An approach of stochastically statistical mechanics and a unified molecular theory of nonlinear viscoelasticity with constraints of Nagai chain entanglement for polymer melts have been proposed. A multimode model stru...An approach of stochastically statistical mechanics and a unified molecular theory of nonlinear viscoelasticity with constraints of Nagai chain entanglement for polymer melts have been proposed. A multimode model structure for a single polymer chain with n tail segments and N reversible entanglement sites on the test polymer chain is developed. Based on the above model structure and the mechanism of molecular flow by the dynamical reorganization of entanglement sites, the probability distribution function of the end-to-end vectr for a single polymer chain at entangled state and the viscoelastic free energy of deformation for polymer melts are calculated by using the method of the stochastically statistical mechanics. The four types of stress-strain relation and the memory function are derived from this thery. The above theoretical relations are verified by the experimentaf data for various polymer melts. These relations are found to be in good agreement with the experimental results展开更多
1 Introduction Potassium is listed as one of the shortage of mineral resources in china.Geophysical and remote sensing technology plays an important role in prospecting for potash ressources.
It is shown theoretically that the viscoelasticity of polymer melts is determined by three combining factorst they are the primary molecular weight and its distribution, the number of entanglement sites on polymer cha...It is shown theoretically that the viscoelasticity of polymer melts is determined by three combining factorst they are the primary molecular weight and its distribution, the number of entanglement sites on polymer chain and the sequence distribution of constituent chains in entanglement spacings. A unified quantity for the three combing factors is the average constrained dimensional number of constituent chains in the long entanglement spacings (v). A new relation of v to the primary molecular weight and the number of testing polymers were derived from the multiple entanglement and reptation model, and a new method for determining v was proposed. The dependences of linear viscoelastic functions on the primary molecular weight and its distribution were derived by the statistical method. When Mn=6Me to 18 Me, the values of (v) can range from 3.33 to 3.70. Their values are in a good agreement with the experiment data, and it can slightjy vary with the different species of polymers and the different ranges of molecular weight of polymers展开更多
Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ...Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.展开更多
文摘An approach of stochastically statistical mechanics and a unified molecular theory of nonlinear viscoelasticity with constraints of Nagai chain entanglement for polymer melts have been proposed. A multimode model structure for a single polymer chain with n tail segments and N reversible entanglement sites on the test polymer chain is developed. Based on the above model structure and the mechanism of molecular flow by the dynamical reorganization of entanglement sites, the probability distribution function of the end-to-end vectr for a single polymer chain at entangled state and the viscoelastic free energy of deformation for polymer melts are calculated by using the method of the stochastically statistical mechanics. The four types of stress-strain relation and the memory function are derived from this thery. The above theoretical relations are verified by the experimentaf data for various polymer melts. These relations are found to be in good agreement with the experimental results
基金financially supported by projects of 2006AA06A208, 2013AA0639, 1212011120188 and 12120113099000
文摘1 Introduction Potassium is listed as one of the shortage of mineral resources in china.Geophysical and remote sensing technology plays an important role in prospecting for potash ressources.
文摘It is shown theoretically that the viscoelasticity of polymer melts is determined by three combining factorst they are the primary molecular weight and its distribution, the number of entanglement sites on polymer chain and the sequence distribution of constituent chains in entanglement spacings. A unified quantity for the three combing factors is the average constrained dimensional number of constituent chains in the long entanglement spacings (v). A new relation of v to the primary molecular weight and the number of testing polymers were derived from the multiple entanglement and reptation model, and a new method for determining v was proposed. The dependences of linear viscoelastic functions on the primary molecular weight and its distribution were derived by the statistical method. When Mn=6Me to 18 Me, the values of (v) can range from 3.33 to 3.70. Their values are in a good agreement with the experiment data, and it can slightjy vary with the different species of polymers and the different ranges of molecular weight of polymers
文摘Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.
