Numerical Study On The Size-dependent Elastic Properties Of Nanocomposites

With the advancement of science and technology and the rising level of understanding of the mankind, the study of materials has moved forward from the macroscopic and mesoscopic levels to the microscopic level. In recent years, the study of nanoscale materials has become a hot topic. In nanoscale materials, as the ratio of the number of surface atoms to the number of total atoms increases sharply, nanoscale materials show enhanced mechanical properties such as material strength, stiffness and toughness, and their mechanical properties show strong size-dependences. In order to investigate these size-dependences, the elastic equilibrium of nanoscale structures is handled with the framework of the classical continuum mechanics by incorporating the surface strain energy to the total strain energy of a nanostructure.In this thesis, the general finite element code ANSYS is used to model nanoscale structures with surface effects. An user subroutine Usermat.F included in ANSYS's User Programmable Features (UPFS) has been developed to implement the Gurtin-Murdoch surface constitutive equation. After compiling and linking of the user subroutine, a nonstandard executable program Ansys.exe is obtained. Thereafter, the equilibrium of a nanoscale elastic structure can be analyzed with the ANSYS code. In the present analysis, the truss element is used to evaluate the contribution of surface stress to the total strain energy of the system in the two-dimensional case, and the membrane element is used to calculate the contribution of surface stress to the total strain energy of the system in the three-dimensional case.The stress concentration around a nanoscale circular hole is investigated first. In the absence of surface stress, the stress concentration factor is independent of the radius of a hole. This is in agreement with the classical elasticity solution. With the consideration of surface effects, the stress concentration around a hole shows strong size-dependence. When the radius of a circular hole is less that 10 nm, the effect of surface stress on stress concentration is significant. However, when the hole radius reaches 25 nm, the effect of surface stress on stress concentration factor is negligible, and tends to the classical elasticity solution.In order to analyze the size-dependent effective elastic moduli of nano-porous materials, a two-dimensional plane with periodically distributed circular holes is modeled. A direct homogenization approach is used to obtain the effective bulk and shear moduli of the two-dimensional nanoporous material. It has been shown that both the bulk and the shear moduli change with the radius of the circular hole in the material. The effective moduli of a three-dimensional material with periodically distributed spherical pores has also been obtained via the direct homogenization approach. The effective moduli are closely related to the pore size, the volume ratio of pore, elastic constants of the matrix and also the elastic constants of the pore surface. They are highly size-dependent especially when the pore size is very small. The present study can serve as a guide for the design of nano-porous materials and nano composites.