An extension of the theory of Ornstein (1906) and Nye (1967) for the drag force on circular wires and other solid bodies creeping through ice by means of pressure-melting and regelation is provided. Nye's theory leads to a form of Stokes law, with rates controlled by heat conduction and lubrication flow in a thin water layer between ice and solid body. New analytical solutions are given for the corresponding drag force and torque on elliptical cylinders and spheroids for the special case of thermally thin water layers and for certain special forms of uncoupled translation and rotation that allow for single-harmonic temperature fields. The present results differ from those proposed by Nye for general body shapes in the limit of negligible thermal resistance of the water layer. Also, the present results for the drag force on elliptic cylinders do not agree with the formulae derived by Tyvand and Bejan (1992) for small ellipticity. A brief review is given for various effects that might account for certain departures of the Nye theory from experiment on circular wires, in the hope that the present results may suggest simpler experiments aimed at systematic modification of the theory to account for such anomalies. © 2014 American Institute of Chemical Engineers.

Generalizing Maxwell's (Maxwell 1867 IV. Phil. Trans. R. Soc. Lond. 157, 49-88 (doi:10.1098/rstl.1867.0004)) classical formula, this paper shows how the dissipation potentials for a dissipative system can be derived from the elastic potential of an elastic system undergoing continual failure and recovery. Hence, stored elastic energy gives way to dissipated elastic energy. This continuum-level response is attributed broadly to dissipative microscopic transitions over a multi-well potential energy landscape of a type studied in several previous works, dating from Prandtl's (Prandtl 1928 Ein Gedankenmodell zur kinetischen Theorie der festen Körper. ZAMM 8, 85-106) model of plasticity. Such transitions are assumed to take place on a characteristic time scale T, with a nonlinear viscous response that becomes a plastic response for T → 0 . We consider both discrete mechanical systems and their continuum mechanical analogues, showing how the Reiner-Rivlin fluid arises from nonlinear isotropic elasticity. A brief discussion is given in the conclusions of the possible extensions to other dissipative processes.

This paper revisits the second law of thermodynamics via certain modifications of the axiomatic foundation provided by the celebrated 1909 work of Carathéodory. It is shown that his postulate of adiabatic inaccessibility represents one of several constraints on the energy balance that serve to establish the existence of thermostatic entropy as a foliation of state space, with temperature representing a force of constraint. To achieve the thermostatic version of the second law, as embodied in the postulates of Clausius and Gibbs, work principles are proposed to define thermostatic equilibrium and stability in terms of the convexity properties of internal energy, entropy and related thermostatic potentials. Comparisons are made with the classic work of Coleman and Noll on thermostatic equilibrium in simple continua, resulting in a few unresolved differences. Perhaps the most novel aspect of the current work is an extension to irreversible processes by means of a non-equilibrium entropy derived from recoverable work, which generalizes similar ideas in continuum viscoelasticity. This definition of entropy calls for certain revisions of modern theories of continuum thermomechanics by Coleman, Noll and others that are based on a generally inaccessible entropy and undefined temperature.

Generalizing Maxwell's (Maxwell 1867 IV. Phil. Trans. R. Soc. Lond. 157, 49-88 (doi:10.1098/rstl.1867.0004)) classical formula, this paper shows how the dissipation potentials for a dissipative system can be derived from the elastic potential of an elastic system undergoing continual failure and recovery. Hence, stored elastic energy gives way to dissipated elastic energy. This continuum-level response is attributed broadly to dissipative microscopic transitions over a multi-well potential energy landscape of a type studied in several previous works, dating from Prandtl's (Prandtl 1928 Ein Gedankenmodell zur kinetischen Theorie der festen Körper. ZAMM 8, 85-106) model of plasticity. Such transitions are assumed to take place on a characteristic time scale T, with a nonlinear viscous response that becomes a plastic response for T → 0 . We consider both discrete mechanical systems and their continuum mechanical analogues, showing how the Reiner-Rivlin fluid arises from nonlinear isotropic elasticity. A brief discussion is given in the conclusions of the possible extensions to other dissipative processes.