder, Eran},
      title        = {{D}ynamic {I}nstabilities of {F}rictional {S}liding at a
                      {B}imaterial {I}nterface},
      journal      = {Journal of the mechanics and physics of solids},
      volume       = {89},
      issn         = {0022-5096},
      address      = {Amsterdam [u.a.]},
      publisher    = {Elsevier Science},
      reportid     = {FZJ-2016-02291},
      pages        = {149 - 173},
      year         = {2016},
      abstract     = {Understanding the dynamic stability of bodies in frictional
                      contact steadily sliding one over the other is of basic
                      interest in various disciplines such as physics, solid
                      mechanics, materials science and geophysics. Here we report
                      on a two-dimensional linear stability analysis of a
                      deformable solid of a finite height H, steadily sliding on
                      top of a rigid solid within a generic rate-and-state
                      friction type constitutive framework, fully accounting for
                      elastodynamic effects. We derive the linear stability
                      spectrum, quantifying the interplay between stabilization
                      related to the frictional constitutive law and
                      destabilization related both to the elastodynamic
                      bi-material coupling between normal stress variations and
                      interfacial slip, and to finite size effects. The
                      stabilizing effects related to the frictional constitutive
                      law include velocity-strengthening friction (i.e. an
                      increase in frictional resistance with increasing slip
                      velocity, both instantaneous and under steady-state
                      conditions) and a regularized response to normal stress
                      variations. We first consider the small wave-number k limit
                      and demonstrate that homogeneous sliding in this case is
                      universally unstable, independent of the details of the
                      friction law. This universal instability is mediated by
                      propagating waveguide-like modes, whose fastest growing mode
                      is characterized by a wave-number satisfying
                      kH∼O(1)kH∼O(1) and by a growth rate that scales with
                      H−1. We then consider the limit kH→∞kH→∞ and
                      derive the stability phase diagram in this case. We show
                      that the dominant instability mode travels at nearly the
                      dilatational wave-speed in the opposite direction to the
                      sliding direction. In a certain parameter range this
                      instability is manifested through unstable modes at all
                      wave-numbers, yet the frictional response is shown to be
                      mathematically well-posed. Instability modes which travel at
                      nearly the shear wave-speed in the sliding direction also
                      exist in some range of physical parameters. Previous results
                      obtained in the quasi-static regime appear relevant only
                      within a narrow region of the parameter space. Finally, we
                      show that a finite-time regularized response to normal
                      stress variations, within the framework of generalized
                      rate-and-state friction models, tends to promote stability.
                      The relevance of our results to the rupture of bi-material
                      interfaces is briefly discussed},
      cin          = {PGI-2 / IEK-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)PGI-2-20110106 / I:(DE-Juel1)IEK-2-20101013},
      pnm          = {111 - Efficient and Flexible Power Plants (POF3-111) / 144
                      - Controlling Collective States (POF3-144)},
      pid          = {G:(DE-HGF)POF3-111 / G:(DE-HGF)POF3-144},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000374355900009},
      doi          = {10.1016/j.jmps.2016.01.009},
      url          = {https://juser.fz-juelich.de/record/808658},
}