A Derivation of Continuum Nonlinear Plate Theory from Atomistic Models
A Derivation of Continuum Nonlinear Plate Theory from Atomistic Models
复制标题
从原子模型推导连续非线性板理论
DOI：
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发表时间：
2006
影响因子：
1.6
通讯作者：
B. Schmidt
中科院分区：
文献类型：
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作者：
B. Schmidt
我们本着[G.]的精神，从原子模型推导出板块理论。R. D. James和S. Muller, Comm. Pure apple。数学。， 55 (2002), pp. 1461-1506]作为Γ‐限制，因为原子的数量趋于无穷大。而在“厚膜制度”中，即当薄膜由许多层原子组成时，我们恢复了由[G]中的三维弹性导出的众所周知的板理论。R. D. James和S. Muller, Comm. Pure apple。数学。， 55 (2002), pp. 1461-1506]；对于“薄膜”，得到了极限泛函中的新项。这些术语是由于原子模型和表面效应的离散性，不能从连续弹性中检测到。
We derive plate theory from atomistic models in the spirit of [G. Friesecke, R. D. James, and S. Muller, Comm. Pure Appl. Math., 55 (2002), pp. 1461–1506] as a Γ‐limit as the number of atoms tends to infinity. While in the “thick film regime,” i.e., when the film consists of many layers of atoms, we recover the well‐known plate theory derived from three‐dimensional elasticity in [G. Friesecke, R. D. James, and S. Muller, Comm. Pure Appl. Math., 55 (2002), pp. 1461–1506]; for “thin films” new terms in the limit functional are obtained. These terms are due to the discrete nature of atomic models and surface effects and cannot be detected from continuum elasticity.