A general approximation of the exponential Cauchy–Born hypothesis to model arbitrarily shaped shell‐like nanostructures within continuum mechanics
A general approximation of the exponential Cauchy–Born hypothesis to model arbitrarily shaped shell‐like nanostructures within continuum mechanics
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DOI：
10.1002/nme.4992
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发表时间：
2016-03
影响因子：
2.9
通讯作者：
Claudio Findeisen;J. Wackerfuß
中科院分区：
文献类型：
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作者：
Claudio Findeisen;J. Wackerfuß
本文提出了一种描述任意壳状纳米结构(如石墨烯纳米结构)的连续膜理论及其有限元近似。这是通过应用多尺度方法来实现的，其中连续体膜连接到下面的原子晶格。这种联系是由柯西出生假设的指数推广实现的，因为经典的柯西出生假设仅限于三维体结构，因此不适用于壳状结构。然而，到目前为止发表的指数柯西假设的近似仅限于具有平面参考构型的结构。在本文中，我们提出了一种扩展的近似，它不要求参考构型是平面的，因此适用于任意形状的壳状纳米结构。文中详细阐述了相关的有限元实现和重要的计算问题。最后，通过几个数值算例验证了该方法及其实现的准确性。版权所有©2015 John Wiley&Sons，Ltd.
In this paper, a continuum membrane theory and its subsequent finite element approximation for the description of arbitrary shell‐like nanostructures such as graphene‐based nanostructures is presented. This is carried out by applying a multiscale approach where the continuum membrane is linked to the underlying atomistic lattice. This linkage is performed by the exponential generalization of the Cauchy–Born hypothesis, because the classical Cauchy–Born hypothesis is restricted to three‐dimensional bulk structures and is thus not applicable to shell‐like structures. However, the approximations of the exponential Cauchy–Born hypothesis published so far are limited to structures with a planar reference configuration. In this paper, we present an extended approximation, which does not require the reference configuration to be planar and is thus applicable to arbitrarily shaped shell‐like nanostructures. A detailed elaboration of the related finite element implementation with important computational aspects is presented. Finally, the accuracy of the proposed method and its implementation is verified with several numerical examples. Copyright © 2015 John Wiley & Sons, Ltd.