Only two macroscopic parameters are needed to describe the mechanical properties of linear elastic solids, i.e. the Poisson＇s ratio and Young＇s modulus. Correspondingly, there should be two microscopic parameters to...Only two macroscopic parameters are needed to describe the mechanical properties of linear elastic solids, i.e. the Poisson＇s ratio and Young＇s modulus. Correspondingly, there should be two microscopic parameters to determine the mechanical properties of material if the macroscopic mechanical properties of linear elastic solids are derived from the microscopic level. Enlightened by this idea, a multiscale mechanical model for material, the virtual multi-dimensional internal bonds （VMIB） model, is proposed by incorporating a shear bond into the virtual internal bond （VIB） model. By this modification, the VMIB model associates the macro mechanical properties of material with the microscopic mechanical properties of discrete structure and the corresponding relationship between micro and macro parameters is derived. The tensor quality of the energy density function, which contains coordinate vector, is mathematically proved. From the point of view of VMIB, the macroscopic nonlinear behaviors of material could be attributed to the evolution of virtual bond distribution density induced by the imposed deformation. With this theoretical hypothesis, as an application example, a uniaxial compressive failure of brittle material is simulated. Good agreement between the experimental results and the simulated ones is found.展开更多
The structures of complexes [MⅡ2Cl4L2] and [MⅢ2Cl7L]- （M = Mo, Re; L = Ph2Ppy, （Ph2P）2py） were calculated by using density functional theory （DFT） PBE0 method. Based on the optimized geometries, the natural bo...The structures of complexes [MⅡ2Cl4L2] and [MⅢ2Cl7L]- （M = Mo, Re; L = Ph2Ppy, （Ph2P）2py） were calculated by using density functional theory （DFT） PBE0 method. Based on the optimized geometries, the natural bond orbital （NBO） analyses were carried out to study the nature of Re-Re and Mo-Mo bonds. The conclusions are as follows： the M-M distances in two-Ph2Ppy or （Ph2P）2py complexes [MⅡ2Cl4L2] are shorter than those in mono-Ph2Ppy or （Ph2P）2py complexes [MⅢ2Cl7L]- due to the double bridged N-C-P interactions. For singlet of all complexes, there is ReⅢ-ReⅢ or MoⅡ-MoⅡ quadruply bond in complex [Re2Cl7L]- or [Mo2Cl4L2], while only ReⅡ-ReⅡ or MoⅢ-MoⅢ triply bond in complex [Re2Cl4L2] or [Mo2Cl7L]-. The most stable spin state of 2 and 6, triplet, only contains triple ReⅢ-ReⅢ bond. Because the LPCl → BD＊Re-Re delocalizations weaken the Re-Re bond, the distance of ReⅢ-ReⅢ quadruple bonds in [Re2Cl7L]- is slightly longer than that of ReⅡ-ReⅡ triple bonds in [Re2Cl4L2]. Moreover, due to the delocalizations from the lone pair electrons of the remaining P’ atom to the M-M antibonding orbitals, the M-M distance in （Ph2P）2py complexes is slightly longer than that in Ph2Ppy complexes.展开更多
基金Project supported by the National Basic Research Program of China (973 Project) (No. 2002CB412704).
文摘Only two macroscopic parameters are needed to describe the mechanical properties of linear elastic solids, i.e. the Poisson＇s ratio and Young＇s modulus. Correspondingly, there should be two microscopic parameters to determine the mechanical properties of material if the macroscopic mechanical properties of linear elastic solids are derived from the microscopic level. Enlightened by this idea, a multiscale mechanical model for material, the virtual multi-dimensional internal bonds （VMIB） model, is proposed by incorporating a shear bond into the virtual internal bond （VIB） model. By this modification, the VMIB model associates the macro mechanical properties of material with the microscopic mechanical properties of discrete structure and the corresponding relationship between micro and macro parameters is derived. The tensor quality of the energy density function, which contains coordinate vector, is mathematically proved. From the point of view of VMIB, the macroscopic nonlinear behaviors of material could be attributed to the evolution of virtual bond distribution density induced by the imposed deformation. With this theoretical hypothesis, as an application example, a uniaxial compressive failure of brittle material is simulated. Good agreement between the experimental results and the simulated ones is found.
基金the Natural Science Foundation of Guangdong Province (9151063101000037)Ministry of Education and Guangdong Province (2010B090400184)+2 种基金Program of Talent Introduction of Guangdong Province (C10133)Science and Technology Program of Guangzhou City (2011J4300063)Science and Technology Program of Guangdong Province (2010B060900007)
文摘The structures of complexes [MⅡ2Cl4L2] and [MⅢ2Cl7L]- （M = Mo, Re; L = Ph2Ppy, （Ph2P）2py） were calculated by using density functional theory （DFT） PBE0 method. Based on the optimized geometries, the natural bond orbital （NBO） analyses were carried out to study the nature of Re-Re and Mo-Mo bonds. The conclusions are as follows： the M-M distances in two-Ph2Ppy or （Ph2P）2py complexes [MⅡ2Cl4L2] are shorter than those in mono-Ph2Ppy or （Ph2P）2py complexes [MⅢ2Cl7L]- due to the double bridged N-C-P interactions. For singlet of all complexes, there is ReⅢ-ReⅢ or MoⅡ-MoⅡ quadruply bond in complex [Re2Cl7L]- or [Mo2Cl4L2], while only ReⅡ-ReⅡ or MoⅢ-MoⅢ triply bond in complex [Re2Cl4L2] or [Mo2Cl7L]-. The most stable spin state of 2 and 6, triplet, only contains triple ReⅢ-ReⅢ bond. Because the LPCl → BD＊Re-Re delocalizations weaken the Re-Re bond, the distance of ReⅢ-ReⅢ quadruple bonds in [Re2Cl7L]- is slightly longer than that of ReⅡ-ReⅡ triple bonds in [Re2Cl4L2]. Moreover, due to the delocalizations from the lone pair electrons of the remaining P’ atom to the M-M antibonding orbitals, the M-M distance in （Ph2P）2py complexes is slightly longer than that in Ph2Ppy complexes.
