The Mechanics and Thermodynamics of Continuous Media (Theoretical and Mathematical Physics)

this Book Presents The Non-linear Theories Of Continuum Thermomechanics. The Author Emphasizes Issues That Are Foundational In Nature And Seeks Results Common To Materials Of Arbitrary Symmetry. The Central Part Deals With Thermoelastic Bodies With Heat Conduction And Viscosity, Including The Inviscid Or Ideal Dissipationless Bodies. A Surprising Variety Of Phenomena Can Be Modeled Within This Framework. The Main Ideas Can Be Transferred Into More Complicated Theories Of Materials With Memory Or Microstructure. A Large Portion Is An Extension Of Gibbs' Ideas To Bodies Of General Symmetry By The Methods Of The Calculus Of Variations. The Interplay Between The Convexity Properties Of The Stored Energy Functions, The Resulting Equations, And The Physics Is Also Discussed. This book presents the nonlinear theories of continuum thermomechanics. Through­ out 1 emphasize issues that are foundational in nature, and seek results common to materials of arbitrary symmetry. The central part of the book deals with thermoelastic bodies with heat conduction and viscosity, including the inviscid or ideal dissipation­ less bodies. A surprising variety of phenomena can be modeled within this frame­ work. Moreover, the main ideas can be transferred into more complicated theories. At present, the major challenge to the non linear thermoelasticity is posed by phase transformations with changes in symmetry. 1. W. Gibbs'immensely inftuen­ tiaI treatise On the equilibrium of heterogeneous substances has provided a highly successful theory of phase transitions in ftuids. Gibbs brought the view that the ther­ modynamics is not only the theory of heat, but also a theory of equilibrium, with the of the book is an extension of main tool the minimum principles. A large portion Gibbs'ideas to bodies of general symmetry by the methods of the calculus of varia­ tions. The interplay between the convexity properties of the stored energy functions, the resulting equations, and the physics of the phenomena is a leading theme. This textbook presents the theories of nonlinear continuum thermomechanics. It emphasizes issues that are foundational in nature and seeks results common materials of arbitrary symmetry. The central part deals with thermoelastic bodies, with heat conduction and viscosity From the reviews: "The book is excellent, and covers a very broad area (usually treated as separate topics) from a unified perspective. [...] It will be very useful for both mathematicians and physicists." EMS Newsletter The reader is assumed to have some familiarity with the elements of linear algebra.