Mathematical and Experimental Approaches to Structural Characterization and Mechanical Properties of Polymeric Solids

Abstract

Various novel mathematical approaches to analyze the tensile properties and molecular structure in polymeric solids are introduced. The failure behavior such as yielding and necking is treated as a phase modification resulting from an elemental catastrophe phenomenon. The ductile fracture behavior under tension is characterized by a stochastic Ito-process where the probability density functions of fracture time, strength, and toughness followed Gaussian statistics. In addition, a grath-theoretical approach is applied to give the radius of gyration and dynamics of polymer molecules which is a key parameter in morphology formation being directly related to mechanical failure and fracture.