An extended finite element/level set method to study surface effects on the mechanical behavior and properties of nanomaterials
An extended finite element/level set method to study surface effects on the mechanical behavior and properties of nanomaterials
复制标题
DOI：
10.1002/nme.2946
复制
发表时间：
2010-12-17
影响因子：
2.9
通讯作者：
Park, Harold S.
中科院分区：
文献类型：
--
作者：
Farsad, Mehdi;Vernerey, Franck J.;Park, Harold S.
本文提出了一种基于扩展有限元法（XFEM）和水平集耦合的方法来研究表面和界面效应对纳米结构力学行为的影响。耦合XFEM水平集方法使连续解决方案的纳米力学边界值问题，其中不连续的应变和位移，由于表面和界面很容易处理，同时占关键的纳米级表面效应，包括表面能，应力，弹性和界面脱粘。我们通过研究均匀和双层纳米板的表面应力驱动松弛以及表面弹性对纳米梁有效刚度的贡献来验证所提出的方法。对于每一种情况下，我们比较的数值结果与新的解析解，我们已经推导出这些简单的问题;对于涉及表面应力驱动的松弛均匀的纳米片的问题，我们进一步验证了所提出的方法，通过比较的结果与完全原子模拟和以前的多尺度计算的基础上的表面柯西-玻恩模型。这些数值结果表明，所提出的方法可以用来获得关键的见解，表面效应如何影响的力学行为和性能的均匀和复合纳米梁广义机械变形。版权所有（C）2010约翰威利父子有限公司
We present a new approach based on coupling the extended finite element method (XFEM) and level sets to study surface and interface effects on the mechanical behavior of nanostructures. The coupled XFEM-level set approach enables a continuum solution to nanomechanical boundary value problems in which discontinuities in both strain and displacement due to surfaces and interfaces are easily handled, while simultaneously accounting for critical nanoscale surface effects, including surface energy, stress, elasticity and interface decohesion. We validate the proposed approach by studying the surface-stress-driven relaxation of homogeneous and bi-layer nanoplates as well as the contribution from the surface elasticity to the effective stiffness of nanobeams. For each case, we compare the numerical results with new analytical solutions that we have derived for these simple problems; for the problem involving the surface-stress-driven relaxation of a homogeneous nanoplate, we further validate the proposed approach by comparing the results with those obtained from both fully atomistic simulations and previous multiscale calculations based upon the surface Cauchy-Born model. These numerical results show that the proposed method can be used to gain critical insights into how surface effects impact the mechanical behavior and properties of homogeneous and composite nanobeams under generalized mechanical deformation. Copyright (C) 2010 John Wiley & Sons, Ltd.