Mechanical & Materials Engineering, Department of


Date of this Version

Summer 8-7-2013


A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mechanical Engineering and Applied Mechanics, Under the Supervision of Professor Mehrdad Negahban. Lincoln, Nebraska: August, 2013

Copyright (c) 2013 Lili Zhang


This work studies the propagation of thermo-mechanical disturbances in bodies made of viscoelastic materials that might already be loaded such that they are undergoing large inhomogeneous time varying deformations. In the process of this study we develop the general equations governing the thermo-mechanical motion of such disturbances and ones for internally constrained systems, provide the general structure of the solution, match the solution to existing results for the special case of time harmonic plane waves in elastic bodies and in viscoelastic bodies under constant homogenous loading, and consider some special applications.

The results of this work should have applications in the study of anisotropic and inhomogeneous bodies that are inhomogenously loaded with the possibility that these loads are time varying, and may become part of tools used for non-invasive and non-destructive testing of such bodies. Many common materials are anisotropic and inhomogeneous. These include most polymers, composites, soft and hard tissues, and all kinds of bio-mass. Many bodies are undergoing static or time varying inhomogeneous loading. Examples can vary from conditions that result in or from earthquakes and landslides to composites and live tissues functioning in loaded structures and bio-MEMS.

Some of the contributions of this dissertation are to introduce a full, thermodynamically consistent, nonlinear viscoelastic model to represent the material, to properly introduce thermo-mechanical coupling, to remove current limitations on the pre-deformation to be static, homogenous and around the equilibrium, to remove existing restrictions on the rate of loading of the perturbations, and to consider perturbations in the presence of material constraints.

Adviser: Mehrdad Negahban