MechE PhD Dissertation Defense: Eric Abercrombie

TITLE: TRANSIENT ANALYSES OF VISCOELASTIC MATERIALS WITH APPLICATIONS TO NUMERICAL MODELS

ABSTRACT: Viscoelastic materials are present everywhere in everyday life from engineered materials like rubber and cork, to natural materials like bird feathers and human tissue. Consequently, analyzing the behavior of such materials is paramount not only to design, but to understand-ing the natural world. In this work, current analyses are developed, implemented, and used to discover new and significant viscoelastic material behavior, as well as advance techniques for their study. The research is presented in three parts. In the first part, the time-domain finite element approach used by commercial tools like ABAQUS and ANSYS is reformulated in a general expression of viscoelasticity that does not require a constitutive relation. An alternative interpolation scheme for the relaxation function and the results of that approach are also presented. The work highlights the potential advantage of eschewing common schemes like the General Maxwell Model. In the second part, some alternative models to commercial finite element approaches are explored. A simple model of damping in viscoelastic layers is presented to illuminate the role of viscoelasticity in acoustic absorption. A new solver type for time-domain viscoelastic finite elements is also presented. Rather than step through time in a time marching scheme, the solver expresses the solution of the equation of motion in the form of a Taylor series. This Taylor series, in combination with a Leibniz integral rule, provides a faster approach to approximating viscoelastic behavior for some problems. The third part considers non-monotonic relaxation functions. While it is generally assumed that viscoelastic relaxation functions must decay for all time, in some natural and synthetic materials they do not. Such behavior is sometimes the result of experimental measurement error and sometimes the result of real phenomena. The stability of numerical solvers is considered in the context of this unique behavior. The dynamic behavior of non-monotonic viscoelastic materials in this context are also considered and the case for use as a metamaterial is made.

COMMITTEE: ADVISOR Professor J. Gregory McDaniel, ME/MSE; CHAIR Professor Roberto Tron, ME/SE; Professor Raymond Nagem, ME; Professor Emma Lejeune, ME; Professor Katherine Yanhang Zhang, ME/BME/MSE