TY  - JOUR
AU  - Hüter, Claas
AU  - Friák, Martin
AU  - Weikamp, Marc
AU  - Neugebauer, Jörg
AU  - Goldenfeld, Nigel
AU  - Svendsen, Bob
AU  - Spatschek, Robert
TI  - Nonlinear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene
JO  - Physical review / B
VL  - 93
IS  - 21
SN  - 2469-9950
CY  - College Park, Md.
PB  - APS
M1  - FZJ-2016-03101
SP  - 214105
PY  - 2016
AB  - 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.
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000377299100002
DO  - DOI:10.1103/PhysRevB.93.214105
UR  - https://juser.fz-juelich.de/record/810241
ER  -