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NEW ADVANCEMENT OF NANOMECHANICS-EXISTENCE OF LOWER LIMIT OF APPLICATION OF CLASSIC CONTINUUM MECHANICS IN NANOREGION-

纳米力学新进展-经典连续体力学在纳米区域应用下限的存在-

基本信息

批准号：
21360051
负责人：
KOGUCHI Hideo
金额：
$ 10.98万
依托单位：
Nagaoka University of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2009
资助国家：
日本
起止时间：
2009 至 2011
项目状态：
已结题

项目摘要

The present study is to reveal the applicable range of nanomechanics through the classic continuum mechanics and the effect of surface stress on stress singular region in focusing on the stress singular field at a nano region in a three-dimensional joint.1. Strain distribution in the stress singular field of the joint composing of Silicon and resin could be obtained by means of a digital image correlation method. Data were obtained through a digital microscope. The order of singularity of strain singular fields was agreed with the value obtained by eigenanalysis of 3D joint.2. In the present study, singular stress fields in a nanoscaled joint under an external force were investigated using molecular dynamic(MD) method. The atomic stress fields had a singularity even if the size of joint was in nanoscale. Characteristic equation for determining the order of stress singularity was derived using a boundary condition with surface/interface mechanical properties. From the result of the MD analysis, interface mechanical properties were a function of the distance from the edge of interface. Then, the order of stress singularity increased with approaching to the edge of interface. The atomic stress distribution near the edge of interface could be well expressed using the order of stress singularity obtained from the characteristic equation. This indicates the validity and usefulness of nanomechanics at the objective of this project and the results which extend the applicability of continuum mechanics.3. Green's functions for anisotropic-anisotropic materials and isotropic-anisotropic materials were newly derived on the basis of Stroh's formalism and incorporated into the boundary element program. Furthermore, it was shown that the solutions for isotropic-anisotropic materials could be smoothly derived from those for anisotropic-anisotropic materials.

本研究旨在通过经典的连续介质力学来揭示纳米力学的适用范围，以及三维节点纳米区域应力奇异场时表面应力对应力奇异区的影响。利用数字图像相关方法，可以得到硅树脂接头应力奇异场中的应变分布。数据通过数字显微镜获得。应变奇异场的奇异性级数与三维节点特征分析得到的值基本一致。本文用分子动力学方法研究了纳米尺度关节在外力作用下的奇异应力场。即使节理尺寸为纳米级，原子应力场也具有奇异性。利用具有表面/界面力学性质的边界条件，推导了确定应力奇异性阶数的特征方程。从MD分析的结果来看，界面力学性能是离界面边缘的距离的函数。然后，应力奇异性的阶数随着接近界面边缘而增大。由特征方程得到的应力奇异性级数可以很好地表示界面边缘附近的原子应力分布。这表明纳米力学在本项目目标下的有效性和有用性，以及扩展连续介质力学适用性的结果。在Stroh公式的基础上，新推导了各向异性-各向异性材料和各向同性-各向异性材料的格林函数，并将其纳入边界元程序。结果表明，各向同性-各向异性材料的解与各向异性-各向异性材料的解是一致的。