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

本研究旨在通过经典的连续介质力学和表面应力对应力奇异区的影响揭示纳米力学的适用范围，重点研究三维节理中纳米区域的应力奇异场。采用数字图像相关方法，可以得到硅树脂结合部应力奇异场的应变分布。数据通过数码显微镜获得。应变奇异场的奇异顺序与三维节理的特征分析结果一致。本文采用分子动力学方法研究了受外力作用下纳米级关节的奇异应力场。即使在纳米尺度上，原子应力场也存在奇异性。利用具有表面/界面力学性能的边界条件，推导了确定应力奇异阶数的特征方程。从MD分析的结果来看，界面力学性能是与界面边缘距离的函数。然后，随着界面边缘的逼近，应力奇点的阶数逐渐增大。由特征方程得到的应力奇异度阶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上的有效性和实用性，并且结果扩展了连续介质力学的适用性。各向异性-各向异性材料的Green函数和各向同性-各向异性材料的Green函数是在Stroh的形式化基础上新导出的，并纳入了边界元程序。此外，还证明了各向异性-各向异性材料的解可以由各向异性-各向异性材料的解推导出来。

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.