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arXiv 1602.02537cond-mat.mtrl-sci
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相场晶体和振幅方程中的非线性弹性效应:与bcc金属和石墨烯的从头计算模拟的比较

Non-linear elastic effects in phase field crystal and amplitude equations: Comparison to ab initio simulations of bcc metals and graphene

C. Hüter, M. Friák, M. Weikamp, J. Neugebauer, N. Goldenfeld, B. Svendsen, R. Spatschek

摘要:

我们研究了相位场晶体模型中的非线性弹性形变,并推导了振幅方程。两个来源的非线性被发现,其中之一是基于几何非线性表示通过有限应变张量。它反映了连续体模型的欧拉结构,并正确地描述了刚度的应变依赖性。通常,相关应变张量与左柯西-格林变形张量有关。在各向同性的一维和二维情况下,弹性能可以通过正确的变形张量等效地表示。预测的各向同性低温非线性弹性效应与体心立方的体积模量导数$K'=4$的Birch-Murnaghan状态方程直接相关。二维的推广建议使用$K'_{2D}=5$。这些预测是在协议与各种体心立方元素和石墨烯的大应变体变形的从头计算结果。如果考虑密度波振幅的应变依赖性,则会出现物理非线性,并导致弹性弱化。对于各向异性变形,振幅的大小取决于它们与所施加应变的相对取向。

英文摘要:

We investigate non-linear elastic deformations in the phase field crystal model and derived amplitude equations formulations. Two sources of non-linearity are found, one of them based on geometric non-linearity expressed through a finite strain tensor. It reflects the Eulerian structure of the continuum models and correctly describes the strain dependence of the stiffness. In general, the relevant strain tensor is related to the left Cauchy-Green deformation tensor. In isotropic one- and two-dimensional situations the elastic energy can be expressed equivalently through the right deformation tensor. The predicted isotropic low temperature non-linear 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 non-linearity arises if the strain dependence of the density wave amplitudes is taken into account and leads to elastic weakening. For anisotropic deformations the magnitudes of the amplitudes depend on their relative orientation to the applied strain.

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