Józef Ignaczak, Martin Ostoja-Starzewski
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199541645
- eISBN:
- 9780191716164
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199541645.001.0001
- Subject:
- Mathematics, Applied Mathematics, Mathematical Physics
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 ...
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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 to a fast transient loading (say, due to short laser pulses) or at low temperatures. Several models were developed and intensively studied over the past four decades, and this book is the first monograph on the subject since the 1970s, aiming to provide a point of reference in the field. It 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 theories is due to the coupling of mechanical with thermal fields. The book is concerned with the mathematical aspects of both theories — existence and uniqueness theorems, domain of influence theorems, convolutional variational principles — as well as with the methods for various initial/boundary value problems. In the latter respect, following the establishment of the central equation of thermoelasticity with finite wave speeds, there are extensive presentations of: the exact, aperiodic‐in‐time solutions of Green‐Lindsay theory; Kirchhoff‐type formulas and integral equations in Green‐Lindsay theory; thermoelastic polynomials; moving discontinuity surfaces; and time‐periodic solutions. This is followed by a chapter on physical aspects of generalized thermoelasticity, with a review of several applications. The book closes with a chapter on a nonlinear hyperbolic theory of a rigid heat conductor for which a number of asymptotic solutions are obtained using a method of weakly nonlinear geometric optics. The book is augmented by an extensive bibliography.
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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 to a fast transient loading (say, due to short laser pulses) or at low temperatures. Several models were developed and intensively studied over the past four decades, and this book is the first monograph on the subject since the 1970s, aiming to provide a point of reference in the field. It 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 theories is due to the coupling of mechanical with thermal fields. The book is concerned with the mathematical aspects of both theories — existence and uniqueness theorems, domain of influence theorems, convolutional variational principles — as well as with the methods for various initial/boundary value problems. In the latter respect, following the establishment of the central equation of thermoelasticity with finite wave speeds, there are extensive presentations of: the exact, aperiodic‐in‐time solutions of Green‐Lindsay theory; Kirchhoff‐type formulas and integral equations in Green‐Lindsay theory; thermoelastic polynomials; moving discontinuity surfaces; and time‐periodic solutions. This is followed by a chapter on physical aspects of generalized thermoelasticity, with a review of several applications. The book closes with a chapter on a nonlinear hyperbolic theory of a rigid heat conductor for which a number of asymptotic solutions are obtained using a method of weakly nonlinear geometric optics. The book is augmented by an extensive bibliography.
