Matthew F. McCarthy

Constitutive equations for thermomechanical materials with memory

Abstract A theory of thermomechanical materials with memory is developed. The response functionals are assumed to depend on the histories of the deformation gradient temperature and the integrated history of the temperature gradient. The second law of thermodynamics is used to restrict the forms of the response functionals and it is shown that the stress tensor, heat conduction vector and specific entropy depend on the free energy functional.

A theory of viscoelastic composites modeled as interpenetrating solid continua with memory

An existing description of composite materials modeled as interpenetrating solid continua is extended to include constitutive response functionals over the histories of the constitutive variables of the n-consistent composite. As in the earlier work, the relative displacement of the individual constituents is required to be infinitesimal in order that the composite not rupture even though the motion of the combined composite is finite. Conditions on the response functionals under the assumption of fading memory are obtained from the Clausius-Duhem inequality for the combined composite. Relaxation and cyclical processes are discussed and it is shown that the equilibrium response of the composite considered is the same as that of the elastic composites treated in the earlier work. Some detailed results are obtained for the case of two-constituents under the additional assumption of finite linear viscoelastic response.

Wave propagation in generalized thermoelasticity

Abstract The propagation of waves in generalized thermoelasticity is discussed. Isotropic materials are treated in detail and it is found that four principal waves may propagate in such media.

The propagation and growth of plane acceleration waves in a perfectly electrically conducting elastic material in a magnetic field

Abstract The propagation and growth of acceleration waves in a perfectly electrically conducting Cauchy elastic material in the presence of a uniform magnetic field are investigated. A propagation condition and growth equation are derived and the effect of the magnetic field on the growth of the waves is assessed.

Thermodynamic influences on the propagation of waves in electroelastic materials

Abstract The propagation of acceleration waves in deformable dielectric media is analysed on the assumption that the electromagnetic field is quasi static. The influence of the heat conduction properties of the material on acceleration waves is discussed in detail. Propagation conditions are derived and the growth of plane waves is discussed.

The growth of thermal waves

Abstract The propagation and growth of thermal disturbances in rigid materials in which thermal effects propagate at a finite speed is discussed. The growth equation for first order thermal waves of arbitrary shape is derived. Solutions of the equation are given for waves which propagate in isotropic materials.

THE GROWTH OF DISCONTINUITIES IN RELATIVISTIC GAS DYNAMICS.

Abstract A relativistic theory of the growth of second order discontinuities in a perfect gas is given. Results generalizing the classical gas-dynamical relations are derived.

Thermodynamic influences on the behavior of curved shock waves in elastic fluids and the vorticity jump

In addition to examining the infuence of thermodynamic effects on the evolutionary behavior of curved shock waves in elastic fluids, we derive certain compatibility relations which must be satisfied behind the shocks. These relations arise because the shock strengths are not uniform over the shock surfaces. We also present an alternate method of derivation of the well-known result concerning the vorticity jump.ZusammenfassungEs wird der Einfluß thermodynamischer Effekte auf die Entwicklung gekrümmter kurzer Wellen in elastischen Flüssigkeiten untersucht. Zusätzlich werden bestimmte Kompatibilitätsbedingungen abgeleitet die hinter den Stoßfronten erfüllt werden müssen und die darin begründet sind, daß die Stoßintensitäten nicht gleichförmig über die Stoßflächen verteilt sind. Es wird auch eine zusätzliche Ableitung des bekannten Ergebnisses über den Wirbelsprung gebracht.

Thermodynamics of deformable magnetic materials with memory

Abstract The theory of deformable heat conducting magnetic materials with fading memory is developed. The case of saturated ferrogmagnetic type materials is treated in detail. The restrictions placed on the response functionals by the Clausius-Duhem inequality are derived. Relaxation is discussed and integrated dissipation inequalities are derived. Finally, the theory of deformable paramagnetic materials with memory is briefly developed.

One-dimensional pulse propagation in composite materials modelled as interpenetrating solid continua

Abstract Modulated simple wave theory is used to study the propagation of one dimensional, finite amplitude, high frequency pulses in composites which are modelled as interpenetrating solid continua with two identifiable constituents. The equations which govern the propagation of high frequency pulses are derived and their properties are studied in detail. Particular attention is paid to small amplitude high frequency pulses and results for pulses propagating into composites of a rather general nature are presented. The special results which hold for pulses which propagate into uniform regions are discussed in detail. The influence of the structure of the composite on pulse propagation is also assessed by examining pulse propagation in a number of different types of composite.