Thermomechanical Constitutive Modeling of Viscoelastic Materials undergoing Degradation
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Materials like asphalt, asphalt concrete and polyimides that are used in the transportation and aerospace industry show viscoelastic behavior. These materials in the working environment are subject to degradation due to temperature, diffusion of moisture and chemical reactions (for instance, oxidation) and there is need for a good understanding of the various degradation mechanisms. This work focuses on: 1) some topics related to development of viscoelastic fluid models that can be used to predict the response of materials like asphalt, asphalt concrete, and other geomaterials, and 2) developing a framework to model degradation due to the various mechanisms (such as temperature, diffusion of moisture and oxidation) on polyimides that show nonlinear viscoelastic solid-like response. Such a framework can be extended to model similar degradation phenomena in the area of asphalt mechanics and biomechanics. The thermodynamic framework that is used in this work is based on the notion that the 'natural configuration' of a body evolves as the body undergoes a process and the evolution is determined by maximizing the rate of entropy production. The Burgers' fluid model is known to predict the non-linear viscoelastic fluid-like response of asphalt, asphalt concrete and other geomaterials. We first show that different choices for the manner in which the body stores energy and dissipates energy and satisfies the requirement of maximization of the rate of entropy production that leads to many three dimensional models. All of these models, in one dimension, reduce to the model proposed by Burgers. A thermodynamic framework to develop rate-type models for viscoelastic fluids which do not possess instantaneous elasticity (certain types of asphalt show such a behavior) is developed next. To illustrate the capabilities of such models we make a specific choice for the specific Helmholtz potential and the rate of dissipation and consider the creep and stress relaxation response associated with the model. We then study the effect of degradation and healing due to the diffusion of a fluid on the response of a solid which prior to the diffusion can be described by the generalized neo-Hookean model. We show that a generalized neo-Hookean solid - which behaves like an elastic body (i.e., it does not produce entropy) within a purely mechanical context - creeps and stress relaxes when infused with a fluid and behaves like a body whose material properties are time dependent. A framework is then developed to predict the viscoelastic response of polyimide resins under different temperature conditions. The developed framework is further extended to model the phenomena of swelling due to diffusion of a fluid through a viscoelastic solid using the theory of mixtures. Finally, degradation due to oxidation is incorporated into such a framework by introducing a variable that represents the extent of oxidation. The data from the resulting models are shown to be in good agreement with the experiments for polyimide resins.
Karra, Satish (2011). Thermomechanical Constitutive Modeling of Viscoelastic Materials undergoing Degradation. Doctoral dissertation, Texas A&M University. Available electronically from