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@ARTICLE{Hter:810241,
      author       = {Hüter, Claas and Friák, Martin and Weikamp, Marc and
                      Neugebauer, Jörg and Goldenfeld, Nigel and Svendsen, Bob
                      and Spatschek, Robert},
      title        = {{N}onlinear elastic effects in phase field crystal and
                      amplitude equations: {C}omparison to ab initio simulations
                      of bcc metals and graphene},
      journal      = {Physical review / B},
      volume       = {93},
      number       = {21},
      issn         = {2469-9950},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {FZJ-2016-03101},
      pages        = {214105},
      year         = {2016},
      abstract     = {We investigate nonlinear elastic deformations in the phase
                      field crystal model and derived amplitude equation
                      formulations. Two sources of nonlinearity are found, one of
                      them is based on geometric nonlinearity expressed through a
                      finite strain tensor. This strain tensor is based on the
                      inverse right Cauchy-Green deformation tensor and correctly
                      describes the strain dependence of the stiffness for
                      anisotropic and isotropic behavior. In isotropic one- and
                      two-dimensional situations, the elastic energy can be
                      expressed equivalently through the left deformation tensor.
                      The predicted isotropic low-temperature nonlinear elastic
                      effects are directly related to the Birch-Murnaghan equation
                      of state with bulk modulus derivative K′=4 for bcc. A
                      two-dimensional generalization suggests K′2D=5. These
                      predictions are in agreement with ab initio results for
                      large strain bulk deformations of various bcc elements and
                      graphene. Physical nonlinearity arises if the strain
                      dependence of the density wave amplitudes is taken into
                      account and leads to elastic weakening. For anisotropic
                      deformation, the magnitudes of the amplitudes depend on
                      their relative orientation to the applied strain.},
      cin          = {IEK-2},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IEK-2-20101013},
      pnm          = {111 - Efficient and Flexible Power Plants (POF3-111)},
      pid          = {G:(DE-HGF)POF3-111},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000377299100002},
      doi          = {10.1103/PhysRevB.93.214105},
      url          = {https://juser.fz-juelich.de/record/810241},
}