Research Objectives and Approaches The principal objective of this project is to develop a continuum thermoelasticity of materials with anomalous (non-Fourier type) heat conduction from the standpoint of fractal material structures. This will substantially broaden the scope of materials whose mechanics can be handled by partial differential equations. While the conventional mate¬rials in most continuum theories are assumed to be smooth and to satisfy the postulate of separation of scales, the planned research, being focused on fractal materials, will drop that requirement. New forms of differential equations will be derived and employed in solution of the initial-boundary value problems, and new fundamental understanding of constitutive responses (thermo-elasticity and thermo-viscoelasticity) of various materials having fractal geometries will be developed.
Societal Benefits This project will have impact on the applicability of continuum mechanics (and physics) to studies of material response. The highly complex media which have so far been the domain of condensed matter physics, geophysics and biophysics etc. (polymer clusters, gels, rock systems, percolating networks, nervous systems, pulmonary systems...) will become open to studies conventionally reserved for smooth materials. This will allow the set-up and solution of initial-boundary value problems of very complex/multiscale materials of both elastic and inelastic type. Two graduate students will be involved in this research. The proposed research goes hand-in-hand with the writing of a monograph Thermoelasticity with Finite Wave Speeds (for Oxford Mathematical Monographs) on thermoelastodynamics of materials with anoma¬lous heat conduction.
