氨基硝基苯并二氧化呋咱结构的密度泛函理论研究

在B3LYP/6 31G 水平下用密度泛函理论(DFT)全优化了氨基硝基苯并二氧化呋咱(CL 18)的分子几何构型,进行了电子结构计算。分析了红外振动频率并以0.96加以校正,通过比较,计算值与实测值符合较好。结果表明,CL 18分子骨架为平面构型。从集居数分析发现氧化呋咱环内的NO键最弱,预示该部位易引发分解和起爆。AM1、MINDO/3、MINDO、MINDO d方法不适于CL 18生成热计算,PM3方法较适用。     

Non-periodic finite-element formulation of Kohn-Sham density functional theory

We present a real-space, non-periodic, finite-element formulation for Kohn-Sham density functional theory (KS-DFT). We transform the original variational problem into a local saddle-point problem, and show its well-posedness by proving the existence of minimizers. Further, we prove the convergence of finite-element approximations including numerical quadratures. Based on domain decomposition, we develop a parallel finite-element implementation of this formulation capable of performing both all-electron and pseudopotential calculations. We assess the accuracy of the formulation through selected test cases and demonstrate good agreement with the literature. We also evaluate the numerical performance of the implementation with regard to its scalability and convergence rates. We view this work as a step towards developing a method that can accurately study defects like vacancies, dislocations and crack tips using density functional theory (DFT) at reasonable computational cost by retaining electronic resolution where it is necessary and seamlessly coarse-graining far away.     

A combined first principles and analytical determination of the modulus of cohesion,surface energy,and the additional constants in the second strain gradient elasticity

Mindlin’s (1965) second strain gradient theory due to its competency in capturing the effects of edges, corners, and surfaces is of particular interest. Formulation in this framework, in addition to the usual Lamé constants, requires the knowledge of sixteen additional materials constants. To date, there are no successful experimental techniques for measuring these material parameters which reflect the discrete nature of matter. The present work gives an accurate remedy for the atomistic calculations of these parameters by utilizing the first principles density functional theory (DFT) for the calculations of the atomic force constants combined with an analytical formulation. It will be shown that writing the consistency conditions obtained from the equivalency between the atomistic crystal lattice dynamics of the bulk material and its counterpart in the second strain gradient elasticity is insufficient for the calculations of all the additional constants. As it will be discussed, there are two missing conditions which are then provided by consideration of the free standing film problem that bring the surface effect into account. As a consequence of surface effect consideration, the modulus of cohesion which is one of the important additional constants is calculated. Moreover, an analytical expression for the surface energy in terms of the modulus of cohesion, Lamé constants, materials characteristic lengths, and the film thickness is presented. If the film thickness is much bigger than the magnitude of the characteristic lengths of the material, then the surface energy would no longer depend on the film thickness.     

Replacing ordinary derivatives by gauge derivatives in the continuum theory of dislocations to compensate the action of the symmetry group

When the symmetry group of a body is continuous it plays a fundamental role on the nonlinear continuum theory of dislocations: it induces a non-uniqueness to the field that describes the defects – the uniform reference – and affects also other fundamental ingredients of the theory. The purpose of the present paper is to examine how certain important quantities of the dislocation theory are affected from symmetry's group action. Apart from the uniform reference we study how the deformation gradient, the first and second Piola–Kirchhoff stress tensors, the elasticities of the material and the momentum equation are affected from the action of the symmetry group. This action is inhomogeneous, namely, differs from point to point. A similar inhomogeneous action of a group may be found in gauge theories. Prompt by the gauge approach, we propose the use of the gauge covariant exterior derivative to compensate for the action of the symmetry group on the uniform reference. The main advantage of using this derivative is that the momentum equation for the static case retains its divergence form. It remains an open question how the Yang–Mills potentials may be determined for the present theory.     

A universal method to calculate the surface energy density of spherical surfaces in crystals

Surface energy plays an important role in the mechanical performance of nanomaterials;however, deter-mining the surface energy density of curved surfaces remains a challenge. In this paper, we conduct atomic simulations to calculate the surface energy density of spherical surfaces in various crystalline metals. It is found that the average sur-face energy density of spherical surfaces remains almost constant once its radius exceeds 5 nm. Then, using a geomet-rical analysis and the scaling law, we develop an analytical approach to estimate the surface energy density of spherical surfaces through that of planar surfaces. The theoretical pre-diction agrees well with the direct atomic simulations, and thus provides a simple and general method to calculate the surface energy density in crystals.     

A MICRO-MECHANICAL MODEL OF KNITTED FABRIC AND ITS APPLICATION TO THE ANALYSIS OF BUCKLING UNDER TENSION IN WALE DIRECTION： MICRO-MECHANICAL MODEL

The typical micro-knitting structure of knitted fabric, which makes it very different from woven fabric, is described. The tensile tests of knitted fabric are reported. The deformations of the micro-knitting structures are carefully studied. The study indicates that when a knitted fabric sheet is subjected to a tension along w-direction an extra compressive stress field inside loop in c-direction is induced. The extra stress field is also determined through analysis. Finally, a micro-mechanical model of knitted fabric is proposed. This work paves the way for the simulations of buckling modes of a knitted fabric sheet as are observed in experiments. The project supported by the National Natural Science Foundation of China (10272079)