Mechanics and Thermodynamics of Continua: A Collection of Papers Dedicated to B.D. Coleman on His Sixtieth Birthday

ISBN-13: 9783540529996 / Angielski / Miękka / 1991 / 578 str.

Hershel Markovitz; Victor J. Mizel; David R. Owen

Opis

by Noll, then scantly known, at the Carnegie Institute of Technology. An invita tional meeting on visco-elasticity in the following April at Lancaster, Pennsyl vania, brought Coleman and Noll together. In those days a person went to a meet ing so as to learn from a few competent lectures without having to be himself one more "invited speaker" or to listen to many multiples of ten minutes of trivial trash. Ericksen lectured on "laminar shear flows" of incompressible, Rivlin-Erick sen fluids. That class of flows contains all those for which Rivlin and others had obtained exact solutions. Ericksen's paper, with Criminale & Filbey as co-authors, was to appear soon in Volume 1 of the Archive. At the meeting, Coleman and Noll found that they had similar views on thermodynamics. The rheologists there, like those we had encountered elsewhere, told us that classical thermodynamics was a complete, closed, perfect science, all in Gibbs's paper, and they laughed at us. We laughed at them, but silently, for we had read fundamental parts of Gibbs's work, especially that on the isothermal and isentropic theories of three-dimensional elasticity, which, surely, the rheologists could not understand. We knew also the basic inequality for increase of entropy asserted by Duhem (1901) and in "The Mechanical Foundations" (1952) called "the Clausius-Duhem inequality" (Eq. (28. 5-, from which Eckart (1940) had drawn consequences by guessing the signs oftwo terms ("Mechanical Foundations," text following Eq. (31. 1-."

Spis treści

The Homogeneous Field Approximation of Classical Thermodynamics.- On the Stored Energy Functions of Hyperelastic Materials with Internal Constraints.- The Bianchi Identities in an Explicit Form.- On the Vorticity Numbers of Monotonous Motions.- A Limiting “Viscosity” Approach to the Riemann Problem for Materials Exhibiting Change of Phase.- One Dimensional Infinite-horizon Variational Problems arising in Continuum Mechanics.- Admissible Wave Fans in Nonlinear Hyperbolic Systems.- Weak Martensitic Transformations in Bravais Lattices.- Necessary Conditions at the Boundary for Minimizers in Finite Elasticity.- Phase Transitions of Elastic Solid Materials.- Drops of Nematic Liquid Crystals.- Stability of Deformation of an Elastic Layer.- Conditions for Mechanical Self-Annealing in Motions of Elastic-Plastic Oscillators.- On Saint-Venant’s Principle in Finite Anti-Plane Shear: An Energy Approach.- Mixture Invariance and its Applications.- Interactions in General Continua with Microstructure.- Surface Interaction Potentials in Elasticity.- Some Kinematical Results Concerning Steady Flows and Extensional Flows.- Material Symmetry and Crystals.- A Mathematical Theory of the Guillotine.- Global Properties of Buckled States of Plates that can Suffer Thickness Changes.- Regular Precessions in a Central Newtonian Field of Forces.- A Mechanical Theory for Crystallization of a Rigid Solid in a Liquid Melt; Melting-Freezing Waves.- On Edge Interactions and Surface Tension.- On a Statistical-Kinetic Model for Generalized Continua.- Memory Effects and Homogenization.- On Formation of Singularities in One-Dimensional Nonlinear Thermoelasticity.- Published Works of Bernard D. Coleman.- Places of First Publication.

O autorze

In honor of B. D. Coleman, leading scientists have collected here their most recent research papers on theoretical thermodynamics, elasticity, and material science. The book addresses physicists as well as engineers.