Prediction of relaxation behavior of polymeric materials from molecular architecture attracts industrial interests and scientific challenges. In this study a coarse-grained molecular model called primitive chain network model is developed. The model is capable for quantitative prediction of linear and non-linear viscoelasticity of entangled polymers. Also it is indicated that the simulation for cross-linked network is fair, though quantitative test is demanded.
A brief review of constitutive equations based on the molecular chain network theory for elastic deformation behavior and the reptation theory for viscoelastic deformation behavior of rubbers were presented. The typical strain-rate-dependent deformation behaviors under monotonic and cyclic straining with different strain rates were reproduced and they corresponded well to the experimentally obtained results, particularly softening and hysteresis loss, that is, the Mullins effect, occurring in stress-stretch curves under cyclic deformation processes. The deformation behaviors of carbon-black (CB) filled rubber under monotonic and cyclic straining are modeled by using the proposed constitutive equation and 3D homogenization method. The results reveal the mechanism in substantial enhancement of the resistance of CB-filled rubber to macroscopic deformation, hysteresis loss, and the effects of the distribution morphology and the volume fraction of CB on the deformation behavior.
Recently the physical properties of the surface and the interface of polymeric materials are analyzed by several experimental methods in a few nanometer scales. On the other hand, the analysis is also needed from the point of view of polymer chain. Our group studied the phenomena of polymer materials in the point of view of polymer chain dynamics using the coarse-grained molecular dynamics simulation. In this review, we show two topics listed below; the local glass transition temperature at the surface and interface, and the polymer chain dynamics at the friction force microscopy using atomic force microscopy. In the first topics, we studied the local dynamics of polymer chains. The surface and interfacial glass transition temperatures which are also estimated by the experiments are measured by the mean square displacement analysis. In the second topics, we study the model simulation of the friction force to the polymer surface by probe tip in atomic force microscopy. In the series of simulation, we can observe the chain withdrawing and it is one of the important origin of the friction.
Many rubber-like materials consist of a cross-linked elastomeric substance with a dispersed small carbon particles as fillers. A piece of filler loaded rubber subjected to a series of loadings typically displays pronounced stress softening associated with damage. This stress softening phenomenon is referred to as the Mullins effect. The effects of strain history on the stresses and the formulation of constitutive models for filled and unfilled elastomers have been a particular focus of attention during the last few years. In this general remark, some representative damage functions are explicated through general purpose FEM programs. Furthermore, the anisotropic Mullins effect is indicated by biaxial experimental cyclic test. The numerical model of anisotropic Mullins effect, eventually, is expounded, and its numerical analysis is illustrated by using user-subroutine on Marc.