Thermoelasticity with Finite Wave Speeds

Józef Ignaczak · Martin Ostoja-Starzewski

Sep 2009 · OUP Oxford

About this ebook

Generalized dynamic thermoelasticity is a vital area of research in continuum mechanics, free of the classical paradox of infinite propagation speeds of thermal signals in Fourier-type heat conduction. Besides that paradox, the classical dynamic thermoelasticity theory offers either unsatisfactory or poor descriptions of a solid's response at low temperatures or to a fast transient loading (say, due to short laser pulses). Several models have been developed and intensively studied over the past four decades, yet this book, which aims to provide a point of reference in the field, is the first monograph on the subject since the 1970s. Thermoelasticity with Finite Wave Speeds focuses on dynamic thermoelasticity governed by hyperbolic equations, and, in particular, on the two leading theories: that of Lord-Shulman (with one relaxation time), and that of Green-Lindsay (with two relaxation times). While the resulting field equations are linear partial differential ones, the complexity of the theories is due to the coupling of mechanical with thermal fields. The mathematical aspects of both theories - existence and uniqueness theorems, domain of influence theorems, convolutional variational principles - as well as the methods for various initial/boundary value problems are explained and illustrated in detail and several applications of generalized thermoelasticity are reviewed.

About the author

Józef Ignaczak has been at the Polish Academy of Sciences since 1957. He was also a research associate at Brown University in USA from 1961 to 1962; a senior lecturer at Monash University in Australia from 1965 to 1969; and held several other visiting posts. Before retiring from the Polish Academy of Sciences in 2005 he was also a member of the American Mathematical Society, the Planetary Society, the Acoustical Society of America, the New York Academy of Sciences, and a consulting editor of the Contemporary Who's Who (American Biographical Institute). The major part of his scientific effort has been directed to the development of linear elastodynamics and dynamic coupled classical and non-classical thermoelasticity. This work includes 2 books and over 100 research papers published between 1957 and 2007. In honor of his outstanding work and achievements in his field he has received many awards. Martin Ostoja-Starzewski obtained his undergraduate education at the Cracow University of Technology (Poland), followed by a Master's Thesis (1980) and a Ph.D. (Dean's Honour List, 1983) at McGill University, all in mechanical engineering. Following academic posts at Purdue University, Michigan State University, Institute of Paper Science and Technology, and McGill University (where he held a Canada Research Chair in Mechanics of Materials), from 2006 he has been Professor of Mechanical Science & Engineering at the University of Illinois at Urbana-Champaign. He has published over 100 journals papers in applied/theoretical mechanics, materials science, applied mathematics/physics and geophysics, as well as over 80 conference proceedings papers and two book chapters. His research is in stochastic mechanics; thermomechanics of generalized continua; wave propagation; random and fractal media; biomechanics of head trauma.