Angelo Morro

Inhomogeneous waves in viscoelastic media

Abstract Inhomogeneous, plane, monochromatic waves travelling in viscoelastic media are considered. Through a description in terms of complex potentials, detailed expressions of phase speed and attenuation are derived by having recourse to thermodynamic restrictions and to the properties of the complex propagation vector under inversion of the frequency. The complex amplitude vector for transverse and longitudinal waves is also discussed. Next, reflection and refraction at the common boundary of different types of media are investigated. As an application, the problem of a longitudinal wave propagating within an inviscid fluid and entering a viscoelastic solid is analyzed numerically. In particular it is shown that an analysis of the dependence of the reflected wave on the frequency leads to the determination of the relaxation time for an exponential-type relaxation function.

Phase-field models for fluid mixtures

The paper investigates the modelling of phase transitions in multiphase fluid mixtures. The order parameter is identified with the set of concentrations and is a phase field in that it varies smoothly in the space region. This in turn requires that the continuity equations be regarded as constraints on the pertinent fields. The phase field is viewed as an internal variable whose evolution is subject to thermodynamic requirements. The second law allows for an extra entropy flux which proves to be proportional to the time derivative of the order parameter. Previous papers on the subject are revisited. It follows that their recourse to external mass supplies or to ad-hoc entropy fluxes can be avoided. The analogy of the phase-field model, with that of mixtures with mass-density gradients and extra entropy flux, is emphasized.

Evolution equations and thermodynamic restrictions for dissipative solids

Heat conduction and viscosity in solids are modelled by means of evolution equations. The appropriate time derivative is determined by requiring that both objectivity and compatibility with thermodynamics be satisfied. This is performed by investigating the balance law and the entropy inequality in the reference configuration. It follows that the evolution for the heat flux and the stress tensor involves the Oldroyd derivative, irrespective of the occurrence of nonlocal terms.

Riccati equations for wave propagation in planarly-stratified solids

Abstract Wave propagation and scattering are investigated in three-dimensional, dissipative, anisotropic bodies with one-dimensional inhomogeneity. The constitutive equations are taken to be linear. The incidence is allowed to be oblique. Three different procedures are set up which involve the impedance matrix and two local reflection matrices. All three matrix functions are shown to satisfy appropriate Riccati equations and jump conditions (at discontinuities). The operative aspects are examined to solve reflection–transmission problems for a layer sandwiched between two half spaces. The unknown field within the layer is determined through the impedance or the reflection matrices.

Stress, body force, and momentum balance in mixture theory

SommarioUna relazione generale di bilancio della quantità di moto per un costituente di una mistura è ricavata sulla base di considerazioni particellari. Interpretazioni di stress e forza interna di volume sono fornite per costituenti sia carichi sia neutri. In tal modo il paradosso di Gurtin, Oliver e Williams sullinterpretazione degli stress parziali viene risolto e, inoltre, le relazioni tra stress totali e parziali risultano in generale più complesse di quanto si assuma solitamente. Infine si effettua un confronto con la teoria cinetica.SummaryA general momentum balance for a mixture constituent is motivated from corpuscular considerations. The interpretations of stress and internal body force in the separate cases of ionic and non-ionic species are indicated. The Gurtin-Oliver-Williams paradox concerning the interpretation of partial stress is resolved, and relations between total and inner stress shown to be more complex than usually assumed. Comparison is made with kinetic theory.

Temperature waves in rigid materials with memory

SommarioSi esamina il problema della propagazione della temperatura con velocità finita nei conduttori di calore rigidi nel contesto della termodinamica dei materiali con memoria. Le relazioni costitutive sono espresse da funzionali dipendenti dalle storie della temperatura e del gradiente di temperatura ed anche, esplicitamente, dal valore attuale della temperatura. Si deducono le condizioni che assicurano la possibilità di propagazione ondosa per la temperatura.SummaryThe problem of finite speed of propagation of temperature in rigid heat conductors is analysed within the framework of the thermodynamics of materials with memory. The constitutive relations are expressed by functionals depending on the histories of temperature and temperature gradient and also, explicitly, on the present value of the temperature. The condition that ensure the possibility of wave propagation for temperature are derived.

Jump relations and discontinuity waves in conductors with memory

This paper investigates a linear functional of the history of a variable which, along with the derivatives, suffers jump discontinuities. The first purpose is to evaluate the jump of the time and space derivatives, of any order, of the functional. Next, the modelling of conductors with memory is considered, in terms of the history of the temperature gradient, and necessary and sufficient thermodynamic restrictions are established. The propagation and evolution of one-dimensional waves is then investigated. The thermodynamic restrictions are shown to guarantee the finiteness of the wave speed and the decay of the discontinuity.

Surface waves on a solid half‐space

Inhomogeneous waves in viscoelastic solids are considered with the aim of a thorough characterization of surface waves in a solid half‐space. To ascertain the existence of surface waves and to investigate their properties, a general scheme is established that is appropriate for numerical developments. Viscoelastic and elastic solids are examined in detail and previous results on admissible surface waves are generalized.

Time-reversal invariance and thermodynamics of electromagnetic fields in materials with memory

SuntoIn questo lavoro gli Autori studiano la conduzione termica ed elettrica in un materiale rigido con memoria. Vengono esaminate in dettaglio le conseguenze, dovute alla invarianza della produzione entropica per inversione temporale, sulle funzioni di rilassamento per il flusso di calore, la densità di corrente elettrica e la densità di energia interna.SummaryIn this work we consider thermal and electric conduction in rigid materials with memory. The implications due to the invariance of the entropy production under time-reversal are examined in detail. Some interesting conditions on the relaxation functions of the heat flux, the electric current and the internal energy density are discussed.

Modelling of optically active electromagnetic media

By analogy with the DBF model of optically-active electromagnetic media, some generalizations are considered so that memory effects are incorporated. Next, thermodynamic restrictions are derived. It turns out that, via suitable restrictions, the DBF model is compatible with thermodynamics. Also, the analogous terms in a model for nongyrotropic solids are not allowed. The appropriate modification for such a model is indicated.