Constitutive Theories for Polymers Using Non-Classical Continuum Mechanics

Abstract

This thesis is on the development of a few constitutive theories characterising the thermo-mechanical response of polymers. In proposing the theories, some aspects of non-classical continuum mechanics are used. The first few constitutive theories predict the extrinsic and intrinsic mechanical behaviour of different types of polymers across a wide range of ambient temperature, loading rate, and/or solvent concentration. Varied response features characterised by strikingly contrasted timescales are observed as the conditions are altered. For example, for thermoplastics, hyperelastic response is observed for high temperatures or low loading rates. In contrast, the response is nearly viscoplastic at low temperatures or high loading rates. For a unified, seamless modelling approach to transitions across the timescale separated behavioural characteristics, a thermodynamic framework based on effective temperature is used. Separate theories have been constituted for thermoplastics, block-copolymers, and hydrogels, all within this thermodynamic setup. Here a thermodynamic system is split into configurational and kinetic-vibrational subsystems, which are weakly coupled by heat exchange. The configurational subsystems are characterized by states that evolve over larger time scales than the kinetic vibrational subsystem, which evolves with a time scale of atomic vibrations. One or more configurational subsystems are defined for describing submacroscopic phenomena involving multiple time scales or different relaxation rates. Depending on the relaxation processes, the configurational subsystems are chosen. While for thermorheologically simple thermoplastics, a single configurational subsystem is sufficient to capture relaxation, multiple configurational subsystems are necessary for thermorheologically complex polymers such as thermoplastic elastomers, especially to capture such complex phenomena as Mullin's effect. The rate of heat exchange between the configurational and kinetic vibrational subsystems is governed by the structural relaxation time. In the case of thermoplastics and block copolymers that do not contain a solvent, the structural relaxation time may be a function of the ambient temperature. However, for hydrogels, the relaxation time requires to be a function of the solvent concentration as well. All the three constitutive models are validated against experimental observations reported in the literature. They successfully capture the salient features of mechanical response across temperature or rate or solvent phase transition. Besides, the model for block-copolymers is shown to have features that enable it to be used as an effective design tool for the composition, given the requirement of an effective glass transition temperature. In addition to the viscoelastic theories, a brittle damage model for compressible elastomers is also developed. This theory is grounded in non-Euclidean geometry wherein the kinematic variables are derived considering the assumption that, upon damage, the material body no longer remains Euclidean but assumes the structure of a Riemannian manifold. Also, the energy of surface creation due to cracks is assumed to be a function of the Ricci curvature. The theory is used in several numerical simulations. The observations from some of these simulations are used to highlight the superior features of the geometry-driven approach vis-\'a-vis a second-order phase field theory involving a quadratic degradation function.