Continuum Thermodynamics

This book deals with an important topic in rational continuum physics, thermodynamics.Although slim, it is fairly well self-contained; some basic notions in continuum mechanics, which a well-intentioned reader should but may not be familiar with, are collected in a final appendix. Modern continuum thermodynamics is a field theory devised to handle a large class of processes that typically are neither spatially homogeneous nor sequences of equilibrium states. The most basic chapter addresses the continuum theory of heat conduction, in which the constitutive laws furnish a mathematical characterization of the macroscopic manifestations of those fluctuations in position and velocity of the microscopic matter constituents that statistical thermodynamics considers collectively. In addition to a nonstandard exposition of the conceptual steps leading to the classical heat equation, the crucial assumption that energy and entropy inflows should be proportional is discussed and a hyperbolic version of that prototypical parabolic PDE is presented. Thermomechanics comes next, a slightly more complex paradigmatic example of a field theory where microscopic and macroscopic manifestations of motion become intertwined. Finally, a virtual power format for thermomechanics is proposed, whose formulation requires that temperature is regarded formally as the time derivative of thermal displacement. It is shown that this format permits an alternative formulation of the theory of heat conduction, and a physical interpretation of the notion of thermal displacement is given. It is addressed to mathematical modelers - or mathematical modelers to be - of continuous material bodies, be they mathematicians, physicists, or mathematically versed engineers.

Author Biography: Paolo Podio-Guidugli studied Nuclear Engineering at the University of Pisa. He has served as a full professor of Mechanics of Materials and Structures at the Universities of Ancona, Pisa, and Roma Tor Vergata. He is a fellow of the Accademia Nazionale dei Lincei. He has published more than 240 papers and 7 books, and co-edited 4 books. His research interests are in foundational and applied issues in rational continuum physics: elasticity (general and applied to rods, plates, shells, and nanotubes), plasticity, multiscale modeling of condensed matter, materials (oriented, with internal constraints, with elastic range), phase interface motion, phase segregation by atomic rearrangement, crack propagation, deformable ferromagnets, strain and superconductivity, and thermodynamics.

1 Heat Conduction.- 2 Thermomechanics.- 3 The Principle of Virtual Powers.- 4 A virtual power format for thermomechanics.- 5 A Physical Interpretation of Thermal Displacement.- 6 Appendix A: Basic Notions of Continuum Mechanics.